{"id":2518,"date":"2015-04-22T21:29:20","date_gmt":"2015-04-22T21:29:20","guid":{"rendered":"https:\/\/courses.candelalearning.com\/oschemtemp\/?post_type=chapter&#038;p=2518"},"modified":"2015-09-01T17:44:07","modified_gmt":"2015-09-01T17:44:07","slug":"spectroscopic-and-magnetic-properties-of-coordination-compounds-missing-formulas","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-buffstate-chemistryformajorsxmaster\/chapter\/spectroscopic-and-magnetic-properties-of-coordination-compounds-missing-formulas\/","title":{"raw":"Spectroscopic and Magnetic Properties of Coordination Compounds","rendered":"Spectroscopic and Magnetic Properties of Coordination Compounds"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>LEARNING OBJECTIVES<\/h3>\r\nBy the end of this module, you will be able to:\r\n<ul>\r\n\t<li>Outline the basic premise of crystal field theory (CFT)<\/li>\r\n\t<li>Identify molecular geometries associated with various d-orbital splitting patterns<\/li>\r\n\t<li>Predict electron configurations of split d orbitals for selected transition metal atoms or ions<\/li>\r\n\t<li>Explain spectral and magnetic properties in terms of CFT concepts<\/li>\r\n<\/ul>\r\n<\/div>\r\nThe behavior of coordination compounds cannot be adequately explained by the same theories used for main group element chemistry. The observed geometries of coordination complexes are not consistent with hybridized orbitals on the central metal overlapping with ligand orbitals, as would be predicted by valence bond theory. The observed colors indicate that the <em>d<\/em> orbitals often occur at different energy levels rather than all being degenerate, that is, of equal energy, as are the three <em>p<\/em> orbitals. To explain the stabilities, structures, colors, and magnetic properties of transition metal complexes, a different bonding model has been developed. Just as valence bond theory explains many aspects of bonding in main group chemistry, crystal field theory is useful in understanding and predicting the behavior of transition metal complexes.\r\n<h2>Crystal Field Theory<\/h2>\r\nTo explain the observed behavior of transition metal complexes (such as how colors arise), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized <em>d<\/em> orbitals of the central metal atom has been developed. This electrostatic model is <strong>crystal field theory<\/strong> (CFT). It allows us to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.\r\n\r\nCFT focuses on the nonbonding electrons on the central metal ion in coordination complexes not on the metal-ligand bonds. Like valence bond theory, CFT tells only part of the story of the behavior of complexes. However, it tells the part that valence bond theory does not. In its pure form, CFT ignores any covalent bonding between ligands and metal ions. Both the ligand and the metal are treated as infinitesimally small point charges.\r\n\r\nAll electrons are negative, so the electrons donated from the ligands will repel the electrons of the central metal. Let us consider the behavior of the electrons in the unhybridized <em>d<\/em> orbitals in an octahedral complex. The five <em>d<\/em> orbitals consist of lobe-shaped regions and are arranged in space. In an octahedral complex, the six ligands coordinate along the axes.\r\n\r\n&nbsp;\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"885\"]<img class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23212834\/CNX_Chem_19_03_Dorbital1.jpg\" alt=\"This figure includes diagrams of five d orbitals. Each diagram includes three axes. The z-axis is vertical and is denoted with an upward pointing arrow. It is labeled \u201cz\u201d in the first diagram. Arrows similarly identify the x-axis with an arrow pointing from the rear left to the right front, diagonally across the figure and the y-axis with an arrow pointing from the left front diagonally across the figure to the right rear of the diagram. These axes are similarly labeled as \u201cx\u201d and \u201cy.\u201d In this first diagram, four orange balloon-like shapes extend from a point at the origin out along the x- and y- axes in positive and negative directions covering just over half the length of the positive and negative x- and y- axes. Beneath the diagram is the label, \u201cd subscript ( x superscript 2 minus y superscript 2 ).\u201d The second diagram just right of the first is similar except the x, y, and z labels have been replaced in each instance with the letter L. Only a pair of the orange balloon-like shapes are present and extend from the origin above and below along the vertical axis. An orange toroidal or donut shape is positioned around the origin, oriented through the x- and y- axes. This shape extends out to about a third of the length of the positive and negative regions of the x- and y- axes. This diagram is labeled, \u201cd subscript ( z superscript 2 ).\u201d The third through fifth diagrams, similar to the first, show four orange balloon-like shapes. These diagrams differ however in the orientation of the shapes along the axes and the x-, y-, and z-axis labels have each been replaced with the letter L. Planes are added to the figures to help show the orientation differences with these diagrams. In the third diagram, a green plane is oriented vertically through the length of the x-axis and a blue plane is oriented horizontally through the length of the y-axis. The balloon shapes extend from the origin to the spaces between the positive z- and negative y- axes, positive z- and positive y- axes, negative z- and negative y- axes, and negative z- and positive y- axes. This diagram is labeled, \u201cd subscript ( y z ).\u201d In the fourth diagram, a green plane is oriented vertically through the x- and y- axes and a blue plane is oriented horizontally through the length of the x-axis. The balloon shapes extend from the origin to the spaces between the positive z- and negative x- axes, positive z- and positive x- axes, negative z- and negative x- axes, and negative z- and positive x- axes. This diagram is labeled \u201cd subscript ( x z ).\u201d In the fifth diagram, a pink plane is oriented vertically through the length of the y-axis and a green plane is oriented vertically through the length of the x-axis. The balloon shapes extend from the origin to the spaces between the positive x- and negative y- axes, positive x- and positive y- axes, negative x- and negative y- axes, and negative x- and positive y- axes. This diagram is labeled, \u201cd subscript ( x y ).\u201d\" width=\"885\" height=\"260\" data-media-type=\"image\/jpeg\" \/> Figure 1. The directional characteristics of the five <em>d<\/em> orbitals are shown here. The shaded portions indicate the phase of the orbitals. The ligands (L) coordinate along the axes. For clarity, the ligands have been omitted from the <em>d<\/em><sub><em>x<\/em><sup>2<\/sup> \u2212 <em>y<\/em><sup>2<\/sup><\/sub> orbital so that the axis labels could be shown.[\/caption]\r\n\r\nIn an uncomplexed metal ion in the gas phase, the electrons are distributed among the five <em>d<\/em> orbitals in accord with Hund's rule, because the orbitals all have the same energy. However, when ligands coordinate to a metal ion, the energies of the <em>d<\/em> orbitals are no longer the same.\r\n\r\nIn octahedral complexes, the lobes in two of the five <em>d<\/em> orbitals, the [latex]{d}_{{z}^{2}}[\/latex] and [latex]{d}_{{x}^{2}-{y}^{2}}[\/latex] orbitals, point toward the ligands. These two orbitals are called the <strong><em>e<\/em><sub><em>g<\/em><\/sub> orbitals<\/strong> (the symbol actually refers to the symmetry of the orbitals, but we will use it as a convenient name for these two orbitals in an octahedral complex). The other three orbitals, the <em>d<sub>xy<\/sub><\/em>, <em>d<sub>xz<\/sub><\/em>, and <em>d<sub>yz<\/sub><\/em> orbitals, have lobes that point between the ligands and are called the <strong><em>t<\/em><sub>2<em>g<\/em><\/sub> orbitals<\/strong> (again, the symbol really refers to the symmetry of the orbitals). As six ligands approach the metal ion along the axes of the octahedron, their point charges repel the electrons in the <em>d<\/em> orbitals of the metal ion. However, the repulsions between the electrons in the <em>e<sub>g<\/sub><\/em> orbitals (the [latex]{d}_{{z}^{2}}[\/latex] and [latex]{d}_{{x}^{2}-{y}^{2}}[\/latex] orbitals) and the ligands are greater than the repulsions between the electrons in the <em>t<\/em><sub>2<em>g<\/em><\/sub> orbitals (the <em>d<sub>zy<\/sub><\/em>, <em>d<sub>xz<\/sub><\/em>, and <em>d<sub>yz<\/sub><\/em> orbitals) and the ligands. This is because the lobes of the <em>e<sub>g<\/sub><\/em> orbitals point directly at the ligands, whereas the lobes of the <em>t<\/em><sub>2<em>g<\/em><\/sub> orbitals point between them. Thus, electrons in the <em>e<sub>g<\/sub><\/em> orbitals of the metal ion in an octahedral complex have higher potential energies than those of electrons in the <em>t<\/em><sub>2<em>g<\/em><\/sub> orbitals. The difference in energy may be represented.\r\n\r\n[caption id=\"\" align=\"alignnone\" width=\"650\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23212836\/CNX_Chem_19_03_CFSE1.jpg\" alt=\"A diagram is shown with a vertical arrow pointing upward along the height of the diagram at its left side. This arrow is labeled, \u201cE.\u201d to the right of this arrow are two rows of squares outlined in yellow. The first row has three evenly spaced squares labeled left to right, \u201cd subscript ( x y ),\u201d \u201cd subscript ( x z ),\u201d and, \u201cd subscript ( y z ).\u201d The second row is positioned just above the first and includes two evenly spaced squares labeled, \u201cd subscript ( z superscript 2 ),\u201d and, \u201cd subscript ( x superscript 2 minus y superscript 2 ).\u201d At the right end of the diagram, a short horizontal line segment is drawn just right of the lower side of the rightmost square. A double sided arrow extends from this line segment to a second horizontal line segment directly above the first and right of the lower side of the squares in the second row. The arrow is labeled \u201c capital delta subscript oct.\u201d. The lower horizontal line segment is similarly labeled \u201ct subscript 2 g orbitals\u201d and the upper line segment is labeled \u201ce subscript g orbitals.\u201d\" width=\"650\" height=\"342\" data-media-type=\"image\/jpeg\" \/> Figure 2. In octahedral complexes, the <em>e<sub>g<\/sub><\/em> orbitals are destabilized (higher in energy) compared to the <em>t<\/em><sub>2<em>g<\/em><\/sub> orbitals, because the ligands interact more strongly with the d orbitals at which they are pointed directly.[\/caption]\r\n\r\nThe difference in energy between the <em>e<sub>g<\/sub><\/em> and the <em>t<\/em><sub>2<em>g<\/em><\/sub> orbitals is called the <strong>crystal field splitting<\/strong> and is symbolized by <strong>\u0394oct<\/strong>, where oct stands for octahedral.\r\n\r\nThe magnitude of \u0394<sub>oct<\/sub> depends on many factors, including the nature of the six ligands located around the central metal ion, the charge on the metal, and whether the metal is using 3<em>d<\/em>, 4<em>d<\/em>, or 5<em>d<\/em> orbitals. Different ligands produce different crystal field splittings. The increasing crystal field splitting produced by ligands is expressed in the <strong>spectrochemical series<\/strong>, a short version of which is given here:\r\n\r\n[latex]\\underset{\\text{A few ligands of the spectrochemical series, in order of increasing field strength of the ligand}}{\\overset{\\text{I}^{-}&lt;\\text{Br}^{-}&lt;\\text{Cl}^{-}&lt;\\text{F}^{-}&lt;\\text{H}_2\\text{O}&lt;{\\text{C}_2\\text{O}_4}^{2-}&lt;\\text{NH}_3&lt;en&lt;\\text{NO}_2^{-}&lt;\\text{CN}^{-}}{\\rightarrow}}[\/latex]\r\n\r\nIn this series, ligands on the left cause small crystal field splittings and are <strong>weak-field ligands<\/strong>, whereas those on the right cause larger splittings and are <strong>strong-field ligands<\/strong>. Thus, the \u0394<sub>oct<\/sub> value for an octahedral complex with iodide ligands (I<sup>-<\/sup>) is much smaller than the \u0394<sub>oct<\/sub> value for the same metal with cyanide ligands (CN<sup>-<\/sup>).\r\n\r\nElectrons in the <em>d<\/em> orbitals follow the aufbau (\u201cfilling up\u201d) principle, which says that the orbitals will be filled to give the lowest total energy, just as in main group chemistry. When two electrons occupy the same orbital, the like charges repel each other. The energy needed to pair up two electrons in a single orbital is called the <strong>pairing energy (P)<\/strong>. Electrons will always singly occupy each orbital in a degenerate set before pairing. P is similar in magnitude to \u0394<sub>oct<\/sub>. When electrons fill the <em>d<\/em> orbitals, the relative magnitudes of \u0394<sub>oct<\/sub> and P determine which orbitals will be occupied.