{"id":3639,"date":"2015-05-06T03:51:00","date_gmt":"2015-05-06T03:51:00","guid":{"rendered":"https:\/\/courses.candelalearning.com\/oschemtemp\/?post_type=chapter&#038;p=3639"},"modified":"2016-10-27T15:42:59","modified_gmt":"2016-10-27T15:42:59","slug":"standard-reduction-potentials","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/chapter\/standard-reduction-potentials\/","title":{"raw":"Standard Reduction Potentials","rendered":"Standard Reduction Potentials"},"content":{"raw":"<div class=\"textbox learning-objectives\">\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>Determine standard cell potentials for oxidation-reduction reactions<\/li>\r\n \t<li>Use standard reduction potentials to determine the better oxidizing or reducing agent from among several possible choices<\/li>\r\n<\/ul>\r\n<\/div>\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"700\"]<img class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/05\/23214133\/CNX_Chem_17_02_Galvanicel.jpg\" alt=\"This figure contains a diagram of an electrochemical cell. Two beakers are shown. Each is just over half full. The beaker on the left contains a blue solution and is labeled below as \u201c1 M solution of copper (II) nitrate ( C u ( N O subscript 3 ) subscript 2 ).\u201d The beaker on the right contains a colorless solution and is labeled below as \u201c1 M solution of silver nitrate ( A g N O subscript 3 ).\u201d A glass tube in the shape of an inverted U connects the two beakers at the center of the diagram. The tube contents are colorless. The ends of the tubes are beneath the surface of the solutions in the beakers and a small grey plug is present at each end of the tube. The plug in the left beaker is labeled \u201cPorous plug.\u201d At the center of the diagram, the tube is labeled \u201cSalt bridge ( N a N O subscript 3 ). Each beaker shows a metal strip partially submerged in the liquid. The beaker on the left has an orange brown strip that is labeled \u201cC u anode negative\u201d at the top. The beaker on the right has a silver strip that is labeled \u201cA g cathode positive\u201d at the top. A wire extends from the top of each of these strips to a rectangular digital readout indicating a reading of positive 0.46 V that is labeled \u201cVoltmeter.\u201d An arrow points toward the voltmeter from the left which is labeled \u201cFlow of electrons.\u201d Similarly, an arrow points away from the voltmeter to the right which is also labeled \u201cFlow of electrons.\u201d A curved arrow extends from the C u strip into the surrounding solution. The tip of this arrow is labeled \u201cC u superscript 2 plus.\u201d A curved arrow extends from the salt bridge into the beaker on the left into the blue solution. The tip of this arrow is labeled \u201cN O subscript 3 superscript negative.\u201d A curved arrow extends from the solution in the beaker on the right to the A g strip. The base of this arrow is labeled \u201cA g superscript plus.\u201d A curved arrow extends from the colorless solution to salt bridge in the beaker on the right. The base of this arrow is labeled \u201cN O subscript 3 superscript negative.\u201d Just right of the center of the salt bridge on the tube an arrow is placed on the salt bridge that points down and to the right. The base of this arrow is labeled \u201cN a superscript plus.\u201d Just above this region of the tube appears the label \u201cFlow of cations.\u201d Just left of the center of the salt bridge on the tube an arrow is placed on the salt bridge that points down and to the left. The base of this arrow is labeled \u201cN O subscript 3 superscript negative.\u201d Just above this region of the tube appears the label \u201cFlow of anions.\u201d\" width=\"700\" height=\"696\" data-media-type=\"image\/jpeg\" \/> Figure\u00a01. In this standard galvanic cell, the half-cells are separated; electrons can flow through an external wire and become available to do electrical work.[\/caption]\r\n\r\nThe cell potential in Figure\u00a01\u00a0(+0.46 V) results from the difference in the electrical potentials for each electrode. While it is impossible to determine the electrical potential of a single electrode, we can assign an electrode the value of zero and then use it as a reference. The electrode chosen as the zero is shown in Figure\u00a02\u00a0and is called the <b>standard hydrogen electrode (SHE)<\/b>. The SHE consists of 1 atm of hydrogen gas bubbled through a 1 M HCl solution, usually at room temperature. Platinum, which is chemically inert, is used as the electrode. The reduction half-reaction chosen as the reference is\r\n<p style=\"text-align: center;\">[latex]2\\text{H}^{+}\\left(aq, 1M\\right)+2\\text{e}^{-}\\rightleftharpoons\\text{H}_{2}\\left(g,1\\text{ atm}\\right)\\,\\,\\,\\,\\,\\,\\,E^{\\circ}=0\\text{ V}[\/latex]<\/p>\r\n<em>E<\/em>\u00b0 is the standard reduction potential. The superscript \u201c\u00b0\u201d on the <em>E<\/em> denotes standard conditions (1 bar or 1 atm for gases, 1 <em>M<\/em> for solutes). The voltage is defined as zero for all temperatures.\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"701\"]<img class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/05\/23214137\/CNX_Chem_17_03_SHE.jpg\" alt=\"The figure shows a beaker just over half full of a blue liquid. A glass tube is partially submerged in the liquid. Bubbles, which are labeled \u201cH subscript 2 ( g )\u201d are rising from the dark grey square, labeled \u201cP t electrode\u201d at the bottom of the tube. A curved arrow points up to the right, indicating the direction of the bubbles. A black wire which is labeled \u201cP t wire\u201d extends from the dark grey square up the interior of the tube through a small port at the top. A second small port extends out the top of the tube to the left. An arrow points to the port opening from the left. The base of this arrow is labeled \u201cH subscript 2 ( g ) at 1 a t m.\u201d A light grey arrow points to a diagram in a circle at the right that illustrates the surface of the P t electrode in a magnified view. P t atoms are illustrated as a uniform cluster of grey spheres which are labeled \u201cP t electrode atoms.\u201d On the grey atom surface, the label \u201ce superscript negative\u201d is shown 4 times in a nearly even vertical distribution to show electrons on the P t surface. A curved arrow extends from a white sphere labeled \u201cH superscript plus\u201d at the right of the P t atoms to the uppermost electron shown. Just below, a straight arrow extends from the P t surface to the right to a pair of linked white spheres which are labeled \u201cH subscript 2.\u201d A curved arrow extends from a second white sphere labeled \u201cH superscript plus\u201d at the right of the P t atoms to the second electron shown. A curved arrow extends from the third electron on the P t surface to the right to a white sphere labeled \u201cH superscript plus.\u201d Just below, an arrow points left from a pair of linked white spheres which are labeled \u201cH subscript 2\u201d to the P t surface. A curved arrow extends from the fourth electron on the P t surface to the right to a white sphere labeled \u201cH superscript plus.\u201d Beneath this atomic view is the label \u201cHalf-reaction at P t surface: 2 H superscript plus ( a q, 1 M ) plus 2 e superscript negative right pointing arrow H subscript 2 ( g, 1 a t m ).\u201d\" width=\"701\" height=\"414\" data-media-type=\"image\/jpeg\" \/> Figure\u00a02. Hydrogen gas at 1 atm is bubbled through 1 <em>M<\/em> HCl solution. Platinum, which is inert to the action of the 1 <em>M<\/em> HCl, is used as the electrode. Electrons on the surface of the electrode combine with H<sup>+<\/sup> in solution to produce hydrogen gas.