\r\n\r\nIn\u00a0[latex]{\\left[\\text{Fe}{\\left(\\text{CN}\\right)}_{6}\\right]}^{4-}[\/latex], the strong field of six cyanide ligands produces a large \u0394<sub>oct<\/sub>. Under these conditions, the electrons require less energy to pair than they require to be excited to the <em>e<sub>g<\/sub><\/em> orbitals (\u0394<sub>oct<\/sub> &gt; P). The six 3<em>d<\/em> electrons of the Fe<sup>2+<\/sup> ion pair in the three <em>t<\/em><sub>2<em>g<\/em><\/sub> orbitals. Complexes in which the electrons are paired because of the large crystal field splitting are called <strong>low-spin complexes<\/strong>, because the number of unpaired electrons (spins) is minimized.\r\n\r\n&nbsp;\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"893\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23212837\/CNX_Chem_19_03_Lowhigh1.jpg\" alt=\"A diagram is shown with a vertical arrow pointing upward along the height of the diagram at its left side. This arrow is labeled, \u201cE.\u201d to the right of this arrow are several rows of squares outlined in yellow. The first row has three linked squares at the lower right side of the diagram labeled, \u201c[ F e ( C N ) subscript 6 ] superscript 4 negative sign.\u201d Each square contains two half arrows, with the left half arrow pointing up and the right half arrow pointing down. A second row is positioned just above and to the left of the first, with the bottom of the squares at a height equal with the top of the squares in the first row. This group is also composed of 3 linked squares. The square to the left contains two half arrows, with the left half arrow pointing up and the right half arrow pointing down. The remaining two squares in this row only have upward pointing half arrows. At the bottom of the figure, just below this group is the label \u201c[ F e ( H subscript 2 O ) subscript 6] superscript 2 plus sign.\u201d To the left of this row, a third row that includes 5 linked squares is positioned with the lower edge of the squares at a height equal to the tops of the squares in row two. The square to the left contains two half arrows, one up and one down. All other squares in this group contain single upward pointing arrows. At the bottom of the figure beneath this row appears the label, \u201cF e superscript 2 plus sign no ligands.\u201d A fourth row composed of 2 linked squares appears to the right and above the second row. The lower edge of the squares is at a height level with the top of the squares of the third row. Each of these squares contains a single upward pointing half arrow. A fifth row of 2 squares is positioned above and to the right directly above the first row with the base of the squares positioned at a level equal to the top of the previous row of squares. These squares are empty. At the right of the diagram, a short horizontal line segment is drawn just right of the lower side of the rightmost square of the first row. A double-headed arrow extends from this line segment to a second horizontal line segment directly above the first and right of the lower side of the fifth row of squares. The arrow is labeled, \u201cLow spin, large delta subscript oct,\u201d to the right. The lower horizontal line segment is similarly labeled, \u201ct subscript 2 g,\u201d and the upper line segment is labeled, \u201ce subscript g.\u201d To the right of the second and fourth rows, a short horizontal line segment is drawn just right of the lower side of the rightmost square of the second row. A double-headed arrow extends from this line segment to a second horizontal line segment directly above the first and right of the lower side of the fourth row of squares. The arrow is labeled, \u201cHigh spin, small capital delta subscript oct,\u201d to the right. The lower horizontal line segment is similarly labeled, \u201ct subscript 2 g,\u201d and the upper line segment is labeled, \u201ce subscript g.\u201d\" width=\"893\" height=\"305\" data-media-type=\"image\/jpeg\" \/> Figure 3.\u00a0Iron(II) complexes have six electrons in the 5<em>d<\/em> orbitals. In the absence of a crystal field, the orbitals are degenerate. For coordination complexes with strong-field ligands such as [Fe(CN)<sub>6<\/sub>]<sup>4\u2212<\/sup>\u00a0, \u0394<sub>oct<\/sub> is greater than P, and the electrons pair in the lower energy t<sub>2<em>g<\/em><\/sub> orbitals before occupying the <em>e<sub>g<\/sub><\/em> orbitals. With weak-field ligands such as H<sub>2<\/sub>O, the ligand field splitting is less than the pairing energy, \u0394<sub>oct<\/sub> less than P, so the electrons occupy all <em>d<\/em> orbitals singly before any pairing occurs.[\/caption]In [latex]{\\left[\\text{Fe}{\\left({\\text{H}}_{2}\\text{O}\\right)}_{6}\\right]}^{2+},[\/latex] on the other hand, the weak field of the water molecules produces only a small crystal field splitting (\u0394<sub>oct<\/sub> &lt; P). Because it requires less energy for the electrons to occupy the <em>e<sub>g<\/sub><\/em> orbitals than to pair together, there will be an electron in each of the five 3<em>d<\/em> orbitals before pairing occurs. For the six <em>d<\/em> electrons on the iron(II) center in [latex]{\\left[\\text{Fe}{\\left({\\text{H}}_{2}\\text{O}\\right)}_{6}\\right]}^{2+},[\/latex] there will be one pair of electrons and four unpaired electrons. Complexes such as the [latex]{\\left[\\text{Fe}{\\left({\\text{H}}_{2}\\text{O}\\right)}_{6}\\right]}^{2+}[\/latex] ion, in which the electrons are unpaired because the crystal field splitting is not large enough to cause them to pair, are called <strong>high-spin complexes<\/strong>, because the number of unpaired electrons (spins) is maximized.\r\n\r\nA similar line of reasoning shows why the [latex]{\\left[\\text{Fe}{\\left(\\text{CN}\\right)}_{6}\\right]}^{3-}[\/latex] ion is a low-spin complex with only one unpaired electron, whereas both the [latex]{\\left[\\text{Fe}{\\left({\\text{H}}_{2}\\text{O}\\right)}_{6}\\right]}^{3+}[\/latex] and [latex]{\\left[{\\text{FeF}}_{6}\\right]}^{3-}[\/latex] ions are high-spin complexes with five unpaired electrons.\r\n<div class=\"textbox shaded\">\r\n<h3>Example 1<\/h3>\r\n<h4>High- and Low-Spin Complexes<\/h4>\r\nPredict the number of unpaired electrons.\r\n\r\n(a) K<sub>3<\/sub>[CrI<sub>6<\/sub>]\r\n\r\n(b) [Cu(en)<sub>2<\/sub>(H<sub>2<\/sub>O)<sub>2<\/sub>]Cl<sub>2<\/sub>\r\n\r\n(c) Na<sub>3<\/sub>[Co(NO<sub>2<\/sub>)<sub>6<\/sub>]\r\n<h4>Solution<\/h4>\r\nThe complexes are octahedral.\r\n\r\n(a) Cr<sup>3+<\/sup> has a <em>d<\/em><sup>3<\/sup> configuration. These electrons will all be unpaired.\r\n\r\n(b) Cu<sup>2+<\/sup> is <em>d<\/em><sup>9<\/sup>, so there will be one unpaired electron.\r\n\r\n(c) Co<sup>3+<\/sup> has <em>d<\/em><sup>6<\/sup> valence electrons, so the crystal field splitting will determine how many are paired. Nitrite is a strong-field ligand, so the complex will be low spin. Six electrons will go in the <em>t<\/em><sub>2<em>g<\/em><\/sub> orbitals, leaving 0 unpaired.\r\n<h4>Check Your Learning<\/h4>\r\nThe size of the crystal field splitting only influences the arrangement of electrons when there is a choice between pairing electrons and filling the higher-energy orbitals. For which <em>d<\/em>-electron configurations will there be a difference between high- and low-spin configurations in octahedral complexes?\r\n<p style=\"text-align: right;\"><strong>Answer:\u00a0<\/strong><em>d<\/em><sup>4<\/sup>, <em>d<\/em><sup>5<\/sup>, <em>d<\/em><sup>6<\/sup>, and <em>d<\/em><sup>7<\/sup><\/p>\r\n\r\n<\/div>\r\n<div class=\"textbox shaded\">\r\n<h3>Example\u00a02<\/h3>\r\n<h4>CFT for Other Geometries<\/h4>\r\nCFT is applicable to molecules in geometries other than octahedral. In octahedral complexes, remember that the lobes of the <em>e<sub>g<\/sub><\/em> set point directly at the ligands. For tetrahedral complexes, the <em>d<\/em> orbitals remain in place, but now we have only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the <em>e<sub>g<\/sub><\/em> set (along the Cartesian axes) overlaps with the ligands less than does the <em>t<\/em><sub>2<em>g<\/em><\/sub> set. By analogy with the octahedral case, predict the energy diagram for the <em>d<\/em> orbitals in a tetrahedral crystal field. To avoid confusion, the octahedral <em>e<sub>g<\/sub><\/em> set becomes a tetrahedral <em>e<\/em> set, and the octahedral <em>t<\/em><sub>2<em>g<\/em><\/sub> set becomes a <em>t<\/em><sub>2<\/sub> set.\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"650\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23212839\/CNX_Chem_19_03_TetCube1.jpg\" alt=\"This figure includes a three dimensional diagram. At the origin appears the letter M. An arrow, labeled, \u201cz,\u201d at its tip, points upward through the center. An arrow, labeled, \u201cx,\u201d at its tip, points right through the center. A third arrow, labeled, \u201cy,\u201d at its tip, points through the center from the left front to the right back portion of the diagram. A rectangular prism is drawn in green, extending out approximately three-quarters of the lengths from the origin along the positive and negative x-, y-, and z- axes. Small red spheres are positioned at the left upper front, right upper back, right lower front, and left lower back vertices of the prism. Red lines extend from the central M through the prism to these four small red spheres.\" width=\"650\" height=\"428\" data-media-type=\"image\/jpeg\" \/> Figure 4. This diagram shows the orientation of the tetrahedral ligands with respect to the axis system for the orbitals.[\/caption]\r\n<h4>Solution<\/h4>\r\nSince CFT is based on electrostatic repulsion, the orbitals closer to the ligands will be destabilized and raised in energy relative to the other set of orbitals. The splitting is less than for octahedral complexes, because the overlap is less, so \u0394<sub>tet<\/sub> is usually small [latex]\\left({\\Delta}_{\\text{tet}}=\\frac{4}{9}{\\Delta}_{\\text{oct}}\\right)\\text{:}[\/latex]\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23212840\/CNX_Chem_19_03_Smalldeltt_img1.jpg\" alt=\"A diagram is shown with a vertical arrow pointing upward along the height of the diagram at its left side. This arrow is labeled, \u201cE.\u201d to the right of this arrow are two rows of squares outlined in yellow. The first row has two adjacent squares. The second row is positioned just above the first and includes three adjacent squares. At the right side of the diagram, a short horizontal line segment is drawn just right of the lower side of the rightmost square in the first row. A double-headed arrow extends from this line segment to a second horizontal line segment directly above the first and right of the lower side of the squares in the second row. The arrow is labeled, \u201csmall capital delta subscript tet,\u201d to the right. The lower horizontal line segment is similarly labeled, \u201ce subscript,\u201d and the upper line segment is labeled, \u201ct subscript 2.\u201d\" data-media-type=\"image\/jpeg\" \/>\r\n<h4>Check Your Learning<\/h4>\r\nExplain how many unpaired electrons a tetrahedral <em>d<\/em><sup>4<\/sup> ion will have.\r\n<p style=\"text-align: right;\"><strong>Answer:\u00a0<\/strong>4; because \u0394<sub>tet<\/sub> is small, all tetrahedral complexes are high spin and the electrons go into the <em>t<\/em><sub>2<\/sub> orbitals before pairing<\/p>\r\n\r\n<\/div>\r\nThe other common geometry is square planar. It is possible to consider a square planar geometry as an octahedral structure with a pair of <em>trans<\/em> ligands removed. The removed ligands are assumed to be on the <em>z<\/em>-axis. This changes the distribution of the <em>d<\/em> orbitals, as orbitals on or near the <em>z<\/em>-axis become more stable, and those on or near the <em>x-<\/em> or <em>y<\/em>-axes become less stable. This results in the octahedral <em>t<\/em><sub>2<em>g<\/em><\/sub> and the <em>e<sub>g<\/sub><\/em> sets splitting and gives a more complicated pattern with no simple \u0394<sub>oct<\/sub>. The basic pattern is:\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23212842\/CNX_Chem_19_03_Pattern_img1.jpg\" alt=\"A diagram is shown with four rows of vertically oriented rectangles. The lower level has two rectangles with a space between them. The rectangle on the left is labeled, \u201cd subscript x z,\u201d below. The rectangle to its right is similarly labeled, \u201cd subscript y z.\u201d Just above, the second row contains only 1 rectangle above and between the lower two. This rectangle is labeled, \u201cd subscript z squared.\u201d Just above, the third row contains only 1 rectangle directly above. This rectangle is labeled, \u201cd subscript x z.\u201d Just above, the fourth row contains only 1 rectangle directly above. This rectangle is labeled, \u201cd subscript x squared minus y squared.\u201d\" data-media-type=\"image\/jpeg\" \/>\r\n<h2>Magnetic Moments of Molecules and Ions<\/h2>\r\nExperimental evidence of magnetic measurements supports the theory of high- and low-spin complexes. Remember that molecules such as O<sub>2<\/sub> that contain unpaired electrons are paramagnetic. Paramagnetic substances are attracted to magnetic fields. Many transition metal complexes have unpaired electrons and hence are paramagnetic. Molecules such as N<sub>2<\/sub> and ions such as Na<sup>+<\/sup> and [latex]{\\left[\\text{Fe}{\\left(\\text{CN}\\right)}_{6}\\right]}^{4-}[\/latex] that contain no unpaired electrons are diamagnetic. Diamagnetic substances have a slight tendency to be repelled by magnetic fields.\r\n\r\nWhen an electron in an atom or ion is unpaired, the magnetic moment due to its spin makes the entire atom or ion paramagnetic. The size of the magnetic moment of a system containing unpaired electrons is related directly to the number of such electrons: the greater the number of unpaired electrons, the larger the magnetic moment. Therefore, the observed magnetic moment is used to determine the number of unpaired electrons present. The measured magnetic moment of low-spin <em>d<\/em><sup>6<\/sup> [latex]{\\left[\\text{Fe}{\\left(\\text{CN}\\right)}_{6}\\right]}^{4-}[\/latex] confirms that iron is diamagnetic, whereas high-spin <em>d<\/em><sup>6<\/sup> [latex]{\\left[\\text{Fe}{\\left({\\text{H}}_{2}\\text{O}\\right)}_{6}\\right]}^{2+}[\/latex] has four unpaired electrons with a magnetic moment that confirms this arrangement.\r\n<h2>Colors of Transition Metal Complexes<\/h2>\r\nWhen atoms or molecules absorb light at the proper frequency, their electrons are excited to higher-energy orbitals. For many main group atoms and molecules, the absorbed photons are in the ultraviolet range of the electromagnetic spectrum, which cannot be detected by the human eye. For coordination compounds, the energy difference between the <em>d<\/em> orbitals often allows photons in the visible range to be absorbed.\r\n\r\nThe human eye perceives a mixture of all the colors, in the proportions present in sunlight, as white light. Complementary colors, those located across from each other on a color wheel, are also used in color vision. The eye perceives a mixture of two complementary colors, in the proper proportions, as white light. Likewise, when a color is missing from white light, the eye sees its complement. For example, when red photons are absorbed from white light, the eyes see the color green. When violet photons are removed from white light, the eyes see lemon yellow. The blue color of the [latex]{\\left[\\text{Cu}{\\left({\\text{NH}}_{3}\\right)}_{4}\\right]}^{2+}[\/latex] ion results because this ion absorbs orange and red light, leaving the complementary colors of blue and green.\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"888\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23212844\/CNX_Chem_19_03_Lightper1.jpg\" alt=\"This figure includes three diagrams. In a, red, orange, yellow, green, blue, indigo, and violet incident arrows point from the upper left to the lower right toward one black, one white, and two yellow rectangular surfaces. No arrows are indicated leaving the black surface. On the white surface, arrows of all included colors extend from the surface of the rectangle extending from just right of the tips of the incident arrows that approach the rectangle to the upper right. For the first yellow surface, only a yellow arrow extends from a point just past the tip of the yellow incident arrow to the upper right. For the second yellow surface, all colors of arrows except indigo extend from points just past the tips of the incident arrows to the upper right. In b, a circle shaded in red at the upper left blends to orange, yellow, green, blue, indigo, and violet moving clockwise about the circle. The leftmost side of the red region has a radius that is labeled, \u201c800 n m,\u201d at the edge of the circle. A radius drawn to the top of the circle in the red-orange region is labeled, \u201c620 n m.\u201d A radius drawn to a point near the center of the first quadrant of the circle in the orange-yellow region is labeled, \u201c580 n m.\u201d A radius drawn to a point near the center of the second quadrant of the circle in the yellow-green region is labeled, \u201c560 n m.\u201d A radius drawn to the bottom of the circle in the blue region is labeled, \u201c490 n m.\u201d A radius drawn to a point near the center of the third quadrant of the circle in the indigo region is labeled, \u201c430 n m.\u201d An unlabeled radius is drawn to the leftmost point on the circle in the violet region. The violet region ends where the red region began on the circle. This radius is labeled, \u201c400 n m,\u201d just to the left and below the, \u201c800 n m,\u201d label associated with the red region. In c, a test tube containing a blue substance is shown. To the left of the test tube, incident colored arrows are shown pointing to the test tube. The colors of the arrows in order from bottom to top are red, orange, yellow, green, blue, indigo, and violet. Above these arrows is the label, \u201cWhite light.\u201d To the right of the test tube, yellow, green, blue, indigo, and violet arrows point right. These arrows are positioned at the same level on the test tube as their matching incident arrows on the left of the test tube. Above these arrows is the label, \u201cBlue-appearing light.\u201d\" width=\"888\" height=\"708\" data-media-type=\"image\/jpeg\" \/> Figure 5. (a) An object is black if it absorbs all colors of light. If it reflects all colors of light, it is white. An object has a color if it absorbs all colors except one, such as this yellow strip. The strip also appears yellow if it absorbs the complementary color from white light (in this case, indigo). (b) Complementary colors are located directly across from one another on the color wheel. (c)A solution of [Cu(NH<sub>3<\/sub>)<sub>4<\/sub>]<sup>2+<\/sup> ions absorbs red and orange light, so the transmitted light appears as the complementary color, blue.[\/caption]\r\n<div class=\"textbox shaded\">\r\n<h3>Example\u00a03<\/h3>\r\n<h4>Colors of Complexes<\/h4>\r\nThe octahedral complex [latex]{\\left[\\text{Ti}{\\left({\\text{H}}_{2}\\text{O}\\right)}_{6}\\right]}^{3+}[\/latex] has a single <em>d<\/em> electron. To excite this electron from the ground state <em>t<\/em><sub>2<em>g<\/em><\/sub> orbital to the <em>e<sub>g<\/sub><\/em> orbital, this complex absorbs light from 450 to 600 nm. The maximum absorbance corresponds to \u0394<sub>oct<\/sub> and occurs at 499 nm. Calculate the value of \u0394<sub>oct<\/sub> in Joules and predict what color the solution will appear.\r\n<h4>Solution<\/h4>\r\nUsing Planck's equation (refer to the section on electromagnetic energy), we calculate:\r\n\r\n[latex]v=\\frac{c}{\\lambda }\\text{so}\\frac{3.00\\times {10}^{8}\\text{m\/s}}{\\frac{\\text{499 nm}\\times \\text{1 m}}{{10}^{9}\\text{nm}}}=6.01\\times {10}^{14}\\text{Hz}[\/latex]\r\n\r\n[latex]\\text{E}=\\text{hv so}6.63\\times {10}^{-34}\\text{J}\\cdot\u00a0\\text{s}\\times 6.01\\times {10}^{14}\\text{Hz}=3.99\\times {10}^{-19}\\text{Joules\/ion}[\/latex]Because the complex absorbs 600 nm (orange) through 450 (blue), the indigo, violet, and red wavelengths will be transmitted, and the complex will appear purple.\r\n<h4>Check Your Learning<\/h4>\r\nA complex that appears green, absorbs photons of what wavelengths?\r\n<p style=\"text-align: right;\"><strong>Answer:\u00a0<\/strong>red, 620\u2013800 nm<\/p>\r\n\r\n<\/div>\r\nSmall changes in the relative energies of the orbitals that electrons are transitioning between can lead to drastic shifts in the color of light absorbed. Therefore, the colors of coordination compounds depend on many factors. Different aqueous metal ions can have different colors. In addition, different oxidation states of one metal can produce different colors, as shown for the vanadium complexes in the link below.\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"650\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23212845\/CNX_Chem_19_03_ColorAq1.jpg\" alt=\"This figure shows three containers filled with liquids of different colors. The first appears to be purple, the second, orange, and the third red.\" width=\"650\" height=\"433\" data-media-type=\"image\/jpeg\" \/> Figure 6. The partially filled d orbitals of the stable ions Cr<sup>3+<\/sup>(<em>aq<\/em>), Fe<sup>3+<\/sup>(<em>aq<\/em>), and Co<sup>2+<\/sup>(<em>aq<\/em>) (left, center and right, respectively) give rise to various colors. (credit: Sahar Atwa)[\/caption]\r\n\r\nThe specific ligands coordinated to the metal center also influence the color of coordination complexes. For example, the iron(II) complex [Fe(H<sub>2<\/sub>O)<sub>6<\/sub>]SO<sub>4<\/sub> appears blue-green because the high-spin complex absorbs photons in the red wavelengths. In contrast, the low-spin iron(II) complex K<sub>4<\/sub>[Fe(CN)<sub>6<\/sub>] appears pale yellow because it absorbs higher-energy violet photons.\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"893\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23212847\/CNX_Chem_19_03_Feabs1.jpg\" alt=\"Two photos are shown. Photo a on the left shows a small mound of a white crystalline powder with a very faint yellow tint on a watch glass. Photo b shows a small mound of a yellow-tan crystalline powder.\" width=\"893\" height=\"358\" data-media-type=\"image\/jpeg\" \/> Figure 7. Both (a) hexaaquairon(II) sulfate and (b) potassium hexacyanoferrate(II) contain <em>d<\/em><sup>6<\/sup> iron(II) octahedral metal centers, but they absorb photons in different ranges of the visible spectrum.[\/caption]\r\n\r\nIn general, strong-field ligands cause a large split in the energies of <em>d<\/em> orbitals of the central metal atom (large \u0394<sub>oct<\/sub>). Transition metal coordination compounds with these ligands are yellow, orange, or red because they absorb higher-energy violet or blue light. On the other hand, coordination compounds of transition metals with weak-field ligands are often blue-green, blue, or indigo because they absorb lower-energy yellow, orange, or red light.\r\n\r\nA coordination compound of the Cu<sup>+<\/sup> ion has a <em>d<\/em><sup>10<\/sup> configuration, and all the <em>e<sub>g<\/sub><\/em> orbitals are filled. To excite an electron to a higher level, such as the 4<em>p<\/em> orbital, photons of very high energy are necessary. This energy corresponds to very short wavelengths in the ultraviolet region of the spectrum. No visible light is absorbed, so the eye sees no change, and the compound appears white or colorless. A solution containing [latex]{\\left[\\text{Cu}{\\left(\\text{CN}\\right)}_{2}\\right]}^{-}[\/latex] for example, is colorless. On the other hand, octahedral Cu<sup>2+<\/sup> complexes have a vacancy in the <em>e<sub>g<\/sub><\/em> orbitals, and electrons can be excited to this level. The wavelength (energy) of the light absorbed corresponds to the visible part of the spectrum, and Cu<sup>2+<\/sup> complexes are almost always colored\u2014blue, blue-green violet, or yellow. Although CFT successfully describes many properties of coordination complexes, molecular orbital explanations (beyond the introductory scope provided here) are required to understand fully the behavior of coordination complexes.\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"975\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23212849\/CNX_Chem_19_03_Cu1.jpg\" alt=\"Two photos are shown. Photo a on the left shows a small mound of a white crystalline powder on a watch glass. Photo b shows a small mound of a bright blue crystalline powder.\" width=\"975\" height=\"433\" data-media-type=\"image\/jpeg\" \/> Figure 8. (a) Copper(I) complexes with <em>d<\/em><sup>10<\/sup> configurations such as CuI tend to be colorless, whereas (b) <em>d<\/em><sup>9<\/sup> copper(II) complexes such as Cu(NO<sub>3<\/sub>)<sub>2<\/sub> \u2022 5H<sub>2<\/sub>O are brightly colored.[\/caption]\r\n\r\n<div class=\"bcc-box bcc-success\">\r\n<h2>Key Concepts and Summary<\/h2>\r\nCrystal field theory treats interactions between the electrons on the metal and the ligands as a simple electrostatic effect. The presence of the ligands near the metal ion changes the energies of the metal <em>d<\/em> orbitals relative to their energies in the free ion. Both the color and the magnetic properties of a complex can be attributed to this crystal field splitting. The magnitude of the splitting (\u0394<sub>oct<\/sub>) depends on the nature of the ligands bonded to the metal. Strong-field ligands produce large splitting and favor low-spin complexes, in which the <em>t<\/em><sub>2<em>g<\/em><\/sub> orbitals are completely filled before any electrons occupy the <em>e<sub>g<\/sub><\/em> orbitals. Weak-field ligands favor formation of high-spin complexes. The <em>t<\/em><sub>2<em>g<\/em><\/sub> and the <em>e<sub>g<\/sub><\/em> orbitals are singly occupied before any are doubly occupied.