[\/caption]\r\n\r\nA galvanic cell consisting of a SHE and Cu<sup>2+<\/sup>\/Cu half-cell can be used to determine the standard reduction potential for Cu<sup>2+<\/sup> (Figure\u00a03). In cell notation, the reaction is\r\n<p style=\"text-align: center;\">[latex]\\text{Pt}\\left(s\\right)\\mid {\\text{H}}_{2}\\left(g,\\text{1 atm}\\right)\\mid {\\text{H}}^{\\text{+}}\\left(aq,1M\\right)\\parallel {\\text{Cu}}^{2+}\\left(aq,1M\\right)\\mid \\text{Cu}\\left(s\\right)[\/latex]<\/p>\r\nElectrons flow from the anode to the cathode. The reactions, which are reversible, are\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{rl}\\text{Anode (oxidation):}&amp;\\text{H}_{2}\\left(g\\right)\\longrightarrow2\\text{H}^{+}\\left(aq\\right)+2\\text{e}^{-}\\\\ \\text{Cathode (reduction):}&amp;\\text{Cu}^{2+}\\left(aq\\right)+2\\text{e}^{-}\\longrightarrow\\text{Cu}\\left(s\\right)\\\\ \\\\ \\text{Overall:}&amp;\\text{Cu}^{2+}\\left(aq\\right)+\\text{H}_{2}\\left(g\\right)\\longrightarrow2\\text{H}^{+}\\left(aq\\right)+\\text{Cu}\\left(s\\right)\\end{array}[\/latex]<\/p>\r\nThe standard reduction potential can be determined by subtracting the standard reduction potential for the reaction occurring at the anode from the standard reduction potential for the reaction occurring at the cathode. The minus sign is necessary because oxidation is the reverse of reduction.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{rllll}{}{E}_{\\text{cell}}^{\\circ }&amp;=&amp;{E}_{\\text{cathode}}^{\\circ }-{E}_{\\text{anode}}^{\\circ }\\\\\\text{+0.34 V}&amp;=&amp;{E}_{{\\text{Cu}}^{2+}\\text{\/Cu}}^{\\circ }-{E}_{{\\text{H}}^{\\text{+}}{\\text{\/H}}_{2}}^{\\circ }\\\\{}&amp;=&amp;{E}_{{\\text{Cu}}^{2+}\\text{\/Cu}}^{\\circ }-0&amp;=&amp;{E}_{{\\text{Cu}}^{2+}\\text{\/Cu}}^{\\circ }\\end{array}[\/latex]<\/p>\r\n\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"700\"]<img class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/05\/23214139\/CNX_Chem_17_03_GalvanCu.jpg\" alt=\"This figure contains a diagram of an electrochemical cell. Two beakers are shown. Each is just over half full. The beaker on the left contains a clear, colorless solution and is labeled below as \u201c1 M H superscript plus.\u201d The beaker on the right contains a blue solution and is labeled below as \u201c1 M C u superscript 2 plus.\u201d A glass tube in the shape of an inverted U connects the two beakers at the center of the diagram. The tube contents are colorless. The ends of the tubes are beneath the surface of the solutions in the beakers and a small grey plug is present at each end of the tube. The beaker on the left has a glass tube partially submersed in the liquid. Bubbles are rising from the grey square, labeled \u201cStandard hydrogen electrode\u201d at the bottom of the tube. A curved arrow points up to the right, indicating the direction of the bubbles. A black wire extends from the grey square up the interior of the tube through a small port at the top to a rectangle with a digital readout of \u201cpositive 0.337 V\u201d which is labeled \u201cVoltmeter.\u201d A second small port extends out the top of the tube to the left. An arrow points to the port opening from the left. The base of this arrow is labeled \u201cH subscript 2 ( g ).\u201d The beaker on the right has an orange-brown strip that is labeled \u201cC u strip\u201d at the top. A wire extends from the top of this strip to the voltmeter. An arrow points toward the voltmeter from the left which is labeled \u201ce superscript negative flow.\u201d Similarly, an arrow points away from the voltmeter to the right. A curved arrow extends from the standard hydrogen electrode in the beaker on the left into the surrounding solution. The tip of this arrow is labeled \u201cH plus.\u201d An arrow points downward from the label \u201ce superscript negative\u201d on the C u strip in the beaker on the right. A second curved arrow extends from another \u201ce superscript negative\u201d label into the solution below toward the label \u201cC u superscript 2 plus\u201d in the solution. A third \u201ce superscript negative\u201d label positioned at the lower left edge of the C u strip has a curved arrow extending from it to the \u201cC u superscript 2 plus\u201d label in the solution. A curved arrow extends from this \u201cC u superscript 2 plus\u201d label to a \u201cC u\u201d label at the lower edge of the C u strip.\" width=\"700\" height=\"608\" data-media-type=\"image\/jpeg\" \/> Figure\u00a03. A galvanic cell can be used to determine the standard reduction potential of Cu2<sup>+<\/sup>.[\/caption]\r\n\r\nUsing the SHE as a reference, other standard reduction potentials can be determined. Consider the cell shown in Figure\u00a04, where\r\n<p style=\"text-align: center;\">[latex]\\text{Pt}\\left(s\\right)\\mid {\\text{H}}_{2}\\left(g,\\text{1 atm}\\right)\\mid {\\text{H}}^{\\text{+}}\\left(aq\\text{, 1}M\\right)\\parallel {\\text{Ag}}^{\\text{+}}\\left(aq\\text{, 1}M\\right)\\mid \\text{Ag}\\left(s\\right)[\/latex]<\/p>\r\nElectrons flow from left to right, and the reactions are\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{rl}{}\\text{anode (oxidation):}&amp;{\\text{H}}_{2}\\left(g\\right)\\longrightarrow {\\text{2H}}^{\\text{+}}\\left(aq\\right)+{\\text{2e}}^{-}\\\\ \\text{cathode (reduction):}&amp;2{\\text{Ag}}^{\\text{+}}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{2Ag}\\left(s\\right)\\\\ \\\\ \\text{overall:}&amp;2{\\text{Ag}}^{\\text{+}}\\left(aq\\right)+{\\text{H}}_{2}\\left(g\\right)\\longrightarrow {\\text{2H}}^{\\text{+}}\\left(aq\\right)+\\text{2Ag}\\left(s\\right)\\end{array}[\/latex]<\/p>\r\nThe standard reduction potential can be determined by subtracting the standard reduction potential for the reaction occurring at the anode from the standard reduction potential for the reaction occurring at the cathode. The minus sign is needed because oxidation is the reverse of reduction.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{rllll}{E}_{\\text{cell}}^{\\circ }&amp;=&amp;{E}_{\\text{cathode}}^{\\circ }-{E}_{\\text{anode}}^{\\circ }\\\\\\text{+0.80 V}&amp;=&amp;{E}_{{\\text{Ag}}^{\\text{+}}\\text{\/Ag}}^{\\circ }-{E}_{{\\text{H}}^{\\text{+}}{\\text{\/H}}_{2}}^{\\circ }\\\\{}&amp;=&amp;{E}_{{\\text{Ag}}^{\\text{+}}\\text{\/Ag}}^{\\circ }-0&amp;=&amp;{E}_{{\\text{Ag}}^{\\text{+}}\\text{\/Ag}}^{\\circ }\\end{array}[\/latex]<\/p>\r\nIt is important to note that the potential is <em>not<\/em> doubled for the cathode reaction.\r\n\r\nThe SHE is rather dangerous and rarely used in the laboratory. Its main significance is that it established the zero for standard reduction potentials. Once determined, standard reduction potentials can be used to determine the <b>standard cell potential<\/b>, [latex]{E}_{\\text{cell}}^{\\circ }[\/latex], for any cell. For example, for the cell shown in Figure\u00a01, [latex]\\text{Cu}\\left(s\\right)\\mid {\\text{Cu}}^{2+}\\left(aq,1M\\right)\\parallel {\\text{Ag}}^{\\text{+}}\\left(aq,1M\\right)\\mid \\text{Ag}\\left(s\\right)[\/latex].\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{rl}{}\\text{anode (oxidation):}&amp;\\text{Cu}\\left(s\\right)\\longrightarrow {\\text{Cu}}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\\\ \\text{cathode (reduction):}&amp;2{\\text{Ag}}^{\\text{+}}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{2Ag}\\left(s\\right)\\\\ \\\\ \\text{overall:}&amp;\\text{Cu}\\left(s\\right)+{\\text{2Ag}}^{\\text{+}}\\left(aq\\right)\\longrightarrow {\\text{Cu}}^{2+}\\left(aq\\right)+\\text{2Ag}\\left(s\\right)\\end{array}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]{E}_{\\text{cell}}^{\\circ }={E}_{\\text{cathode}}^{\\circ }-{E}_{\\text{anode}}^{\\circ }={E}_{{\\text{Ag}}^{\\text{+}}\\text{\/Ag}}^{\\circ }-{E}_{{\\text{Cu}}^{2+}\\text{\/Cu}}^{\\circ }=\\text{0.80 V}-\\text{0.34 V}=0.4\\text{6 V}[\/latex]<\/p>\r\nAgain, note that when calculating [latex]{E}_{\\text{cell}}^{\\circ }[\/latex], standard reduction potentials always remain the same even when a half-reaction is multiplied by a factor. Standard reduction potentials for selected reduction reactions are shown in Table\u00a01. A more complete list is provided in <a class=\"target-chapter\" href=\".