\r\n\r\n<\/div>\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Chemistry End of Chapter Exercises<\/h3>\r\n<ol>\r\n\t<li>Determine the number of unpaired electrons expected for [latex]{\\left[\\text{Fe}{\\left({\\text{NO}}_{2}\\right)}_{6}\\right]}^{3-}[\/latex] and for [latex]{\\left[{\\text{FeF}}_{6}\\right]}^{3-}[\/latex] in terms of crystal field theory.<\/li>\r\n\t<li>Draw the crystal field diagrams for [latex]{\\left[\\text{Fe}{\\left({\\text{NO}}_{2}\\right)}_{6}\\right]}^{4-}[\/latex] and [latex]{\\left[{\\text{FeF}}_{6}\\right]}^{3-.}[\/latex] State whether each complex is high spin or low spin, paramagnetic or diamagnetic, and compare \u0394<sub>oct<\/sub> to P for each complex.<strong>\r\n<\/strong><\/li>\r\n\t<li>Give the oxidation state of the metal, number of <em>d<\/em> electrons, and the number of unpaired electrons predicted for [Co(NH<sub>3<\/sub>)<sub>6<\/sub>]Cl<sub>3<\/sub>.<\/li>\r\n\t<li>The solid anhydrous solid CoCl<sub>2<\/sub> is blue in color. Because it readily absorbs water from the air, it is used as a humidity indicator to monitor if equipment (such as a cell phone) has been exposed to excessive levels of moisture. Predict what product is formed by this reaction, and how many unpaired electrons this complex will have.<\/li>\r\n\t<li>Is it possible for a complex of a metal in the transition series to have six unpaired electrons? Explain.<\/li>\r\n\t<li>How many unpaired electrons are present in each of the following?\r\n<ol>\r\n\t<li>[latex]{\\left[{\\text{CoF}}_{6}\\right]}^{3-}[\/latex] (high spin)<\/li>\r\n\t<li>[latex]{\\left[\\text{Mn}{\\left(\\text{CN}\\right)}_{6}\\right]}^{3-}[\/latex] (low spin)<\/li>\r\n\t<li>[latex]{\\left[\\text{Mn}{\\left(\\text{CN}\\right)}_{6}\\right]}^{4-}[\/latex] (low spin)<\/li>\r\n\t<li>[latex]{\\left[{\\text{MnCl}}_{6}\\right]}^{4-}[\/latex] (high spin)<\/li>\r\n\t<li>[latex]{\\left[{\\text{RhCl}}_{6}\\right]}^{3-}[\/latex] (low spin)<\/li>\r\n<\/ol>\r\n<\/li>\r\n\t<li>Explain how the diphosphate ion, [latex]{\\left[{\\text{O}}_{3}\\text{P}-\\text{O}-{\\text{PO}}_{3}\\right]}^{4-},[\/latex] can function as a water softener that prevents the precipitation of Fe<sup>2+<\/sup> as an insoluble iron salt.<\/li>\r\n\t<li>For complexes of the same metal ion with no change in oxidation number, the stability increases as the number of electrons in the <em>t<\/em><sub>2<em>g<\/em><\/sub> orbitals increases. Which complex in each of the following pairs of complexes is more stable?\r\n<ol>\r\n\t<li>[latex]{\\left[\\text{Fe}{\\left({\\text{H}}_{2}\\text{O}\\right)}_{6}\\right]}^{2+}[\/latex] or [latex]{\\left[\\text{Fe}{\\text{(CN)}}_{6}\\right]}^{4-}[\/latex]<\/li>\r\n\t<li>[latex]{\\left[\\text{Co}{\\left({\\text{NH}}_{3}\\right)}_{6}\\right]}^{3+}[\/latex] or [latex]{\\left[{\\text{CoF}}_{6}\\right]}^{3-}[\/latex]<\/li>\r\n\t<li>[latex]{\\left[\\text{Mn}{\\text{(CN)}}_{6}\\right]}^{4-}[\/latex] or [latex]{\\left[{\\text{MnCl}}_{6}\\right]}^{4-}[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n\t<li>Trimethylphosphine, P(CH<sub>3<\/sub>)<sub>3<\/sub>, can act as a ligand by donating the lone pair of electrons on the phosphorus atom. If trimethylphosphine is added to a solution of nickel(II) chloride in acetone, a blue compound that has a molecular mass of approximately 270 g and contains 21.5% Ni, 26.0% Cl, and 52.5% P(CH<sub>3<\/sub>)<sub>3<\/sub> can be isolated. This blue compound does not have any isomeric forms. What are the geometry and molecular formula of the blue compound?<\/li>\r\n\t<li>Would you expect the complex [Co(en)<sub>3<\/sub>]Cl<sub>3<\/sub> to have any unpaired electrons? Any isomers?<\/li>\r\n\t<li>Would you expect the Mg<sub>3<\/sub>[Cr(CN)<sub>6<\/sub>]<sub>2<\/sub> to be diamagnetic or paramagnetic? Explain your reasoning.<\/li>\r\n\t<li>Would you expect salts of the gold(I) ion, Au<sup>+<\/sup>, to be colored? Explain.<\/li>\r\n\t<li>[latex]{\\left[{\\text{CuCl}}_{4}\\right]}^{2-}[\/latex] is green. [latex]{\\left[\\text{Cu}{\\left({\\text{H}}_{2}\\text{O}\\right)}_{6}\\right]}^{2+}[\/latex] is blue. Which absorbs higher-energy photons? Which is predicted to have a larger crystal field splitting?<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div class=\"bcc-box bcc-info\">\r\n<h4>Selected Answers<\/h4>\r\n2.\u00a0<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23212852\/CNX_Chem_19_03_FECN6FEH2O_img1.jpg\" alt=\"A diagram is shown with two columns and two rows of squares outlined in yellow. The first column is labeled \u201c[ F e ( N O subscript 2 ) subscript 6 ] superscript 4 negative sign.\u201d The second is labeled, \u201c[ F e F subscript 6 ] superscript 3 negative sign.\u201d In the left column, three linked squares outlined in yellow are shown. Each of the squares contains two half arrows, one pointing up and one pointing down. In a row just above, two empty linked squares are shown. The label, \u201cLow spin, diamagnetic, P less than capital delta subscript oct,\u201d is provided below the column. In the right column, three linked squares outlined in yellow are shown. The square on the left contains two half arrows, one pointing up and one pointing down. The other two squares each contain a single upward pointing half arrow. In a row just above, two linked squares are shown which each contain a single upward pointing half arrow. The label, \u201cHigh spin, paramagnetic, P greater than capital delta subscript oct,\u201d is provided below the column.\" data-media-type=\"image\/jpeg\" \/>\r\n\r\n4.\u00a0[Co(H<sub>2<\/sub>O)<sub>6<\/sub>]Cl<sub>2<\/sub> contains an octahedral Co(II) <em>d<\/em><sup>7<\/sup> central atom. Water is a weak-field ligand, so this will be a high-spin complex with three unpaired electrons.\r\n\r\n6.\u00a0(a) Co<sup>3+<\/sup>: high spin = four unpaired:\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23212854\/CNX_Chem_19_03_Ex06a-ans_img1.jpg\" alt=\"An orbital diagram is shown. At the left appears a small empty circle with a, \u201c4 s,\u201d label below. Following a small gap to its right, a group of five small circles is labeled, \u201c3 d,\u201d below. The first circle contains a pair of half arrows, one pointing up, the other down. The remaining four circles each contain a single upward-pointing half arrow.\" data-media-type=\"image\/jpeg\" \/>\r\n(b) Mn<sup>3+<\/sup>: low spin = two unpaired:\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23212855\/CNX_Chem_19_03_Ex06b-ans_img1.jpg\" alt=\"An orbital diagram is shown. At the left appears a small empty circle with a, \u201c4 s,\u201d label below. Following a small gap to its right, a group of five small circles is labeled, \u201c3 d,\u201d below. The first circle contains a pair of half arrows, one pointing up, the other down. The next two circles each contain a single upwar- pointing half arrow. The remaining two circles are empty.\" data-media-type=\"image\/jpeg\" \/>\r\n(c) Mn<sup>2+<\/sup>: low spin = one unpaired:\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23212856\/CNX_Chem_19_03_Ex06c-ans_img1.jpg\" alt=\"An orbital diagram is shown. At the left appears a small empty circle with a, \u201c4 s,\u201d label below. Following a small gap to its right, a group of five small circles is labeled, \u201c3 d,\u201d below. The first two circles contain pairs of half arrows, one pointing up, the other down. The next circle contains a single upward-pointing half arrow. The remaining two circles are empty.\" data-media-type=\"image\/jpeg\" \/>\r\n(d) Mn<sup>2+<\/sup>: high spin = five unpaired:\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23212858\/CNX_Chem_19_03_Ex06d-ans_img1.jpg\" alt=\"An orbital diagram is shown. At the left appears a small empty circle with a, \u201c4 s,\u201d label below. Following a small gap to its right, a group of five small circles is labeled, \u201c3 d,\u201d below. Each of the five circles contains a single upward pointing half arrow.\" data-media-type=\"image\/jpeg\" \/>\r\n(e) Rh<sup>3+<\/sup>: low spin = zero unpaired:\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23212859\/CNX_Chem_19_03_Ex06e-ans_img1.jpg\" alt=\"An orbital diagram is shown. At the left appears a small empty circle with a, \u201c5 s,\u201d label below. Following a small gap to its right, a group of five small circles is labeled, \u201c4 d,\u201d below. The first three circles each contain pairs of half arrows, one pointing up, the other down. The remaining two circles are empty.\" data-media-type=\"image\/jpeg\" \/>\r\n\r\n8.\u00a0The stability depends on the strength of the ligands. (a) CN<sup>-<\/sup> &gt; H<sub>2<\/sub>O, so [latex]{\\left[\\text{Fe}{\\left(\\text{CN}\\right)}_{6}\\right]}^{4-}[\/latex] is more stable; (b) [latex]{\\text{NH}}_{3}&gt;{\\text{F}}^{-}[\/latex] so [latex]{\\left[\\text{Co}{\\left({\\text{NH}}_{3}\\right)}_{6}\\right]}^{3+}[\/latex] is more stable; (c) CN<sup>-<\/sup> &gt; Cl<sup>-<\/sup>, so [latex]{\\left[\\text{Mn}{\\text{(CN)}}_{6}\\right]}^{4-}[\/latex] is more stable.\r\n\r\n10.\u00a0The chloride ions are in the outer coordination sphere and only affect the coordination compound in terms of stabilizing charge. The complex ion [latex]{\\left[\\text{Co}{\\left(\\text{en}\\right)}_{3}\\right]}^{3+}[\/latex] is diamagnetic because Co<sup>3+<\/sup> is <em>d<\/em><sup>6<\/sup> and en is a strong field ligand, so all six electrons will be in the <em>t<\/em><sub>2<em>g<\/em><\/sub> orbitals. The complex does not have any geometric isomers, but the mirror image is nonsuperimposable, so it has an optical isomer.\r\n\r\n12.\u00a0No. Au<sup>+<\/sup> has a complete 5<em>d<\/em> sublevel.\r\n\r\n<\/div>\r\n<div class=\"bcc-box bcc-success\">\r\n<h3>Glossary<\/h3>\r\n<strong>crystal field splitting (\u0394<sub>oct<\/sub>)<\/strong>\r\ndifference in energy between the <em>t<\/em><sub>2<em>g<\/em><\/sub> and <em>e<sub>g<\/sub><\/em> sets or <em>t<\/em> and <em>e<\/em> sets of orbitals\r\n\r\n<strong>crystal field theory<\/strong>\r\nmodel that explains the energies of the orbitals in transition metals in terms of electrostatic interactions with the ligands but does not include metal ligand bonding\r\n\r\n<strong><em>e<sub>g<\/sub><\/em> orbitals<\/strong>\r\nset of two <em>d<\/em> orbitals that are oriented on the Cartesian axes for coordination complexes; in octahedral complexes, they are higher in energy than the <em>t<\/em><sub>2<em>g<\/em><\/sub> orbitals\r\n\r\n<strong>high-spin complex<\/strong>\r\ncomplex in which the electrons maximize the total electron spin by singly populating all of the orbitals before pairing two electrons into the lower-energy orbitals\r\n\r\n<strong>low-spin complex<\/strong>\r\ncomplex in which the electrons minimize the total electron spin by pairing in the lower-energy orbitals before populating the higher-energy orbitals\r\n\r\n<strong>pairing energy (P)<\/strong>\r\nenergy required to place two electrons with opposite spins into a single orbital\r\n\r\n<strong>spectrochemical series<\/strong>\r\nranking of ligands according to the magnitude of the crystal field splitting they induce\r\n\r\n<strong>strong-field ligand<\/strong>\r\nligand that causes larger crystal field splittings\r\n\r\n<strong><em>t<\/em><sub>2<em>g<\/em><\/sub> orbitals<\/strong>\r\nset of three <em>d<\/em> orbitals aligned between the Cartesian axes for coordination complexes; in octahedral complexes, they are lowered in energy compared to the <em>e<sub>g<\/sub><\/em> orbitals according to CFT\r\n\r\n<strong>weak-field ligand<\/strong>\r\nligand that causes small crystal field splittings\r\n\r\n<\/div>","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>LEARNING OBJECTIVES<\/h3>\n<p>By the end of this module, you will be able to:<\/p>\n<ul>\n<li>Outline the basic premise of crystal field theory (CFT)<\/li>\n<li>Identify molecular geometries associated with various d-orbital splitting patterns<\/li>\n<li>Predict electron configurations of split d orbitals for selected transition metal atoms or ions<\/li>\n<li>Explain spectral and magnetic properties in terms of CFT concepts<\/li>\n<\/ul>\n<\/div>\n<p>The behavior of coordination compounds cannot be adequately explained by the same theories used for main group element chemistry. The observed geometries of coordination complexes are not consistent with hybridized orbitals on the central metal overlapping with ligand orbitals, as would be predicted by valence bond theory. The observed colors indicate that the <em>d<\/em> orbitals often occur at different energy levels rather than all being degenerate, that is, of equal energy, as are the three <em>p<\/em> orbitals. To explain the stabilities, structures, colors, and magnetic properties of transition metal complexes, a different bonding model has been developed. Just as valence bond theory explains many aspects of bonding in main group chemistry, crystal field theory is useful in understanding and predicting the behavior of transition metal complexes.<\/p>\n<h2>Crystal Field Theory<\/h2>\n<p>To explain the observed behavior of transition metal complexes (such as how colors arise), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized <em>d<\/em> orbitals of the central metal atom has been developed. This electrostatic model is <strong>crystal field theory<\/strong> (CFT). It allows us to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.<\/p>\n<p>CFT focuses on the nonbonding electrons on the central metal ion in coordination complexes not on the metal-ligand bonds. Like valence bond theory, CFT tells only part of the story of the behavior of complexes. However, it tells the part that valence bond theory does not. In its pure form, CFT ignores any covalent bonding between ligands and metal ions. Both the ligand and the metal are treated as infinitesimally small point charges.<\/p>\n<p>All electrons are negative, so the electrons donated from the ligands will repel the electrons of the central metal. Let us consider the behavior of the electrons in the unhybridized <em>d<\/em> orbitals in an octahedral complex. The five <em>d<\/em> orbitals consist of lobe-shaped regions and are arranged in space. In an octahedral complex, the six ligands coordinate along the axes.<\/p>\n<p>&nbsp;<\/p>\n<div style=\"width: 895px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23212834\/CNX_Chem_19_03_Dorbital1.jpg\" alt=\"This figure includes diagrams of five d orbitals. Each diagram includes three axes. The z-axis is vertical and is denoted with an upward pointing arrow. It is labeled \u201cz\u201d in the first diagram. Arrows similarly identify the x-axis with an arrow pointing from the rear left to the right front, diagonally across the figure and the y-axis with an arrow pointing from the left front diagonally across the figure to the right rear of the diagram. These axes are similarly labeled as \u201cx\u201d and \u201cy.\u201d In this first diagram, four orange balloon-like shapes extend from a point at the origin out along the x- and y- axes in positive and negative directions covering just over half the length of the positive and negative x- and y- axes. Beneath the diagram is the label, \u201cd subscript ( x superscript 2 minus y superscript 2 ).\u201d The second diagram just right of the first is similar except the x, y, and z labels have been replaced in each instance with the letter L. Only a pair of the orange balloon-like shapes are present and extend from the origin above and below along the vertical axis. An orange toroidal or donut shape is positioned around the origin, oriented through the x- and y- axes. This shape extends out to about a third of the length of the positive and negative regions of the x- and y- axes. This diagram is labeled, \u201cd subscript ( z superscript 2 ).\u201d The third through fifth diagrams, similar to the first, show four orange balloon-like shapes. These diagrams differ however in the orientation of the shapes along the axes and the x-, y-, and z-axis labels have each been replaced with the letter L. Planes are added to the figures to help show the orientation differences with these diagrams. In the third diagram, a green plane is oriented vertically through the length of the x-axis and a blue plane is oriented horizontally through the length of the y-axis. The balloon shapes extend from the origin to the spaces between the positive z- and negative y- axes, positive z- and positive y- axes, negative z- and negative y- axes, and negative z- and positive y- axes. This diagram is labeled, \u201cd subscript ( y z ).\u201d In the fourth diagram, a green plane is oriented vertically through the x- and y- axes and a blue plane is oriented horizontally through the length of the x-axis. The balloon shapes extend from the origin to the spaces between the positive z- and negative x- axes, positive z- and positive x- axes, negative z- and negative x- axes, and negative z- and positive x- axes. This diagram is labeled \u201cd subscript ( x z ).\u201d In the fifth diagram, a pink plane is oriented vertically through the length of the y-axis and a green plane is oriented vertically through the length of the x-axis. The balloon shapes extend from the origin to the spaces between the positive x- and negative y- axes, positive x- and positive y- axes, negative x- and negative y- axes, and negative x- and positive y- axes. This diagram is labeled, \u201cd subscript ( x y ).\u201d\" width=\"885\" height=\"260\" data-media-type=\"image\/jpeg\" \/><\/p>\n<p class=\"wp-caption-text\">Figure 1. The directional characteristics of the five <em>d<\/em> orbitals are shown here. The shaded portions indicate the phase of the orbitals. The ligands (L) coordinate along the axes. For clarity, the ligands have been omitted from the <em>d<\/em><sub><em>x<\/em><sup>2<\/sup> \u2212 <em>y<\/em><sup>2<\/sup><\/sub> orbital so that the axis labels could be shown.<\/p>\n<\/div>\n<p>In an uncomplexed metal ion in the gas phase, the electrons are distributed among the five <em>d<\/em> orbitals in accord with Hund&#8217;s rule, because the orbitals all have the same energy. However, when ligands coordinate to a metal ion, the energies of the <em>d<\/em> orbitals are no longer the same.<\/p>\n<p>In octahedral complexes, the lobes in two of the five <em>d<\/em> orbitals, the [latex]{d}_{{z}^{2}}[\/latex] and [latex]{d}_{{x}^{2}-{y}^{2}}[\/latex] orbitals, point toward the ligands. These two orbitals are called the <strong><em>e<\/em><sub><em>g<\/em><\/sub> orbitals<\/strong> (the symbol actually refers to the symmetry of the orbitals, but we will use it as a convenient name for these two orbitals in an octahedral complex). The other three orbitals, the <em>d<sub>xy<\/sub><\/em>, <em>d<sub>xz<\/sub><\/em>, and <em>d<sub>yz<\/sub><\/em> orbitals, have lobes that point between the ligands and are called the <strong><em>t<\/em><sub>2<em>g<\/em><\/sub> orbitals<\/strong> (again, the symbol really refers to the symmetry of the orbitals). As six ligands approach the metal ion along the axes of the octahedron, their point charges repel the electrons in the <em>d<\/em> orbitals of the metal ion. However, the repulsions between the electrons in the <em>e<sub>g<\/sub><\/em> orbitals (the [latex]{d}_{{z}^{2}}[\/latex] and [latex]{d}_{{x}^{2}-{y}^{2}}[\/latex] orbitals) and the ligands are greater than the repulsions between the electrons in the <em>t<\/em><sub>2<em>g<\/em><\/sub> orbitals (the <em>d<sub>zy<\/sub><\/em>, <em>d<sub>xz<\/sub><\/em>, and <em>d<sub>yz<\/sub><\/em> orbitals) and the ligands. This is because the lobes of the <em>e<sub>g<\/sub><\/em> orbitals point directly at the ligands, whereas the lobes of the <em>t<\/em><sub>2<em>g<\/em><\/sub> orbitals point between them. Thus, electrons in the <em>e<sub>g<\/sub><\/em> orbitals of the metal ion in an octahedral complex have higher potential energies than those of electrons in the <em>t<\/em><sub>2<em>g<\/em><\/sub> orbitals. The difference in energy may be represented.<\/p>\n<div style=\"width: 660px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23212836\/CNX_Chem_19_03_CFSE1.jpg\" alt=\"A diagram is shown with a vertical arrow pointing upward along the height of the diagram at its left side. This arrow is labeled, \u201cE.\u201d to the right of this arrow are two rows of squares outlined in yellow. The first row has three evenly spaced squares labeled left to right, \u201cd subscript ( x y ),\u201d \u201cd subscript ( x z ),\u201d and, \u201cd subscript ( y z ).\u201d The second row is positioned just above the first and includes two evenly spaced squares labeled, \u201cd subscript ( z superscript 2 ),\u201d and, \u201cd subscript ( x superscript 2 minus y superscript 2 ).\u201d At the right end of the diagram, a short horizontal line segment is drawn just right of the lower side of the rightmost square. A double sided arrow extends from this line segment to a second horizontal line segment directly above the first and right of the lower side of the squares in the second row. The arrow is labeled \u201c capital delta subscript oct.\u201d. The lower horizontal line segment is similarly labeled \u201ct subscript 2 g orbitals\u201d and the upper line segment is labeled \u201ce subscript g orbitals.\u201d\" width=\"650\" height=\"342\" data-media-type=\"image\/jpeg\" \/><\/p>\n<p class=\"wp-caption-text\">Figure 2. In octahedral complexes, the <em>e<sub>g<\/sub><\/em> orbitals are destabilized (higher in energy) compared to the <em>t<\/em><sub>2<em>g<\/em><\/sub> orbitals, because the ligands interact more strongly with the d orbitals at which they are pointed directly.<\/p>\n<\/div>\n<p>The difference in energy between the <em>e<sub>g<\/sub><\/em> and the <em>t<\/em><sub>2<em>g<\/em><\/sub> orbitals is called the <strong>crystal field splitting<\/strong> and is symbolized by <strong>\u0394oct<\/strong>, where oct stands for octahedral.<\/p>\n<p>The magnitude of \u0394<sub>oct<\/sub> depends on many factors, including the nature of the six ligands located around the central metal ion, the charge on the metal, and whether the metal is using 3<em>d<\/em>, 4<em>d<\/em>, or 5<em>d<\/em> orbitals. Different ligands produce different crystal field splittings. The increasing crystal field splitting produced by ligands is expressed in the <strong>spectrochemical series<\/strong>, a short version of which is given here:<\/p>\n<p>[latex]\\underset{\\text{A few ligands of the spectrochemical series, in order of increasing field strength of the ligand}}{\\overset{\\text{I}^{-}<\\text{Br}^{-}<\\text{Cl}^{-}<\\text{F}^{-}<\\text{H}_2\\text{O}<{\\text{C}_2\\text{O}_4}^{2-}<\\text{NH}_3<en<\\text{NO}_2^{-}<\\text{CN}^{-}}{\\rightarrow}}[\/latex]\n\nIn this series, ligands on the left cause small crystal field splittings and are <strong>weak-field ligands<\/strong>, whereas those on the right cause larger splittings and are <strong>strong-field ligands<\/strong>. Thus, the \u0394<sub>oct<\/sub> value for an octahedral complex with iodide ligands (I<sup>&#8211;<\/sup>) is much smaller than the \u0394<sub>oct<\/sub> value for the same metal with cyanide ligands (CN<sup>&#8211;<\/sup>).<\/p>\n<p>Electrons in the <em>d<\/em> orbitals follow the aufbau (\u201cfilling up\u201d) principle, which says that the orbitals will be filled to give the lowest total energy, just as in main group chemistry. When two electrons occupy the same orbital, the like charges repel each other. The energy needed to pair up two electrons in a single orbital is called the <strong>pairing energy (P)<\/strong>. Electrons will always singly occupy each orbital in a degenerate set before pairing. P is similar in magnitude to \u0394<sub>oct<\/sub>. When electrons fill the <em>d<\/em> orbitals, the relative magnitudes of \u0394<sub>oct<\/sub> and P determine which orbitals will be occupied.<\/p>\n<p>In\u00a0[latex]{\\left[\\text{Fe}{\\left(\\text{CN}\\right)}_{6}\\right]}^{4-}[\/latex], the strong field of six cyanide ligands produces a large \u0394<sub>oct<\/sub>. Under these conditions, the electrons require less energy to pair than they require to be excited to the <em>e<sub>g<\/sub><\/em> orbitals (\u0394<sub>oct<\/sub> &gt; P). The six 3<em>d<\/em> electrons of the Fe<sup>2+<\/sup> ion pair in the three <em>t<\/em><sub>2<em>g<\/em><\/sub> orbitals. Complexes in which the electrons are paired because of the large crystal field splitting are called <strong>low-spin complexes<\/strong>, because the number of unpaired electrons (spins) is minimized.<\/p>\n<p>&nbsp;<\/p>\n<div style=\"width: 903px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23212837\/CNX_Chem_19_03_Lowhigh1.jpg\" alt=\"A diagram is shown with a vertical arrow pointing upward along the height of the diagram at its left side. This arrow is labeled, \u201cE.\u201d to the right of this arrow are several rows of squares outlined in yellow. The first row has three linked squares at the lower right side of the diagram labeled, \u201c[ F e ( C N ) subscript 6 ] superscript 4 negative sign.\u201d Each square contains two half arrows, with the left half arrow pointing up and the right half arrow pointing down. A second row is positioned just above and to the left of the first, with the bottom of the squares at a height equal with the top of the squares in the first row. This group is also composed of 3 linked squares. The square to the left contains two half arrows, with the left half arrow pointing up and the right half arrow pointing down. The remaining two squares in this row only have upward pointing half arrows. At the bottom of the figure, just below this group is the label \u201c[ F e ( H subscript 2 O ) subscript 6] superscript 2 plus sign.