\/chapter\/standard-electrode-half-cell-potentials\/\" target=\"_blank\">Standard Electrode (Half-Cell) Potentials<\/a>.\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"701\"]<img class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/05\/23214140\/CNX_Chem_17_03_GalvanAg.jpg\" alt=\"This figure contains a diagram of an electrochemical cell. Two beakers are shown. Each is just over half full. The beaker on the left contains a clear, colorless solution which is labeled \u201cH N O subscript 3 ( a q ).\u201d The beaker on the right contains a clear, colorless solution which is labeled \u201cA g N O subscript 3 ( a q ).\u201d A glass tube in the shape of an inverted U connects the two beakers at the center of the diagram and is labeled \u201cSalt bridge.\u201d The tube contents are colorless. The ends of the tubes are beneath the surface of the solutions in the beakers and a small grey plug is present at each end of the tube. The label \u201c2 N a superscript plus\u201d appears on the upper right portion of the tube. A curved arrow extends from this label down and to the right. The label \u201c2 N O subscript 3 superscript negative\u201d appears on the upper left portion of the tube. A curved arrow extends from this label down and to the left. The beaker on the left has a glass tube partially submerged in the liquid. Bubbles are rising from the grey square, labeled \u201cSHE anode\u201d at the bottom of the tube. A curved arrow points up to the right. The labels \u201c2 H superscript plus\u201d and \u201c2 N O subscript 3 superscript negative\u201d appear on the liquid in the beaker. A black wire extends from the grey square up the interior of the tube through a small port at the top to a rectangle with a digital readout of \u201cpositive 0.80 V\u201d which is labeled \u201cVoltmeter.\u201d A second small port extends out the top of the tube to the left. An arrow points to the port opening from the left. The base of this arrow is labeled \u201cH subscript 2 ( g ).\u201d The beaker on the right has a silver strip that is labeled \u201cA g cathode.\u201d A wire extends from the top of this strip to the voltmeter. An arrow points toward the voltmeter from the left which is labeled \u201ce superscript negative flow.\u201d Similarly, an arrow points away from the voltmeter to the right. The solution in the beaker on the right has the labels \u201cN O subscript 3 superscript negative\u201d and \u201cA g superscript plus\u201d on the solution. A curved arrow extends from the A g superscript plus label to the A g cathode. Below the left beaker at the bottom of the diagram is the label \u201cOxidation half-reaction: H subscript 2 ( g ) right pointing arrow 2 H superscript plus ( a q ) plus 2 e superscript negative.\u201d Below the right beaker at the bottom of the diagram is the label \u201cReduction half-reaction: 2 A g superscript plus ( a q ) right pointing arrow 2 A g ( s ).\u201d\" width=\"701\" height=\"521\" data-media-type=\"image\/jpeg\" \/> Figure\u00a04. A galvanic cell can be used to determine the standard reduction potential of Ag<sup>+<\/sup>. The SHE on the left is the anode and assigned a standard reduction potential of zero.[\/caption]\r\n<table id=\"fs-idm42585168\" class=\"span-all\" summary=\"This table has two columns and thirty eight rows. The first row is a header row and it labels each column, \u201cHalf Reaction,\u201d and \u201cE degree symbol ( V ).\u201d Under the \u201cHalf Reaction\u201d column are the following reactions: F subscript 2 ( g ) plus 2 e superscript negative sign yields 2 F superscript negative sign ( a q ); P b O subscript 2 ( g ) plus S O subscript 4 superscript 2 negative sign ( a q ) plus 4 h superscript plus sing ( a q ) plus 2 e superscript negative sign yields P b S O subscript 4 ( g ) plus 2 H subscript 2 O ( l ); M n O subscript 4 superscript negative sing ( a q ) plus 8 H superscript plus sign ( a q ) plus 5 e superscript negative sign yield M n superscript 2 positive sign ( a q ) plus 4 H subscript 2 O ( l ); A u superscript 3 positive sign ( a q ) plus 3 e superscript negative sign yields A u ( s ); C l subscript 2 ( g ) plus 2 e superscript negative sign yields 2 C l superscript negative sign ( a q ); O subscript 2 ( g ) plus 4 h superscript positive sign ( a q ) plus 4 e superscript negative sign yields 2 H subscript 2 O ( l ); P t superscript 2 positive sign ( a q ) plus 2 e superscript negative sign yields P t ( s ); B r subscript 2 ( l ) plus 2 e superscript negative sign yields 2 B r superscript negative sign ( a q ); A g superscript positive sign ( a q ) plus e superscript negative sign yields A g ( s ); H g subscript 2 superscript 2 positive sign ( a q ) plus 2 e superscript negative sing yields F e superscript 2 plus ( a q ); M n O subscript 4 superscript negative sign ( a q ) plus 2 H subscript 2 O ( l ) plus 3 e superscript negative sign yields M n O subscript 2 ( s ) plus 4 O H superscript negative sign ( a q ); I subscript 2 ( g ) plus 2 e superscript negative sign yields 2 I superscript negative sign ( a q ); N i O subscript 2 ( s ) plus 2 H subscript 2 O ( l ) plus 2 e superscript negative sign yields N i ( O H ) subscript 2 ( s ) plus 2 O H superscript negative sign ( a q ); C u superscript 2 positive sign ( a q ) plus 2 e superscript negative sign yields C u ( s ); H g subscript 2 C l subscript 2 ( s ) plus 2 e superscript negative sign yields 2 H g ( l ) plus 2 C l superscript negative sign ( a q ); A g C l ( s ) plus 2 e superscript negative sign yields A g ( s ) plus C l superscript negative sign ( a q ); S n superscript 4 positive sign ( a q ) plus 2 e superscript negative sign yields Sn superscript 2 positive sing ( a q ); 2 H superscript positive sign ( a q ) plus 2 e superscript negative sign yields H subscript 2 ( g ); P b superscript 2 positive sign ( a q ) plus 2 e superscript negative sign yields P b ( s ); S n superscript two positive sign ( a q ) plus 2 e superscript negative sing yields S n ( s ); N i superscript 2 positive sign ( a q ) plus 2 e superscript negative sign yields S n ( s ); N I superscript 2 positive sign ( a q ) plus 2 e superscript negative sign yields N I ( s ); C o superscript 2 positive sign ( a q ) plus 2 e superscript negative sign C o ( s ); P b S O subscript 4 ( s ) plus 2 e superscript negative sing yields P b ( s ) plus S O subscript 4 superscript two negative ( a q ); C d superscript 2 positive sign ( a q ) plus 2 e superscript negative sign yields C d ( s ); F e superscript 2 positive sign ( a q ) plus 2 e superscript negative sign yields F e ( s ); C r superscript 3 positive sign ( a q ) plus 3 e superscript negative sing yields C r ( s ); M n superscript 2 positive sign ( a q ) plus 2 e superscript negative sing yields M n ( s ); Z n ( O H ) subscript 2 ( s ) plus 2 e superscript negative sing yields Z n ( s ) plus 2 O H superscript negative sign ( a q ); Z n superscript 2 positive sign ( a q ) plus 2 e superscript negative sign yields Z n ( s ); A l superscript 3 positive sign ( a q ) plus 3 e superscript negative sign yields A l ( s ); M g superscript 2 ( a q ) plus 2 e superscript negative sign yields M g ( s ); N a superscript positive sign ( a q ) plus e superscript negative sign yields N a ( s ); C a superscript 2 positive sign ( a q ) plus 2 e superscript negative sign yields C a ( s ); B a superscript 2 positive sing ( a q ) plus 2 e superscript negative sing yields B a ( s ); K superscript positive sign ( a q ) plus e