\u201d To the left of this row, a third row that includes 5 linked squares is positioned with the lower edge of the squares at a height equal to the tops of the squares in row two. The square to the left contains two half arrows, one up and one down. All other squares in this group contain single upward pointing arrows. At the bottom of the figure beneath this row appears the label, \u201cF e superscript 2 plus sign no ligands.\u201d A fourth row composed of 2 linked squares appears to the right and above the second row. The lower edge of the squares is at a height level with the top of the squares of the third row. Each of these squares contains a single upward pointing half arrow. A fifth row of 2 squares is positioned above and to the right directly above the first row with the base of the squares positioned at a level equal to the top of the previous row of squares. These squares are empty. At the right of the diagram, a short horizontal line segment is drawn just right of the lower side of the rightmost square of the first row. A double-headed arrow extends from this line segment to a second horizontal line segment directly above the first and right of the lower side of the fifth row of squares. The arrow is labeled, \u201cLow spin, large delta subscript oct,\u201d to the right. The lower horizontal line segment is similarly labeled, \u201ct subscript 2 g,\u201d and the upper line segment is labeled, \u201ce subscript g.\u201d To the right of the second and fourth rows, a short horizontal line segment is drawn just right of the lower side of the rightmost square of the second row. A double-headed arrow extends from this line segment to a second horizontal line segment directly above the first and right of the lower side of the fourth row of squares. The arrow is labeled, \u201cHigh spin, small capital delta subscript oct,\u201d to the right. The lower horizontal line segment is similarly labeled, \u201ct subscript 2 g,\u201d and the upper line segment is labeled, \u201ce subscript g.\u201d\" width=\"893\" height=\"305\" data-media-type=\"image\/jpeg\" \/><\/p>\n<p class=\"wp-caption-text\">Figure 3.\u00a0Iron(II) complexes have six electrons in the 5<em>d<\/em> orbitals. In the absence of a crystal field, the orbitals are degenerate. For coordination complexes with strong-field ligands such as [Fe(CN)<sub>6<\/sub>]<sup>4\u2212<\/sup>\u00a0, \u0394<sub>oct<\/sub> is greater than P, and the electrons pair in the lower energy t<sub>2<em>g<\/em><\/sub> orbitals before occupying the <em>e<sub>g<\/sub><\/em> orbitals. With weak-field ligands such as H<sub>2<\/sub>O, the ligand field splitting is less than the pairing energy, \u0394<sub>oct<\/sub> less than P, so the electrons occupy all <em>d<\/em> orbitals singly before any pairing occurs.<\/p>\n<\/div>\n<p>In [latex]{\\left[\\text{Fe}{\\left({\\text{H}}_{2}\\text{O}\\right)}_{6}\\right]}^{2+},[\/latex] on the other hand, the weak field of the water molecules produces only a small crystal field splitting (\u0394<sub>oct<\/sub> &lt; P). Because it requires less energy for the electrons to occupy the <em>e<sub>g<\/sub><\/em> orbitals than to pair together, there will be an electron in each of the five 3<em>d<\/em> orbitals before pairing occurs. For the six <em>d<\/em> electrons on the iron(II) center in [latex]{\\left[\\text{Fe}{\\left({\\text{H}}_{2}\\text{O}\\right)}_{6}\\right]}^{2+},[\/latex] there will be one pair of electrons and four unpaired electrons. Complexes such as the [latex]{\\left[\\text{Fe}{\\left({\\text{H}}_{2}\\text{O}\\right)}_{6}\\right]}^{2+}[\/latex] ion, in which the electrons are unpaired because the crystal field splitting is not large enough to cause them to pair, are called <strong>high-spin complexes<\/strong>, because the number of unpaired electrons (spins) is maximized.<\/p>\n<p>A similar line of reasoning shows why the [latex]{\\left[\\text{Fe}{\\left(\\text{CN}\\right)}_{6}\\right]}^{3-}[\/latex] ion is a low-spin complex with only one unpaired electron, whereas both the [latex]{\\left[\\text{Fe}{\\left({\\text{H}}_{2}\\text{O}\\right)}_{6}\\right]}^{3+}[\/latex] and [latex]{\\left[{\\text{FeF}}_{6}\\right]}^{3-}[\/latex] ions are high-spin complexes with five unpaired electrons.<\/p>\n<div class=\"textbox shaded\">\n<h3>Example 1<\/h3>\n<h4>High- and Low-Spin Complexes<\/h4>\n<p>Predict the number of unpaired electrons.<\/p>\n<p>(a) K<sub>3<\/sub>[CrI<sub>6<\/sub>]<\/p>\n<p>(b) [Cu(en)<sub>2<\/sub>(H<sub>2<\/sub>O)<sub>2<\/sub>]Cl<sub>2<\/sub><\/p>\n<p>(c) Na<sub>3<\/sub>[Co(NO<sub>2<\/sub>)<sub>6<\/sub>]<\/p>\n<h4>Solution<\/h4>\n<p>The complexes are octahedral.<\/p>\n<p>(a) Cr<sup>3+<\/sup> has a <em>d<\/em><sup>3<\/sup> configuration. These electrons will all be unpaired.<\/p>\n<p>(b) Cu<sup>2+<\/sup> is <em>d<\/em><sup>9<\/sup>, so there will be one unpaired electron.<\/p>\n<p>(c) Co<sup>3+<\/sup> has <em>d<\/em><sup>6<\/sup> valence electrons, so the crystal field splitting will determine how many are paired. Nitrite is a strong-field ligand, so the complex will be low spin. Six electrons will go in the <em>t<\/em><sub>2<em>g<\/em><\/sub> orbitals, leaving 0 unpaired.<\/p>\n<h4>Check Your Learning<\/h4>\n<p>The size of the crystal field splitting only influences the arrangement of electrons when there is a choice between pairing electrons and filling the higher-energy orbitals. For which <em>d<\/em>-electron configurations will there be a difference between high- and low-spin configurations in octahedral complexes?<\/p>\n<p style=\"text-align: right;\"><strong>Answer:\u00a0<\/strong><em>d<\/em><sup>4<\/sup>, <em>d<\/em><sup>5<\/sup>, <em>d<\/em><sup>6<\/sup>, and <em>d<\/em><sup>7<\/sup><\/p>\n<\/div>\n<div class=\"textbox shaded\">\n<h3>Example\u00a02<\/h3>\n<h4>CFT for Other Geometries<\/h4>\n<p>CFT is applicable to molecules in geometries other than octahedral. In octahedral complexes, remember that the lobes of the <em>e<sub>g<\/sub><\/em> set point directly at the ligands. For tetrahedral complexes, the <em>d<\/em> orbitals remain in place, but now we have only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the <em>e<sub>g<\/sub><\/em> set (along the Cartesian axes) overlaps with the ligands less than does the <em>t<\/em><sub>2<em>g<\/em><\/sub> set. By analogy with the octahedral case, predict the energy diagram for the <em>d<\/em> orbitals in a tetrahedral crystal field. To avoid confusion, the octahedral <em>e<sub>g<\/sub><\/em> set becomes a tetrahedral <em>e<\/em> set, and the octahedral <em>t<\/em><sub>2<em>g<\/em><\/sub> set becomes a <em>t<\/em><sub>2<\/sub> set.<\/p>\n<div style=\"width: 660px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23212839\/CNX_Chem_19_03_TetCube1.jpg\" alt=\"This figure includes a three dimensional diagram. At the origin appears the letter M. An arrow, labeled, \u201cz,\u201d at its tip, points upward through the center. An arrow, labeled, \u201cx,\u201d at its tip, points right through the center. A third arrow, labeled, \u201cy,\u201d at its tip, points through the center from the left front to the right back portion of the diagram. A rectangular prism is drawn in green, extending out approximately three-quarters of the lengths from the origin along the positive and negative x-, y-, and z- axes. Small red spheres are positioned at the left upper front, right upper back, right lower front, and left lower back vertices of the prism. Red lines extend from the central M through the prism to these four small red spheres.\" width=\"650\" height=\"428\" data-media-type=\"image\/jpeg\" \/><\/p>\n<p class=\"wp-caption-text\">Figure 4. This diagram shows the orientation of the tetrahedral ligands with respect to the axis system for the orbitals.<\/p>\n<\/div>\n<h4>Solution<\/h4>\n<p>Since CFT is based on electrostatic repulsion, the orbitals closer to the ligands will be destabilized and raised in energy relative to the other set of orbitals. The splitting is less than for octahedral complexes, because the overlap is less, so \u0394<sub>tet<\/sub> is usually small [latex]\\left({\\Delta}_{\\text{tet}}=\\frac{4}{9}{\\Delta}_{\\text{oct}}\\right)\\text{:}[\/latex]<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23212840\/CNX_Chem_19_03_Smalldeltt_img1.jpg\" alt=\"A diagram is shown with a vertical arrow pointing upward along the height of the diagram at its left side. This arrow is labeled, \u201cE.\u201d to the right of this arrow are two rows of squares outlined in yellow. The first row has two adjacent squares. The second row is positioned just above the first and includes three adjacent squares. At the right side of the diagram, a short horizontal line segment is drawn just right of the lower side of the rightmost square in the first row. A double-headed arrow extends from this line segment to a second horizontal line segment directly above the first and right of the lower side of the squares in the second row. The arrow is labeled, \u201csmall capital delta subscript tet,\u201d to the right. The lower horizontal line segment is similarly labeled, \u201ce subscript,\u201d and the upper line segment is labeled, \u201ct subscript 2.\u201d\" data-media-type=\"image\/jpeg\" \/><\/p>\n<h4>Check Your Learning<\/h4>\n<p>Explain how many unpaired electrons a tetrahedral <em>d<\/em><sup>4<\/sup> ion will have.<\/p>\n<p style=\"text-align: right;\"><strong>Answer:\u00a0<\/strong>4; because \u0394<sub>tet<\/sub> is small, all tetrahedral complexes are high spin and the electrons go into the <em>t<\/em><sub>2<\/sub> orbitals before pairing<\/p>\n<\/div>\n<p>The other common geometry is square planar. It is possible to consider a square planar geometry as an octahedral structure with a pair of <em>trans<\/em> ligands removed. The removed ligands are assumed to be on the <em>z<\/em>-axis. This changes the distribution of the <em>d<\/em> orbitals, as orbitals on or near the <em>z<\/em>-axis become more stable, and those on or near the <em>x-<\/em> or <em>y<\/em>-axes become less stable. This results in the octahedral <em>t<\/em><sub>2<em>g<\/em><\/sub> and the <em>e<sub>g<\/sub><\/em> sets splitting and gives a more complicated pattern with no simple \u0394<sub>oct<\/sub>. The basic pattern is:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23212842\/CNX_Chem_19_03_Pattern_img1.jpg\" alt=\"A diagram is shown with four rows of vertically oriented rectangles. The lower level has two rectangles with a space between them. The rectangle on the left is labeled, \u201cd subscript x z,\u201d below. The rectangle to its right is similarly labeled, \u201cd subscript y z.\u201d Just above, the second row contains only 1 rectangle above and between the lower two. This rectangle is labeled, \u201cd subscript z squared.\u201d Just above, the third row contains only 1 rectangle directly above. This rectangle is labeled, \u201cd subscript x z.\u201d Just above, the fourth row contains only 1 rectangle directly above. This rectangle is labeled, \u201cd subscript x squared minus y squared.\u201d\" data-media-type=\"image\/jpeg\" \/><\/p>\n<h2>Magnetic Moments of Molecules and Ions<\/h2>\n<p>Experimental evidence of magnetic measurements supports the theory of high- and low-spin complexes. Remember that molecules such as O<sub>2<\/sub> that contain unpaired electrons are paramagnetic. Paramagnetic substances are attracted to magnetic fields. Many transition metal complexes have unpaired electrons and hence are paramagnetic. Molecules such as N<sub>2<\/sub> and ions such as Na<sup>+<\/sup> and [latex]{\\left[\\text{Fe}{\\left(\\text{CN}\\right)}_{6}\\right]}^{4-}[\/latex] that contain no unpaired electrons are diamagnetic. Diamagnetic substances have a slight tendency to be repelled by magnetic fields.<\/p>\n<p>When an electron in an atom or ion is unpaired, the magnetic moment due to its spin makes the entire atom or ion paramagnetic. The size of the magnetic moment of a system containing unpaired electrons is related directly to the number of such electrons: the greater the number of unpaired electrons, the larger the magnetic moment. Therefore, the observed magnetic moment is used to determine the number of unpaired electrons present. The measured magnetic moment of low-spin <em>d<\/em><sup>6<\/sup> [latex]{\\left[\\text{Fe}{\\left(\\text{CN}\\right)}_{6}\\right]}^{4-}[\/latex] confirms that iron is diamagnetic, whereas high-spin <em>d<\/em><sup>6<\/sup> [latex]{\\left[\\text{Fe}{\\left({\\text{H}}_{2}\\text{O}\\right)}_{6}\\right]}^{2+}[\/latex] has four unpaired electrons with a magnetic moment that confirms this arrangement.