superscript negative sign yields K ( s ); and L i superscript positive sign ( a q ) plus e superscript negative sign yields L I ( s ). Under the column \u201cE degree symbol ( V )\u201d are the following values: positive 2.866, positive 1.69, positive 1.507, positive 1.498, positive 1.35827, positive 1.229, positive 1.20, positive 1.0873, positive 0.7996, positive 0.7973, positive 0.771, positive 0.558, positive 0.558, positive 0.5355, positive 0.49, positive 0.337, positive 0.26808, positive 0.22233, positive 0.151, 0.00 (which appears bold), negative 0.126, negative 0.1262, negative 0.257, negative 0.28, negative 0.3505, negative 0.4030, negative 0.447, negative 0.744, negative 1.185, negative 1.245, negative 0.7618, negative 1.662, negative 2.372, negative 2.71, ne\">\r\n<thead>\r\n<tr>\r\n<th colspan=\"2\">Table\u00a01. Selected Standard Reduction Potentials at 25 \u00b0C<\/th>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<th>Half-Reaction<\/th>\r\n<th><em>E<\/em>\u00b0 (V)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{F}}_{2}\\left(g\\right)+{\\text{2e}}^{-}\\longrightarrow {\\text{2F}}^{-}\\left(aq\\right)[\/latex]<\/td>\r\n<td>+2.866<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{PbO}}_{2}\\left(s\\right)+{\\text{SO}}_{4}{}^{2-}\\left(aq\\right)+{\\text{4H}}^{\\text{+}}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow {\\text{PbSO}}_{4}\\left(s\\right)+{\\text{2H}}_{2}\\text{O}\\left(l\\right)[\/latex]<\/td>\r\n<td>+1.69<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{MnO}}_{4}{}^{-}\\left(aq\\right)+{\\text{8H}}^{\\text{+}}\\left(aq\\right)+{\\text{5e}}^{-}\\longrightarrow {\\text{Mn}}^{2+}\\left(aq\\right)+{\\text{4H}}_{2}\\text{O}\\left(l\\right)[\/latex]<\/td>\r\n<td>+1.507<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{Au}}^{3+}\\left(aq\\right)+{\\text{3e}}^{-}\\longrightarrow \\text{Au}\\left(s\\right)[\/latex]<\/td>\r\n<td>+1.498<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{Cl}}_{2}\\left(g\\right)+{\\text{2e}}^{-}\\longrightarrow {\\text{2Cl}}^{-}\\left(aq\\right)[\/latex]<\/td>\r\n<td>+1.35827<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{O}}_{2}\\left(g\\right)+{\\text{4H}}^{\\text{+}}\\left(aq\\right)+{\\text{4e}}^{-}\\longrightarrow {\\text{2H}}_{2}\\text{O}\\left(l\\right)[\/latex]<\/td>\r\n<td>+1.229<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{Pt}}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{Pt}\\left(s\\right)[\/latex]<\/td>\r\n<td>+1.20<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{Br}}_{2}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow {\\text{2Br}}^{-}\\left(aq\\right)[\/latex]<\/td>\r\n<td>+1.0873<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{Ag}}^{\\text{+}}\\left(aq\\right)+{\\text{e}}^{-}\\longrightarrow \\text{Ag}\\left(s\\right)[\/latex]<\/td>\r\n<td>+0.7996<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{Hg}}_{2}{}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{2Hg}\\left(l\\right)[\/latex]<\/td>\r\n<td>+0.7973<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{Fe}}^{3+}\\left(aq\\right)+{\\text{e}}^{-}\\longrightarrow {\\text{Fe}}^{2+}\\left(aq\\right)[\/latex]<\/td>\r\n<td>+0.771<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{MnO}}_{4}{}^{-}\\left(aq\\right)+{\\text{2H}}_{2}\\text{O}\\left(l\\right)+{\\text{3e}}^{-}\\longrightarrow {\\text{MnO}}_{2}\\left(s\\right)+{\\text{4OH}}^{-}\\left(aq\\right)[\/latex]<\/td>\r\n<td>+0.558<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{I}}_{2}\\left(s\\right)+{\\text{2e}}^{-}\\longrightarrow {\\text{2I}}^{-}\\left(aq\\right)[\/latex]<\/td>\r\n<td>+0.5355<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{NiO}}_{2}\\left(s\\right)+{\\text{2H}}_{2}\\text{O}\\left(l\\right)+{\\text{2e}}^{-}\\longrightarrow {\\text{Ni(OH)}}_{2}\\left(s\\right)+{\\text{2OH}}^{-}\\left(aq\\right)[\/latex]<\/td>\r\n<td>+0.49<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{Cu}}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{Cu}\\left(s\\right)[\/latex]<\/td>\r\n<td>+0.337<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{Hg}}_{2}{\\text{Cl}}_{2}\\left(s\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{2Hg}\\left(l\\right)+{\\text{2Cl}}^{-}\\left(aq\\right)[\/latex]<\/td>\r\n<td>+0.26808<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]\\text{AgCl}\\left(s\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{Ag}\\left(s\\right)+{\\text{Cl}}^{-}\\left(aq\\right)[\/latex]<\/td>\r\n<td>+0.22233<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{Sn}}^{4+}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow {\\text{Sn}}^{2+}\\left(aq\\right)[\/latex]<\/td>\r\n<td>+0.151<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{2H}}^{\\text{+}}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow {\\text{H}}_{2}\\left(g\\right)[\/latex]<\/td>\r\n<td>0.00<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{Pb}}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{Pb}\\left(s\\right)[\/latex]<\/td>\r\n<td>\u22120.126<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{Sn}}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{Sn}\\left(s\\right)[\/latex]<\/td>\r\n<td>\u22120.1262<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{Ni}}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{Ni}\\left(s\\right)[\/latex]<\/td>\r\n<td>\u22120.257<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{Co}}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{Co}\\left(s\\right)[\/latex]<\/td>\r\n<td>\u22120.28<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{PbSO}}_{4}\\left(s\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{Pb}\\left(s\\right)+{\\text{SO}}_{4}{}^{2-}\\left(aq\\right)[\/latex]<\/td>\r\n<td>\u22120.3505<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{Cd}}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{Cd}\\left(s\\right)[\/latex]<\/td>\r\n<td>\u22120.4030<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{Fe}}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{Fe}\\left(s\\right)[\/latex]<\/td>\r\n<td>\u22120.447<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{Cr}}^{3+}\\left(aq\\right)+{\\text{3e}}^{-}\\longrightarrow \\text{Cr}\\left(s\\right)[\/latex]<\/td>\r\n<td>\u22120.744<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{Mn}}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{Mn}\\left(s\\right)[\/latex]<\/td>\r\n<td>\u22121.185<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{Zn(OH)}}_{2}\\left(s\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{Zn}\\left(s\\right)+{\\text{2OH}}^{-}\\left(aq\\right)[\/latex]<\/td>\r\n<td>\u22121.245<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{Zn}}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{Zn}\\left(s\\right)[\/latex]<\/td>\r\n<td>\u22120.7618<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{Al}}^{3+}\\left(aq\\right)+{\\text{3e}}^{-}\\longrightarrow \\text{Al}\\left(s\\right)[\/latex]<\/td>\r\n<td>\u22121.662<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{Mg}}^{2}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{Mg}\\left(s\\right)[\/latex]<\/td>\r\n<td>\u22122.372<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{Na}}^{\\text{+}}\\left(aq\\right)+{\\text{e}}^{-}\\longrightarrow \\text{Na}\\left(s\\right)[\/latex]<\/td>\r\n<td>\u22122.71<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{Ca}}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{Ca}\\left(s\\right)[\/latex]<\/td>\r\n<td>\u22122.868<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{Ba}}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{Ba}\\left(s\\right)[\/latex]<\/td>\r\n<td>\u22122.912<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{K}}^{\\text{+}}\\left(aq\\right)+{\\text{e}}^{-}\\longrightarrow \\text{K}\\left(s\\right)[\/latex]<\/td>\r\n<td>\u22122.931<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]{\\text{Li}}^{\\text{+}}\\left(aq\\right)+{\\text{e}}^{-}\\longrightarrow \\text{Li}\\left(s\\right)[\/latex]<\/td>\r\n<td>\u22123.04<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nTables like this make it possible to determine the standard cell potential for many oxidation-reduction reactions.