<\/p>\n<h2>Colors of Transition Metal Complexes<\/h2>\n<p>When atoms or molecules absorb light at the proper frequency, their electrons are excited to higher-energy orbitals. For many main group atoms and molecules, the absorbed photons are in the ultraviolet range of the electromagnetic spectrum, which cannot be detected by the human eye. For coordination compounds, the energy difference between the <em>d<\/em> orbitals often allows photons in the visible range to be absorbed.<\/p>\n<p>The human eye perceives a mixture of all the colors, in the proportions present in sunlight, as white light. Complementary colors, those located across from each other on a color wheel, are also used in color vision. The eye perceives a mixture of two complementary colors, in the proper proportions, as white light. Likewise, when a color is missing from white light, the eye sees its complement. For example, when red photons are absorbed from white light, the eyes see the color green. When violet photons are removed from white light, the eyes see lemon yellow. The blue color of the [latex]{\\left[\\text{Cu}{\\left({\\text{NH}}_{3}\\right)}_{4}\\right]}^{2+}[\/latex] ion results because this ion absorbs orange and red light, leaving the complementary colors of blue and green.<\/p>\n<div style=\"width: 898px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23212844\/CNX_Chem_19_03_Lightper1.jpg\" alt=\"This figure includes three diagrams. In a, red, orange, yellow, green, blue, indigo, and violet incident arrows point from the upper left to the lower right toward one black, one white, and two yellow rectangular surfaces. No arrows are indicated leaving the black surface. On the white surface, arrows of all included colors extend from the surface of the rectangle extending from just right of the tips of the incident arrows that approach the rectangle to the upper right. For the first yellow surface, only a yellow arrow extends from a point just past the tip of the yellow incident arrow to the upper right. For the second yellow surface, all colors of arrows except indigo extend from points just past the tips of the incident arrows to the upper right. In b, a circle shaded in red at the upper left blends to orange, yellow, green, blue, indigo, and violet moving clockwise about the circle. The leftmost side of the red region has a radius that is labeled, \u201c800 n m,\u201d at the edge of the circle. A radius drawn to the top of the circle in the red-orange region is labeled, \u201c620 n m.\u201d A radius drawn to a point near the center of the first quadrant of the circle in the orange-yellow region is labeled, \u201c580 n m.\u201d A radius drawn to a point near the center of the second quadrant of the circle in the yellow-green region is labeled, \u201c560 n m.\u201d A radius drawn to the bottom of the circle in the blue region is labeled, \u201c490 n m.\u201d A radius drawn to a point near the center of the third quadrant of the circle in the indigo region is labeled, \u201c430 n m.\u201d An unlabeled radius is drawn to the leftmost point on the circle in the violet region. The violet region ends where the red region began on the circle. This radius is labeled, \u201c400 n m,\u201d just to the left and below the, \u201c800 n m,\u201d label associated with the red region. In c, a test tube containing a blue substance is shown. To the left of the test tube, incident colored arrows are shown pointing to the test tube. The colors of the arrows in order from bottom to top are red, orange, yellow, green, blue, indigo, and violet. Above these arrows is the label, \u201cWhite light.\u201d To the right of the test tube, yellow, green, blue, indigo, and violet arrows point right. These arrows are positioned at the same level on the test tube as their matching incident arrows on the left of the test tube. Above these arrows is the label, \u201cBlue-appearing light.\u201d\" width=\"888\" height=\"708\" data-media-type=\"image\/jpeg\" \/><\/p>\n<p class=\"wp-caption-text\">Figure 5. (a) An object is black if it absorbs all colors of light. If it reflects all colors of light, it is white. An object has a color if it absorbs all colors except one, such as this yellow strip. The strip also appears yellow if it absorbs the complementary color from white light (in this case, indigo). (b) Complementary colors are located directly across from one another on the color wheel. (c)A solution of [Cu(NH<sub>3<\/sub>)<sub>4<\/sub>]<sup>2+<\/sup> ions absorbs red and orange light, so the transmitted light appears as the complementary color, blue.<\/p>\n<\/div>\n<div class=\"textbox shaded\">\n<h3>Example\u00a03<\/h3>\n<h4>Colors of Complexes<\/h4>\n<p>The octahedral complex [latex]{\\left[\\text{Ti}{\\left({\\text{H}}_{2}\\text{O}\\right)}_{6}\\right]}^{3+}[\/latex] has a single <em>d<\/em> electron. To excite this electron from the ground state <em>t<\/em><sub>2<em>g<\/em><\/sub> orbital to the <em>e<sub>g<\/sub><\/em> orbital, this complex absorbs light from 450 to 600 nm. The maximum absorbance corresponds to \u0394<sub>oct<\/sub> and occurs at 499 nm. Calculate the value of \u0394<sub>oct<\/sub> in Joules and predict what color the solution will appear.<\/p>\n<h4>Solution<\/h4>\n<p>Using Planck&#8217;s equation (refer to the section on electromagnetic energy), we calculate:<\/p>\n<p>[latex]v=\\frac{c}{\\lambda }\\text{so}\\frac{3.00\\times {10}^{8}\\text{m\/s}}{\\frac{\\text{499 nm}\\times \\text{1 m}}{{10}^{9}\\text{nm}}}=6.01\\times {10}^{14}\\text{Hz}[\/latex]<\/p>\n<p>[latex]\\text{E}=\\text{hv so}6.63\\times {10}^{-34}\\text{J}\\cdot\u00a0\\text{s}\\times 6.01\\times {10}^{14}\\text{Hz}=3.99\\times {10}^{-19}\\text{Joules\/ion}[\/latex]Because the complex absorbs 600 nm (orange) through 450 (blue), the indigo, violet, and red wavelengths will be transmitted, and the complex will appear purple.<\/p>\n<h4>Check Your Learning<\/h4>\n<p>A complex that appears green, absorbs photons of what wavelengths?<\/p>\n<p style=\"text-align: right;\"><strong>Answer:\u00a0<\/strong>red, 620\u2013800 nm<\/p>\n<\/div>\n<p>Small changes in the relative energies of the orbitals that electrons are transitioning between can lead to drastic shifts in the color of light absorbed. Therefore, the colors of coordination compounds depend on many factors. Different aqueous metal ions can have different colors. In addition, different oxidation states of one metal can produce different colors, as shown for the vanadium complexes in the link below.<\/p>\n<div style=\"width: 660px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23212845\/CNX_Chem_19_03_ColorAq1.jpg\" alt=\"This figure shows three containers filled with liquids of different colors. The first appears to be purple, the second, orange, and the third red.\" width=\"650\" height=\"433\" data-media-type=\"image\/jpeg\" \/><\/p>\n<p class=\"wp-caption-text\">Figure 6. The partially filled d orbitals of the stable ions Cr<sup>3+<\/sup>(<em>aq<\/em>), Fe<sup>3+<\/sup>(<em>aq<\/em>), and Co<sup>2+<\/sup>(<em>aq<\/em>) (left, center and right, respectively) give rise to various colors. (credit: Sahar Atwa)<\/p>\n<\/div>\n<p>The specific ligands coordinated to the metal center also influence the color of coordination complexes. For example, the iron(II) complex [Fe(H<sub>2<\/sub>O)<sub>6<\/sub>]SO<sub>4<\/sub> appears blue-green because the high-spin complex absorbs photons in the red wavelengths. In contrast, the low-spin iron(II) complex K<sub>4<\/sub>[Fe(CN)<sub>6<\/sub>] appears pale yellow because it absorbs higher-energy violet photons.<\/p>\n<div style=\"width: 903px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23212847\/CNX_Chem_19_03_Feabs1.jpg\" alt=\"Two photos are shown. Photo a on the left shows a small mound of a white crystalline powder with a very faint yellow tint on a watch glass. Photo b shows a small mound of a yellow-tan crystalline powder.\" width=\"893\" height=\"358\" data-media-type=\"image\/jpeg\" \/><\/p>\n<p class=\"wp-caption-text\">Figure 7. Both (a) hexaaquairon(II) sulfate and (b) potassium hexacyanoferrate(II) contain <em>d<\/em><sup>6<\/sup> iron(II) octahedral metal centers, but they absorb photons in different ranges of the visible spectrum.<\/p>\n<\/div>\n<p>In general, strong-field ligands cause a large split in the energies of <em>d<\/em> orbitals of the central metal atom (large \u0394<sub>oct<\/sub>). Transition metal coordination compounds with these ligands are yellow, orange, or red because they absorb higher-energy violet or blue light. On the other hand, coordination compounds of transition metals with weak-field ligands are often blue-green, blue, or indigo because they absorb lower-energy yellow, orange, or red light.<\/p>\n<p>A coordination compound of the Cu<sup>+<\/sup> ion has a <em>d<\/em><sup>10<\/sup> configuration, and all the <em>e<sub>g<\/sub><\/em> orbitals are filled. To excite an electron to a higher level, such as the 4<em>p<\/em> orbital, photons of very high energy are necessary. This energy corresponds to very short wavelengths in the ultraviolet region of the spectrum. No visible light is absorbed, so the eye sees no change, and the compound appears white or colorless. A solution containing [latex]{\\left[\\text{Cu}{\\left(\\text{CN}\\right)}_{2}\\right]}^{-}[\/latex] for example, is colorless. On the other hand, octahedral Cu<sup>2+<\/sup> complexes have a vacancy in the <em>e<sub>g<\/sub><\/em> orbitals, and electrons can be excited to this level. The wavelength (energy) of the light absorbed corresponds to the visible part of the spectrum, and Cu<sup>2+<\/sup> complexes are almost always colored\u2014blue, blue-green violet, or yellow. Although CFT successfully describes many properties of coordination complexes, molecular orbital explanations (beyond the introductory scope provided here) are required to understand fully the behavior of coordination complexes.<\/p>\n<div style=\"width: 985px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23212849\/CNX_Chem_19_03_Cu1.jpg\" alt=\"Two photos are shown. Photo a on the left shows a small mound of a white crystalline powder on a watch glass. Photo b shows a small mound of a bright blue crystalline powder.\" width=\"975\" height=\"433\" data-media-type=\"image\/jpeg\" \/><\/p>\n<p class=\"wp-caption-text\">Figure 8. (a) Copper(I) complexes with <em>d<\/em><sup>10<\/sup> configurations such as CuI tend to be colorless, whereas (b) <em>d<\/em><sup>9<\/sup> copper(II) complexes such as Cu(NO<sub>3<\/sub>)<sub>2<\/sub> \u2022 5H<sub>2<\/sub>O are brightly colored.<\/p>\n<\/div>\n<div class=\"bcc-box bcc-success\">\n<h2>Key Concepts and Summary<\/h2>\n<p>Crystal field theory treats interactions between the electrons on the metal and the ligands as a simple electrostatic effect. The presence of the ligands near the metal ion changes the energies of the metal <em>d<\/em> orbitals relative to their energies in the free ion. Both the color and the magnetic properties of a complex can be attributed to this crystal field splitting. The magnitude of the splitting (\u0394<sub>oct<\/sub>) depends on the nature of the ligands bonded to the metal. Strong-field ligands produce large splitting and favor low-spin complexes, in which the <em>t<\/em><sub>2<em>g<\/em><\/sub> orbitals are completely filled before any electrons occupy the <em>e<sub>g<\/sub><\/em> orbitals. Weak-field ligands favor formation of high-spin complexes. The <em>t<\/em><sub>2<em>g<\/em><\/sub> and the <em>e<sub>g<\/sub><\/em> orbitals are singly occupied before any are doubly occupied.<\/p>\n<\/div>\n<div class=\"bcc-box bcc-info\">\n<h3>Chemistry End of Chapter Exercises<\/h3>\n<ol>\n<li>Determine the number of unpaired electrons expected for [latex]{\\left[\\text{Fe}{\\left({\\text{NO}}_{2}\\right)}_{6}\\right]}^{3-}[\/latex] and for [latex]{\\left[{\\text{FeF}}_{6}\\right]}^{3-}[\/latex] in terms of crystal field theory.<\/li>\n<li>Draw the crystal field diagrams for [latex]{\\left[\\text{Fe}{\\left({\\text{NO}}_{2}\\right)}_{6}\\right]}^{4-}[\/latex] and [latex]{\\left[{\\text{FeF}}_{6}\\right]}^{3-.}[\/latex] State whether each complex is high spin or low spin, paramagnetic or diamagnetic, and compare \u0394<sub>oct<\/sub> to P for each complex.<strong><br \/>\n<\/strong><\/li>\n<li>Give the oxidation state of the metal, number of <em>d<\/em> electrons, and the number of unpaired electrons predicted for [Co(NH<sub>3<\/sub>)<sub>6<\/sub>]Cl<sub>3<\/sub>.<\/li>\n<li>The solid anhydrous solid CoCl<sub>2<\/sub> is blue in color. Because it readily absorbs water from the air, it is used as a humidity indicator to monitor if equipment (such as a cell phone) has been exposed to excessive levels of moisture. Predict what product is formed by this reaction, and how many unpaired electrons this complex will have.