\r\n<div class=\"textbox examples\">\r\n<h3>Example 1:\u00a0Cell Potentials from Standard Reduction Potentials<\/h3>\r\nWhat is the standard cell potential for a galvanic cell that consists of Au<sup>3+<\/sup>\/Au and Ni<sup>2+<\/sup>\/Ni half-cells? Identify the oxidizing and reducing agents.\r\n[reveal-answer q=\"735792\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"735792\"]\r\n\r\nUsing Table\u00a01, the reactions involved in the galvanic cell, both written as reductions, are\r\n<p style=\"text-align: center;\">[latex]{\\text{Au}}^{3+}\\left(aq\\right)+3{\\text{e}}^{-}\\longrightarrow \\text{Au}\\left(s\\right)\\,\\,\\,\\,\\,\\,\\,{E}_{{\\text{Au}}^{3+}\\text{\/Au}}^{\\circ }=\\text{+1.498 V}[\/latex]\r\n[latex]{\\text{Ni}}^{2+}\\left(aq\\right)+2{\\text{e}}^{-}\\longrightarrow \\text{Ni}\\left(s\\right)\\,\\,\\,\\,\\,\\,\\,{E}_{{\\text{Ni}}^{2+}\\text{\/Ni}}^{\\circ }=-\\text{0.257 V}[\/latex]<\/p>\r\nGalvanic cells have positive cell potentials, and all the reduction reactions are reversible. The reaction at the anode will be the half-reaction with the smaller or more negative standard reduction potential. Reversing the reaction at the anode (to show the oxidation) but <em>not<\/em> its standard reduction potential gives:\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{rl}{}\\text{Anode (oxidation):}&amp;\\text{Ni}\\left(s\\right)\\longrightarrow {\\text{Ni}}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\,\\,\\,\\,\\,\\,\\,{E}_{\\text{anode}}^{\\circ }={E}_{{\\text{Ni}}^{2+}\\text{\/Ni}}^{\\circ }=-\\text{0.257 V}\\\\ \\text{Cathode (reduction):}&amp;\\text{Au}^{3+}\\left(aq\\right)+{\\text{3e}}^{-}\\longrightarrow \\text{Au}\\left(s\\right)\\,\\,\\,\\,\\,\\,\\,{E}_{\\text{cathode}}^{\\circ }={E}_{{\\text{Au}}^{3+}\\text{\/Au}}^{\\circ }=+1.498 V\\end{array}[\/latex]<\/p>\r\nThe least common factor is six, so the overall reaction is\r\n<p style=\"text-align: center;\">[latex]\\text{3Ni}\\left(s\\right)+{\\text{2Au}}^{3+}\\left(aq\\right)\\longrightarrow {\\text{3Ni}}^{2+}\\left(aq\\right)+\\text{2Au}\\left(s\\right)[\/latex]<\/p>\r\nThe reduction potentials are <em>not<\/em> scaled by the stoichiometric coefficients when calculating the cell potential, and the unmodified standard reduction potentials must be used.\r\n<p style=\"text-align: center;\">[latex]{E}_{\\text{cell}}^{\\circ }={E}_{\\text{cathode}}^{\\circ }-{E}_{\\text{anode}}^{\\circ }=\\text{1.498 V}-\\left(-0.2\\text{57 V}\\right)=1.7\\text{55 V}[\/latex]<\/p>\r\nFrom the half-reactions, Ni is oxidized, so it is the reducing agent, and Au<sup>3+<\/sup> is reduced, so it is the oxidizing agent.\r\n\r\n[\/hidden-answer]\r\n<h4 id=\"fs-idp264094080\">Check Your Learning<\/h4>\r\nA galvanic cell consists of a Mg electrode in 1 <em>M<\/em> Mg(NO<sub>3<\/sub>)<sub>2<\/sub> solution and a Ag electrode in 1 <em>M<\/em> AgNO<sub>3<\/sub> solution. Calculate the standard cell potential at 25 \u00b0C.\r\n[reveal-answer q=\"206910\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"206910\"][latex]\\text{Mg}\\left(s\\right)+2{\\text{Ag}}^{\\text{+}}\\left(aq\\right)\\longrightarrow {\\text{Mg}}^{2+}\\left(aq\\right)+2\\text{Ag}\\left(s\\right)\\,\\,\\,\\,\\,\\,\\,{E}_{\\text{cell}}^{\\circ }=0.7\\text{996 V}-\\left(-2.3\\text{72 V}\\right)=3.17\\text{2 V}[\/latex][\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Key Concepts and Summary<\/h3>\r\nAssigning the potential of the standard hydrogen electrode (SHE) as zero volts allows the determination of standard reduction potentials, <em>E\u00b0<\/em>, for half-reactions in electrochemical cells. As the name implies, standard reduction potentials use standard states (1 bar or 1 atm for gases; 1 <em>M<\/em> for solutes, often at 298.15 K) and are written as reductions (where electrons appear on the left side of the equation). The reduction reactions are reversible, so standard cell potentials can be calculated by subtracting the standard reduction potential for the reaction at the anode from the standard reduction for the reaction at the cathode. When calculating the standard cell potential, the standard reduction potentials are <em>not<\/em> scaled by the stoichiometric coefficients in the balanced overall equation.\r\n<h4>Key Equations<\/h4>\r\n<ul>\r\n \t<li>[latex]{E}_{\\text{cell}}^{\\circ }={E}_{\\text{cathode}}^{\\circ }-{E}_{\\text{anode}}^{\\circ }[\/latex]<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Exercises<\/h3>\r\n<ol>\r\n \t<li id=\"fs-idm41082448\">For each reaction listed, determine its standard cell potential at 25 \u00b0C and whether the reaction is spontaneous at standard conditions.\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]\\text{Mg}\\left(s\\right)+{\\text{Ni}}^{2+}\\left(aq\\right)\\longrightarrow {\\text{Mg}}^{2+}\\left(aq\\right)+\\text{Ni}\\left(s\\right)[\/latex]<\/li>\r\n \t<li>[latex]2{\\text{Ag}}^{\\text{+}}\\left(aq\\right)+\\text{Cu}\\left(s\\right)\\longrightarrow {\\text{Cu}}^{2+}\\left(aq\\right)+\\text{2Ag}\\left(s\\right)[\/latex]<\/li>\r\n \t<li>[latex]\\text{Mn}\\left(s\\right)+{\\text{Sn(NO}}_{3}{)}_{2}\\left(aq\\right)\\longrightarrow {\\text{Mn(NO}}_{3}{)}_{2}\\left(aq\\right)+\\text{Sn}\\left(s\\right)[\/latex]<\/li>\r\n \t<li>[latex]3{\\text{Fe(NO}}_{3}{)}_{2}\\left(aq\\right)+{\\text{Au(NO}}_{3}{)}_{3}\\left(aq\\right)\\longrightarrow {\\text{3Fe(NO}}_{3}{)}_{3}\\left(aq\\right)+\\text{Au}\\left(s\\right)[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>For each reaction listed, determine its standard cell potential at 25 \u00b0C and whether the reaction is spontaneous at standard conditions.\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]\\text{Mn}\\left(s\\right)+{\\text{Ni}}^{2+}\\left(aq\\right)\\longrightarrow {\\text{Mn}}^{2+}\\left(aq\\right)+\\text{Ni}\\left(s\\right)[\/latex]<\/li>\r\n \t<li>[latex]3{\\text{Cu}}^{2+}\\left(aq\\right)+\\text{2Al}\\left(s\\right)\\longrightarrow {\\text{2Al}}^{3+}\\left(aq\\right)+\\text{2Cu}\\left(s\\right)[\/latex]<\/li>\r\n \t<li>[latex]\\text{Na}\\left(s\\right)+{\\text{LiNO}}_{3}\\left(aq\\right)\\longrightarrow {\\text{NaNO}}_{3}\\left(aq\\right)+\\text{Li}\\left(s\\right)[\/latex]<\/li>\r\n \t<li>[latex]{\\text{Ca(NO}}_{3}{)}_{2}\\left(aq\\right)+\\text{Ba}\\left(s\\right)\\longrightarrow {\\text{Ba(NO}}_{3}{)}_{2}\\left(aq\\right)+\\text{Ca}\\left(s\\right)[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Determine the overall reaction and its standard cell potential at 25 \u00b0C for this reaction. Is the reaction spontaneous at standard conditions?\r\n[latex]\\text{Cu}\\left(s\\right)\\mid {\\text{Cu}}^{2+}\\left(aq\\right)\\parallel {\\text{Au}}^{3+}\\left(aq\\right)\\mid \\text{Au}\\left(s\\right)[\/latex]<\/li>\r\n \t<li>Determine the overall reaction and its standard cell potential at 25 \u00b0C for the reaction involving the galvanic cell made from a half-cell consisting of a silver electrode in 1 <em>M<\/em> silver nitrate solution and a half-cell consisting of a zinc electrode in 1 <em>M<\/em> zinc nitrate. Is the reaction spontaneous at standard conditions?<\/li>\r\n \t<li>Determine the overall reaction and its standard cell potential at 25 \u00b0C for the reaction involving the galvanic cell in which cadmium metal is oxidized to 1 <em>M<\/em> cadmium(II) ion and a half-cell consisting of an aluminum electrode in 1 <em>M<\/em> aluminum nitrate solution. Is the reaction spontaneous at standard conditions?<\/li>\r\n \t<li>Determine the overall reaction and its standard cell potential at 25 \u00b0C for these reactions. Is the reaction spontaneous at standard conditions? Assume the standard reduction for Br<sub>2<\/sub>(<em>l<\/em>) is the same as for Br<sub>2<\/sub>(<em>aq<\/em>).[latex]\\text{Pt}\\left(s\\right)\\mid {\\text{H}}_{2}\\left(g\\right)\\mid {\\text{H}}^{\\text{+}}\\left(aq\\right)\\parallel {\\text{Br}}_{2}\\left(aq\\right)\\mid {\\text{Br}}^{-}\\left(aq\\right)\\mid \\text{Pt}\\left(s\\right)[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"802553\"]Show Selected Answers[\/reveal-answer]\r\n[hidden-answer a=\"802553\"]\r\n\r\n1. The answers are as follows:\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]{E}_{\\text{cell}}^{\\circ }={E}_{\\text{cathode}}^{\\circ }-{E}_{\\text{anode}}^{\\circ }=-\\text{0.257 V}-\\left(-\\text{2.372 V}\\right)=\\text{+2.115 V (spontaneous)}[\/latex]<\/li>\r\n \t<li>[latex]{E}_{\\text{cell}}^{\\circ }={E}_{\\text{cathode}}^{\\circ }-{E}_{\\text{anode}}^{\\circ }=\\text{0.7996 V}-\\left(\\text{+0.337 V}\\right)=\\text{+0.4626 V (spontaneous)}[\/latex]<\/li>\r\n \t<li>[latex]{E}_{\\text{cell}}^{\\circ }={E}_{\\text{cathode}}^{\\circ }-{E}_{\\text{anode}}^{\\circ }=-\\text{0.1262 V}-\\left(-\\text{1.185 V}\\right)=\\text{+1.0589 V (spontaneous)}[\/latex]<\/li>\r\n \t<li>[latex]{E}_{\\text{cell}}^{\\circ }={E}_{\\text{cathode}}^{\\circ }-{E}_{\\text{anode}}^{\\circ }=\\text{1.498 V}-\\left(\\text{+0.771 V}\\right)=\\text{+0.727 V (spontaneous)}[\/latex]<\/li>\r\n<\/ol>\r\n3. The reaction occurs as follows:\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{rl}\\text{anode:}&amp;3\\times \\left(\\text{Cu}\\left(s\\right)\\longrightarrow {\\text{Cu}}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\right){E}_{{\\text{Cu}}^{2+}\\text{\/Cu}}^{\\circ }\\\\ \\text{cathode:}&amp;2\\times \\left({\\text{Au}}^{3+}\\left(aq\\right)+{\\text{3e}}^{-}\\longrightarrow \\text{Au}\\left(s\\right)\\right)\\\\ \\\\ \\text{overall:}&amp;^3\\text{Cu}\\left(s\\right)+{\\text{2Au}}^{3+}\\left(aq\\right)\\longrightarrow {\\text{3Cu}}^{2+}\\left(aq\\right)+\\text{2Au}\\left(s\\right)\\end{array}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]{E}_{\\text{cell}}^{\\circ }={E}_{\\text{cathode}}^{\\circ }-{E}_{\\text{anode}}^{\\circ }=1.4\\text{98 V}-\\left(\\text{+0.34 V}\\right)=\\text{+1.16 V}\\left(\\text{spontaneous}\\right)[\/latex]<\/p>\r\n5.\u00a0Oxidation occurs at the anode and reduction at the cathode:\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{rl}{}\\text{anode:}&amp;3\\times \\left(\\text{Cd}\\left(s\\right)\\longrightarrow {\\text{Cd}}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\right){E}_{{\\text{Cd}}^{2+}\\text{\/Cd}}^{\\circ }=-\\text{0.4030 V}\\\\ \\text{cathode:}&amp;2\\times \\left({\\text{Al}}^{3+}\\left(aq\\right)+{\\text{3e}}^{-}\\longrightarrow \\text{Al}\\left(s\\right)\\right){E}_{{\\text{Al}}^{3+}\\text{\/Al}}^{\\circ }=-\\text{1.662 V}\\\\ \\\\ \\text{overall:}&amp;3\\text{Cd}\\left(s\\right)+{\\text{2Al}}^{3+}\\left(aq\\right)\\longrightarrow {\\text{3Cd}}^{2+}\\left(aq\\right)+\\text{2Al}\\left(s\\right)\\end{array}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]{E}_{\\text{cell}}^{\\circ }={E}_{\\text{cathode}}^{\\circ }-{E}_{\\text{anode}}^{\\circ }=-\\text{1.662 V}-\\left(-\\text{0.4030 V}\\right)=-\\text{1.259 V}\\left(\\text{nonspontaneous}\\right)[\/latex]<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<h2>Glossary<\/h2>\r\n<b>standard cell potential [latex]\\left({E}_{\\text{cell}}^{\\circ }\\right)[\/latex]: <\/b>the cell potential when all reactants and products are in their standard states (1 bar or 1 atm or gases; 1 <em>M<\/em> for solutes), usually at 298.15 K; can be calculated by subtracting the standard reduction potential for the half-reaction at the anode from the standard reduction potential for the half-reaction occurring at the cathode\r\n\r\n<b>standard hydrogen electrode (SHE): <\/b>the electrode consists of hydrogen gas bubbling through hydrochloric acid over an inert platinum electrode whose reduction at standard conditions is assigned a value of 0 V; the reference point for standard reduction potentials\r\n\r\n<b>standard reduction potential (<em>E<\/em>\u00b0): <\/b>the value of the reduction under standard conditions (1 bar or 1 atm for gases; 1 <em>M<\/em> for solutes) usually at 298.15 K; tabulated values used to calculate standard cell potentials","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<p>By the end of this module, you will be able to:<\/p>\n<ul>\n<li>Determine standard cell potentials for oxidation-reduction reactions<\/li>\n<li>Use standard reduction potentials to determine the better oxidizing or reducing agent from among several possible choices<\/li>\n<\/ul>\n<\/div>\n<div style=\"width: 710px\" 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\/05\/23214133\/CNX_Chem_17_02_Galvanicel.jpg\" alt=\"This figure contains a diagram of an electrochemical cell. Two beakers are shown. Each is just over half full. The beaker on the left contains a blue solution and is labeled below as \u201c1 M solution of copper (II) nitrate ( C u ( N O subscript 3 ) subscript 2 ).\u201d The beaker on the right contains a colorless solution and is labeled below as \u201c1 M solution of silver nitrate ( A g N O subscript 3 ).\u201d A glass tube in the shape of an inverted U connects the two beakers at the center of the diagram. The tube contents are colorless. The ends of the tubes are beneath the surface of the solutions in the beakers and a small grey plug is present at each end of the tube. The plug in the left beaker is labeled \u201cPorous plug.\u201d At the center of the diagram, the tube is labeled \u201cSalt bridge ( N a N O subscript 3 ). Each beaker shows a metal strip partially submerged in the liquid. The beaker on the left has an orange brown strip that is labeled \u201cC u anode negative\u201d at the top. The beaker on the right has a silver strip that is labeled \u201cA g cathode positive\u201d at the top. A wire extends from the top of each of these strips to a rectangular digital readout indicating a reading of positive 0.46 V that is labeled \u201cVoltmeter.\u201d An arrow points toward the voltmeter from the left which is labeled \u201cFlow of electrons.\u201d Similarly, an arrow points away from the voltmeter to the right which is also labeled \u201cFlow of electrons.\u201d A curved arrow extends from the C u strip into the surrounding solution. The tip of this arrow is labeled \u201cC u superscript 2 plus.\u201d A curved arrow extends from the salt bridge into the beaker on the left into the blue solution. The tip of this arrow is labeled \u201cN O subscript 3 superscript negative.\u201d A curved arrow extends from the solution in the beaker on the right to the A g strip. The base of this arrow is labeled \u201cA g superscript plus.\u201d A curved arrow extends from the colorless solution to salt bridge in the beaker on the right. The base of this arrow is labeled \u201cN O subscript 3 superscript negative.\u201d Just right of the center of the salt bridge on the tube an arrow is placed on the salt bridge that points down and to the right. The base of this arrow is labeled \u201cN a superscript plus.\u201d Just above this region of the tube appears the label \u201cFlow of cations.\u201d Just left of the center of the salt bridge on the tube an arrow is placed on the salt bridge that points down and to the left. The base of this arrow is labeled \u201cN O subscript 3 superscript negative.\u201d Just above this region of the tube appears the label \u201cFlow of anions.\u201d\" width=\"700\" height=\"696\" data-media-type=\"image\/jpeg\" \/><\/p>\n<p class=\"wp-caption-text\">Figure\u00a01. In this standard galvanic cell, the half-cells are separated; electrons can flow through an external wire and become available to do electrical work.