<\/li>\n<li>Is it possible for a complex of a metal in the transition series to have six unpaired electrons? Explain.<\/li>\n<li>How many unpaired electrons are present in each of the following?\n<ol>\n<li>[latex]{\\left[{\\text{CoF}}_{6}\\right]}^{3-}[\/latex] (high spin)<\/li>\n<li>[latex]{\\left[\\text{Mn}{\\left(\\text{CN}\\right)}_{6}\\right]}^{3-}[\/latex] (low spin)<\/li>\n<li>[latex]{\\left[\\text{Mn}{\\left(\\text{CN}\\right)}_{6}\\right]}^{4-}[\/latex] (low spin)<\/li>\n<li>[latex]{\\left[{\\text{MnCl}}_{6}\\right]}^{4-}[\/latex] (high spin)<\/li>\n<li>[latex]{\\left[{\\text{RhCl}}_{6}\\right]}^{3-}[\/latex] (low spin)<\/li>\n<\/ol>\n<\/li>\n<li>Explain how the diphosphate ion, [latex]{\\left[{\\text{O}}_{3}\\text{P}-\\text{O}-{\\text{PO}}_{3}\\right]}^{4-},[\/latex] can function as a water softener that prevents the precipitation of Fe<sup>2+<\/sup> as an insoluble iron salt.<\/li>\n<li>For complexes of the same metal ion with no change in oxidation number, the stability increases as the number of electrons in the <em>t<\/em><sub>2<em>g<\/em><\/sub> orbitals increases. Which complex in each of the following pairs of complexes is more stable?\n<ol>\n<li>[latex]{\\left[\\text{Fe}{\\left({\\text{H}}_{2}\\text{O}\\right)}_{6}\\right]}^{2+}[\/latex] or [latex]{\\left[\\text{Fe}{\\text{(CN)}}_{6}\\right]}^{4-}[\/latex]<\/li>\n<li>[latex]{\\left[\\text{Co}{\\left({\\text{NH}}_{3}\\right)}_{6}\\right]}^{3+}[\/latex] or [latex]{\\left[{\\text{CoF}}_{6}\\right]}^{3-}[\/latex]<\/li>\n<li>[latex]{\\left[\\text{Mn}{\\text{(CN)}}_{6}\\right]}^{4-}[\/latex] or [latex]{\\left[{\\text{MnCl}}_{6}\\right]}^{4-}[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>Trimethylphosphine, P(CH<sub>3<\/sub>)<sub>3<\/sub>, can act as a ligand by donating the lone pair of electrons on the phosphorus atom. If trimethylphosphine is added to a solution of nickel(II) chloride in acetone, a blue compound that has a molecular mass of approximately 270 g and contains 21.5% Ni, 26.0% Cl, and 52.5% P(CH<sub>3<\/sub>)<sub>3<\/sub> can be isolated. This blue compound does not have any isomeric forms. What are the geometry and molecular formula of the blue compound?<\/li>\n<li>Would you expect the complex [Co(en)<sub>3<\/sub>]Cl<sub>3<\/sub> to have any unpaired electrons? Any isomers?<\/li>\n<li>Would you expect the Mg<sub>3<\/sub>[Cr(CN)<sub>6<\/sub>]<sub>2<\/sub> to be diamagnetic or paramagnetic? Explain your reasoning.<\/li>\n<li>Would you expect salts of the gold(I) ion, Au<sup>+<\/sup>, to be colored? Explain.<\/li>\n<li>[latex]{\\left[{\\text{CuCl}}_{4}\\right]}^{2-}[\/latex] is green. [latex]{\\left[\\text{Cu}{\\left({\\text{H}}_{2}\\text{O}\\right)}_{6}\\right]}^{2+}[\/latex] is blue. Which absorbs higher-energy photons? Which is predicted to have a larger crystal field splitting?<\/li>\n<\/ol>\n<\/div>\n<div class=\"bcc-box bcc-info\">\n<h4>Selected Answers<\/h4>\n<p>2.\u00a0<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23212852\/CNX_Chem_19_03_FECN6FEH2O_img1.jpg\" alt=\"A diagram is shown with two columns and two rows of squares outlined in yellow. The first column is labeled \u201c[ F e ( N O subscript 2 ) subscript 6 ] superscript 4 negative sign.\u201d The second is labeled, \u201c[ F e F subscript 6 ] superscript 3 negative sign.\u201d In the left column, three linked squares outlined in yellow are shown. Each of the squares contains two half arrows, one pointing up and one pointing down. In a row just above, two empty linked squares are shown. The label, \u201cLow spin, diamagnetic, P less than capital delta subscript oct,\u201d is provided below the column. In the right column, three linked squares outlined in yellow are shown. The square on the left contains two half arrows, one pointing up and one pointing down. The other two squares each contain a single upward pointing half arrow. In a row just above, two linked squares are shown which each contain a single upward pointing half arrow. The label, \u201cHigh spin, paramagnetic, P greater than capital delta subscript oct,\u201d is provided below the column.\" data-media-type=\"image\/jpeg\" \/><\/p>\n<p>4.\u00a0[Co(H<sub>2<\/sub>O)<sub>6<\/sub>]Cl<sub>2<\/sub> contains an octahedral Co(II) <em>d<\/em><sup>7<\/sup> central atom. Water is a weak-field ligand, so this will be a high-spin complex with three unpaired electrons.<\/p>\n<p>6.\u00a0(a) Co<sup>3+<\/sup>: high spin = four unpaired:<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23212854\/CNX_Chem_19_03_Ex06a-ans_img1.jpg\" alt=\"An orbital diagram is shown. At the left appears a small empty circle with a, \u201c4 s,\u201d label below. Following a small gap to its right, a group of five small circles is labeled, \u201c3 d,\u201d below. The first circle contains a pair of half arrows, one pointing up, the other down. The remaining four circles each contain a single upward-pointing half arrow.\" data-media-type=\"image\/jpeg\" \/><br \/>\n(b) Mn<sup>3+<\/sup>: low spin = two unpaired:<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23212855\/CNX_Chem_19_03_Ex06b-ans_img1.jpg\" alt=\"An orbital diagram is shown. At the left appears a small empty circle with a, \u201c4 s,\u201d label below. Following a small gap to its right, a group of five small circles is labeled, \u201c3 d,\u201d below. The first circle contains a pair of half arrows, one pointing up, the other down. The next two circles each contain a single upwar- pointing half arrow. The remaining two circles are empty.\" data-media-type=\"image\/jpeg\" \/><br \/>\n(c) Mn<sup>2+<\/sup>: low spin = one unpaired:<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23212856\/CNX_Chem_19_03_Ex06c-ans_img1.jpg\" alt=\"An orbital diagram is shown. At the left appears a small empty circle with a, \u201c4 s,\u201d label below. Following a small gap to its right, a group of five small circles is labeled, \u201c3 d,\u201d below. The first two circles contain pairs of half arrows, one pointing up, the other down. The next circle contains a single upward-pointing half arrow. The remaining two circles are empty.\" data-media-type=\"image\/jpeg\" \/><br \/>\n(d) Mn<sup>2+<\/sup>: high spin = five unpaired:<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23212858\/CNX_Chem_19_03_Ex06d-ans_img1.jpg\" alt=\"An orbital diagram is shown. At the left appears a small empty circle with a, \u201c4 s,\u201d label below. Following a small gap to its right, a group of five small circles is labeled, \u201c3 d,\u201d below. Each of the five circles contains a single upward pointing half arrow.\" data-media-type=\"image\/jpeg\" \/><br \/>\n(e) Rh<sup>3+<\/sup>: low spin = zero unpaired:<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/04\/23212859\/CNX_Chem_19_03_Ex06e-ans_img1.jpg\" alt=\"An orbital diagram is shown. At the left appears a small empty circle with a, \u201c5 s,\u201d label below. Following a small gap to its right, a group of five small circles is labeled, \u201c4 d,\u201d below. The first three circles each contain pairs of half arrows, one pointing up, the other down. The remaining two circles are empty.\" data-media-type=\"image\/jpeg\" \/><\/p>\n<p>8.\u00a0The stability depends on the strength of the ligands. (a) CN<sup>&#8211;<\/sup> &gt; H<sub>2<\/sub>O, so [latex]{\\left[\\text{Fe}{\\left(\\text{CN}\\right)}_{6}\\right]}^{4-}[\/latex] is more stable; (b) [latex]{\\text{NH}}_{3}>{\\text{F}}^{-}[\/latex] so [latex]{\\left[\\text{Co}{\\left({\\text{NH}}_{3}\\right)}_{6}\\right]}^{3+}[\/latex] is more stable; (c) CN<sup>&#8211;<\/sup> &gt; Cl<sup>&#8211;<\/sup>, so [latex]{\\left[\\text{Mn}{\\text{(CN)}}_{6}\\right]}^{4-}[\/latex] is more stable.<\/p>\n<p>10.\u00a0The chloride ions are in the outer coordination sphere and only affect the coordination compound in terms of stabilizing charge. The complex ion [latex]{\\left[\\text{Co}{\\left(\\text{en}\\right)}_{3}\\right]}^{3+}[\/latex] is diamagnetic because Co<sup>3+<\/sup> is <em>d<\/em><sup>6<\/sup> and en is a strong field ligand, so all six electrons will be in the <em>t<\/em><sub>2<em>g<\/em><\/sub> orbitals. The complex does not have any geometric isomers, but the mirror image is nonsuperimposable, so it has an optical isomer.<\/p>\n<p>12.\u00a0No. Au<sup>+<\/sup> has a complete 5<em>d<\/em> sublevel.<\/p>\n<\/div>\n<div class=\"bcc-box bcc-success\">\n<h3>Glossary<\/h3>\n<p><strong>crystal field splitting (\u0394<sub>oct<\/sub>)<\/strong><br \/>\ndifference in energy between the <em>t<\/em><sub>2<em>g<\/em><\/sub> and <em>e<sub>g<\/sub><\/em> sets or <em>t<\/em> and <em>e<\/em> sets of orbitals<\/p>\n<p><strong>crystal field theory<\/strong><br \/>\nmodel that explains the energies of the orbitals in transition metals in terms of electrostatic interactions with the ligands but does not include metal ligand bonding<\/p>\n<p><strong><em>e<sub>g<\/sub><\/em> orbitals<\/strong><br \/>\nset of two <em>d<\/em> orbitals that are oriented on the Cartesian axes for coordination complexes; in octahedral complexes, they are higher in energy than the <em>t<\/em><sub>2<em>g<\/em><\/sub> orbitals<\/p>\n<p><strong>high-spin complex<\/strong><br \/>\ncomplex in which the electrons maximize the total electron spin by singly populating all of the orbitals before pairing two electrons into the lower-energy orbitals<\/p>\n<p><strong>low-spin complex<\/strong><br \/>\ncomplex in which the electrons minimize the total electron spin by pairing in the lower-energy orbitals before populating the higher-energy orbitals<\/p>\n<p><strong>pairing energy (P)<\/strong><br \/>\nenergy required to place two electrons with opposite spins into a single orbital<\/p>\n<p><strong>spectrochemical series<\/strong><br \/>\nranking of ligands according to the magnitude of the crystal field splitting they induce<\/p>\n<p><strong>strong-field ligand<\/strong><br \/>\nligand that causes larger crystal field splittings<\/p>\n<p><strong><em>t<\/em><sub>2<em>g<\/em><\/sub> orbitals<\/strong><br \/>\nset of three <em>d<\/em> orbitals aligned between the Cartesian axes for coordination complexes; in octahedral complexes, they are lowered in energy compared to the <em>e<sub>g<\/sub><\/em> orbitals according to CFT<\/p>\n<p><strong>weak-field ligand<\/strong><br \/>\nligand that causes small crystal field splittings<\/p>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-2518\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Chemistry. <strong>Provided by<\/strong>: OpenStax College. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/openstaxcollege.org\">http:\/\/openstaxcollege.org<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at https:\/\/openstaxcollege.org\/textbooks\/chemistry\/get<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":5,"menu_order":4,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Chemistry\",\"author\":\"\",\"organization\":\"OpenStax College\",\"url\":\"http:\/\/openstaxcollege.org\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at https:\/\/openstaxcollege.org\/textbooks\/chemistry\/get\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-2518","chapter","type-chapter","status-publish","hentry"],"part":2961,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/suny-buffstate-chemistryformajorsxmaster\/wp-json\/pressbooks\/v2\/chapters\/2518","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/suny-buffstate-chemistryformajorsxmaster\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/suny-buffstate-chemistryformajorsxmaster\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-buffstate-chemistryformajorsxmaster\/wp-json\/wp\/v2\/users\/5"}],"version-history":[{"count":10,"href":"https:\/\/courses.lumenlearning.com\/suny-buffstate-chemistryformajorsxmaster\/wp-json\/pressbooks\/v2\/chapters\/2518\/revisions"}],"predecessor-version":[{"id":5265,"href":"https:\/\/courses.lumenlearning.com\/suny-buffstate-chemistryformajorsxmaster\/wp-json\/pressbooks\/v2\/chapters\/2518\/revisions\/5265"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/suny-buffstate-chemistryformajorsxmaster\/wp-json\/pressbooks\/v2\/parts\/2961"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/suny-buffstate-chemistryformajorsxmaster\/wp-json\/pressbooks\/v2\/chapters\/2518\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/suny-buffstate-chemistryformajorsxmaster\/wp-json\/wp\/v2\/media?parent=2518"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-buffstate-chemistryformajorsxmaster\/wp-json\/pressbooks\/v2\/chapter-type?post=2518"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-buffstate-chemistryformajorsxmaster\/wp-json\/wp\/v2\/contributor?post=2518"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-buffstate-chemistryformajorsxmaster\/wp-json\/wp\/v2\/license?post=2518"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}