<\/p>\n<\/div>\n<p>The cell potential in Figure\u00a01\u00a0(+0.46 V) results from the difference in the electrical potentials for each electrode. While it is impossible to determine the electrical potential of a single electrode, we can assign an electrode the value of zero and then use it as a reference. The electrode chosen as the zero is shown in Figure\u00a02\u00a0and is called the <b>standard hydrogen electrode (SHE)<\/b>. The SHE consists of 1 atm of hydrogen gas bubbled through a 1 M HCl solution, usually at room temperature. Platinum, which is chemically inert, is used as the electrode. The reduction half-reaction chosen as the reference is<\/p>\n<p style=\"text-align: center;\">[latex]2\\text{H}^{+}\\left(aq, 1M\\right)+2\\text{e}^{-}\\rightleftharpoons\\text{H}_{2}\\left(g,1\\text{ atm}\\right)\\,\\,\\,\\,\\,\\,\\,E^{\\circ}=0\\text{ V}[\/latex]<\/p>\n<p><em>E<\/em>\u00b0 is the standard reduction potential. The superscript \u201c\u00b0\u201d on the <em>E<\/em> denotes standard conditions (1 bar or 1 atm for gases, 1 <em>M<\/em> for solutes). The voltage is defined as zero for all temperatures.<\/p>\n<div style=\"width: 711px\" 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\/05\/23214137\/CNX_Chem_17_03_SHE.jpg\" alt=\"The figure shows a beaker just over half full of a blue liquid. A glass tube is partially submerged in the liquid. Bubbles, which are labeled \u201cH subscript 2 ( g )\u201d are rising from the dark grey square, labeled \u201cP t electrode\u201d at the bottom of the tube. A curved arrow points up to the right, indicating the direction of the bubbles. A black wire which is labeled \u201cP t wire\u201d extends from the dark grey square up the interior of the tube through a small port at the top. A second small port extends out the top of the tube to the left. An arrow points to the port opening from the left. The base of this arrow is labeled \u201cH subscript 2 ( g ) at 1 a t m.\u201d A light grey arrow points to a diagram in a circle at the right that illustrates the surface of the P t electrode in a magnified view. P t atoms are illustrated as a uniform cluster of grey spheres which are labeled \u201cP t electrode atoms.\u201d On the grey atom surface, the label \u201ce superscript negative\u201d is shown 4 times in a nearly even vertical distribution to show electrons on the P t surface. A curved arrow extends from a white sphere labeled \u201cH superscript plus\u201d at the right of the P t atoms to the uppermost electron shown. Just below, a straight arrow extends from the P t surface to the right to a pair of linked white spheres which are labeled \u201cH subscript 2.\u201d A curved arrow extends from a second white sphere labeled \u201cH superscript plus\u201d at the right of the P t atoms to the second electron shown. A curved arrow extends from the third electron on the P t surface to the right to a white sphere labeled \u201cH superscript plus.\u201d Just below, an arrow points left from a pair of linked white spheres which are labeled \u201cH subscript 2\u201d to the P t surface. A curved arrow extends from the fourth electron on the P t surface to the right to a white sphere labeled \u201cH superscript plus.\u201d Beneath this atomic view is the label \u201cHalf-reaction at P t surface: 2 H superscript plus ( a q, 1 M ) plus 2 e superscript negative right pointing arrow H subscript 2 ( g, 1 a t m ).\u201d\" width=\"701\" height=\"414\" data-media-type=\"image\/jpeg\" \/><\/p>\n<p class=\"wp-caption-text\">Figure\u00a02. Hydrogen gas at 1 atm is bubbled through 1 <em>M<\/em> HCl solution. Platinum, which is inert to the action of the 1 <em>M<\/em> HCl, is used as the electrode. Electrons on the surface of the electrode combine with H<sup>+<\/sup> in solution to produce hydrogen gas.<\/p>\n<\/div>\n<p>A galvanic cell consisting of a SHE and Cu<sup>2+<\/sup>\/Cu half-cell can be used to determine the standard reduction potential for Cu<sup>2+<\/sup> (Figure\u00a03). In cell notation, the reaction is<\/p>\n<p style=\"text-align: center;\">[latex]\\text{Pt}\\left(s\\right)\\mid {\\text{H}}_{2}\\left(g,\\text{1 atm}\\right)\\mid {\\text{H}}^{\\text{+}}\\left(aq,1M\\right)\\parallel {\\text{Cu}}^{2+}\\left(aq,1M\\right)\\mid \\text{Cu}\\left(s\\right)[\/latex]<\/p>\n<p>Electrons flow from the anode to the cathode. The reactions, which are reversible, are<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{rl}\\text{Anode (oxidation):}&\\text{H}_{2}\\left(g\\right)\\longrightarrow2\\text{H}^{+}\\left(aq\\right)+2\\text{e}^{-}\\\\ \\text{Cathode (reduction):}&\\text{Cu}^{2+}\\left(aq\\right)+2\\text{e}^{-}\\longrightarrow\\text{Cu}\\left(s\\right)\\\\ \\\\ \\text{Overall:}&\\text{Cu}^{2+}\\left(aq\\right)+\\text{H}_{2}\\left(g\\right)\\longrightarrow2\\text{H}^{+}\\left(aq\\right)+\\text{Cu}\\left(s\\right)\\end{array}[\/latex]<\/p>\n<p>The standard reduction potential can be determined by subtracting the standard reduction potential for the reaction occurring at the anode from the standard reduction potential for the reaction occurring at the cathode. The minus sign is necessary because oxidation is the reverse of reduction.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{rllll}{}{E}_{\\text{cell}}^{\\circ }&=&{E}_{\\text{cathode}}^{\\circ }-{E}_{\\text{anode}}^{\\circ }\\\\\\text{+0.34 V}&=&{E}_{{\\text{Cu}}^{2+}\\text{\/Cu}}^{\\circ }-{E}_{{\\text{H}}^{\\text{+}}{\\text{\/H}}_{2}}^{\\circ }\\\\{}&=&{E}_{{\\text{Cu}}^{2+}\\text{\/Cu}}^{\\circ }-0&=&{E}_{{\\text{Cu}}^{2+}\\text{\/Cu}}^{\\circ }\\end{array}[\/latex]<\/p>\n<div style=\"width: 710px\" 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\/05\/23214139\/CNX_Chem_17_03_GalvanCu.jpg\" alt=\"This figure contains a diagram of an electrochemical cell. Two beakers are shown. Each is just over half full. The beaker on the left contains a clear, colorless solution and is labeled below as \u201c1 M H superscript plus.\u201d The beaker on the right contains a blue solution and is labeled below as \u201c1 M C u superscript 2 plus.\u201d A glass tube in the shape of an inverted U connects the two beakers at the center of the diagram. The tube contents are colorless. The ends of the tubes are beneath the surface of the solutions in the beakers and a small grey plug is present at each end of the tube. The beaker on the left has a glass tube partially submersed in the liquid. Bubbles are rising from the grey square, labeled \u201cStandard hydrogen electrode\u201d at the bottom of the tube. A curved arrow points up to the right, indicating the direction of the bubbles. A black wire extends from the grey square up the interior of the tube through a small port at the top to a rectangle with a digital readout of \u201cpositive 0.337 V\u201d which is labeled \u201cVoltmeter.\u201d A second small port extends out the top of the tube to the left. An arrow points to the port opening from the left. The base of this arrow is labeled \u201cH subscript 2 ( g ).\u201d The beaker on the right has an orange-brown strip that is labeled \u201cC u strip\u201d at the top. A wire extends from the top of this strip to the voltmeter. An arrow points toward the voltmeter from the left which is labeled \u201ce superscript negative flow.\u201d Similarly, an arrow points away from the voltmeter to the right. A curved arrow extends from the standard hydrogen electrode in the beaker on the left into the surrounding solution. The tip of this arrow is labeled \u201cH plus.\u201d An arrow points downward from the label \u201ce superscript negative\u201d on the C u strip in the beaker on the right. A second curved arrow extends from another \u201ce superscript negative\u201d label into the solution below toward the label \u201cC u superscript 2 plus\u201d in the solution. A third \u201ce superscript negative\u201d label positioned at the lower left edge of the C u strip has a curved arrow extending from it to the \u201cC u superscript 2 plus\u201d label in the solution. A curved arrow extends from this \u201cC u superscript 2 plus\u201d label to a \u201cC u\u201d label at the lower edge of the C u strip.\" width=\"700\" height=\"608\" data-media-type=\"image\/jpeg\" \/><\/p>\n<p class=\"wp-caption-text\">Figure\u00a03. A galvanic cell can be used to determine the standard reduction potential of Cu2<sup>+<\/sup>.<\/p>\n<\/div>\n<p>Using the SHE as a reference, other standard reduction potentials can be determined. Consider the cell shown in Figure\u00a04, where<\/p>\n<p style=\"text-align: center;\">[latex]\\text{Pt}\\left(s\\right)\\mid {\\text{H}}_{2}\\left(g,\\text{1 atm}\\right)\\mid {\\text{H}}^{\\text{+}}\\left(aq\\text{, 1}M\\right)\\parallel {\\text{Ag}}^{\\text{+}}\\left(aq\\text{, 1}M\\right)\\mid \\text{Ag}\\left(s\\right)[\/latex]<\/p>\n<p>Electrons flow from left to right, and the reactions are<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{rl}{}\\text{anode (oxidation):}&{\\text{H}}_{2}\\left(g\\right)\\longrightarrow {\\text{2H}}^{\\text{+}}\\left(aq\\right)+{\\text{2e}}^{-}\\\\ \\text{cathode (reduction):}&2{\\text{Ag}}^{\\text{+}}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{2Ag}\\left(s\\right)\\\\ \\\\ \\text{overall:}&2{\\text{Ag}}^{\\text{+}}\\left(aq\\right)+{\\text{H}}_{2}\\left(g\\right)\\longrightarrow {\\text{2H}}^{\\text{+}}\\left(aq\\right)+\\text{2Ag}\\left(s\\right)\\end{array}[\/latex]<\/p>\n<p>The standard reduction potential can be determined by subtracting the standard reduction potential for the reaction occurring at the anode from the standard reduction potential for the reaction occurring at the cathode. The minus sign is needed because oxidation is the reverse of reduction.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{rllll}{E}_{\\text{cell}}^{\\circ }&=&{E}_{\\text{cathode}}^{\\circ }-{E}_{\\text{anode}}^{\\circ }\\\\\\text{+0.80 V}&=&{E}_{{\\text{Ag}}^{\\text{+}}\\text{\/Ag}}^{\\circ }-{E}_{{\\text{H}}^{\\text{+}}{\\text{\/H}}_{2}}^{\\circ }\\\\{}&=&{E}_{{\\text{Ag}}^{\\text{+}}\\text{\/Ag}}^{\\circ }-0&=&{E}_{{\\text{Ag}}^{\\text{+}}\\text{\/Ag}}^{\\circ }\\end{array}[\/latex]<\/p>\n<p>It is important to note that the potential is <em>not<\/em> doubled for the cathode reaction.<\/p>\n<p>The SHE is rather dangerous and rarely used in the laboratory. Its main significance is that it established the zero for standard reduction potentials. Once determined, standard reduction potentials can be used to determine the <b>standard cell potential<\/b>, [latex]{E}_{\\text{cell}}^{\\circ }[\/latex], for any cell. For example, for the cell shown in Figure\u00a01, [latex]\\text{Cu}\\left(s\\right)\\mid {\\text{Cu}}^{2+}\\left(aq,1M\\right)\\parallel {\\text{Ag}}^{\\text{+}}\\left(aq,1M\\right)\\mid \\text{Ag}\\left(s\\right)[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{rl}{}\\text{anode (oxidation):}&\\text{Cu}\\left(s\\right)\\longrightarrow {\\text{Cu}}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\\\ \\text{cathode (reduction):}&2{\\text{Ag}}^{\\text{+}}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{2Ag}\\left(s\\right)\\\\ \\\\ \\text{overall:}&\\text{Cu}\\left(s\\right)+{\\text{2Ag}}^{\\text{+}}\\left(aq\\right)\\longrightarrow {\\text{Cu}}^{2+}\\left(aq\\right)+\\text{2Ag}\\left(s\\right)\\end{array}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]{E}_{\\text{cell}}^{\\circ }={E}_{\\text{cathode}}^{\\circ }-{E}_{\\text{anode}}^{\\circ }={E}_{{\\text{Ag}}^{\\text{+}}\\text{\/Ag}}^{\\circ }-{E}_{{\\text{Cu}}^{2+}\\text{\/Cu}}^{\\circ }=\\text{0.80 V}-\\text{0.34 V}=0.4\\text{6 V}[\/latex]<\/p>\n<p>Again, note that when calculating [latex]{E}_{\\text{cell}}^{\\circ }[\/latex], standard reduction potentials always remain the same even when a half-reaction is multiplied by a factor. Standard reduction potentials for selected reduction reactions are shown in Table\u00a01. A more complete list is provided in <a class=\"target-chapter\" href=\".\/chapter\/standard-electrode-half-cell-potentials\/\" target=\"_blank\">Standard Electrode (Half-Cell) Potentials<\/a>.<\/p>\n<div style=\"width: 711px\" 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\/05\/23214140\/CNX_Chem_17_03_GalvanAg.jpg\" alt=\"This figure contains a diagram of an electrochemical cell. Two beakers are shown. Each is just over half full. The beaker on the left contains a clear, colorless solution which is labeled \u201cH N O subscript 3 ( a q ).\u201d The beaker on the right contains a clear, colorless solution which is labeled \u201cA g N O subscript 3 ( a q ).\u201d A glass tube in the shape of an inverted U connects the two beakers at the center of the diagram and is labeled \u201cSalt bridge.\u201d The tube contents are colorless. The ends of the tubes are beneath the surface of the solutions in the beakers and a small grey plug is present at each end of the tube. The label \u201c2 N a superscript plus\u201d appears on the upper right portion of the tube. A curved arrow extends from this label down and to the right. The label \u201c2 N O subscript 3 superscript negative\u201d appears on the upper left portion of the tube. A curved arrow extends from this label down and to the left. The beaker on the left has a glass tube partially submerged in the liquid. Bubbles are rising from the grey square, labeled \u201cSHE anode\u201d at the bottom of the tube. A curved arrow points up to the right. The labels \u201c2 H superscript plus\u201d and \u201c2 N O subscript 3 superscript negative\u201d appear on the liquid in the beaker. A black wire extends from the grey square up the interior of the tube through a small port at the top to a rectangle with a digital readout of \u201cpositive 0.80 V\u201d which is labeled \u201cVoltmeter.\u201d A second small port extends out the top of the tube to the left. An arrow points to the port opening from the left. The base of this arrow is labeled \u201cH subscript 2 ( g ).\u201d The beaker on the right has a silver strip that is labeled \u201cA g cathode.\u201d A wire extends from the top of this strip to the voltmeter. An arrow points toward the voltmeter from the left which is labeled \u201ce superscript negative flow.\u201d Similarly, an arrow points away from the voltmeter to the right. The solution in the beaker on the right has the labels \u201cN O subscript 3 superscript negative\u201d and \u201cA g superscript plus\u201d on the solution. A curved arrow extends from the A g superscript plus label to the A g cathode. Below the left beaker at the bottom of the diagram is the label \u201cOxidation half-reaction: H subscript 2 ( g ) right pointing arrow 2 H superscript plus ( a q ) plus 2 e superscript negative.\u201d Below the right beaker at the bottom of the diagram is the label \u201cReduction half-reaction: 2 A g superscript plus ( a q ) right pointing arrow 2 A g ( s ).\u201d\" width=\"701\" height=\"521\" data-media-type=\"image\/jpeg\" \/><\/p>\n<p class=\"wp-caption-text\">Figure\u00a04. A galvanic cell can be used to determine the standard reduction potential of Ag<sup>+<\/sup>. The SHE on the left is the anode and assigned a standard reduction potential of zero.<\/p>\n<\/div>\n<table id=\"fs-idm42585168\" class=\"span-all\" summary=\"This table has two columns and thirty eight rows. The first row is a header row and it labels each column, \u201cHalf Reaction,\u201d and \u201cE degree symbol ( V ).\u201d Under the \u201cHalf Reaction\u201d column are the following reactions: F subscript 2 ( g ) plus 2 e superscript negative sign yields 2 F superscript negative sign ( a q ); P b O subscript 2 ( g ) plus S O subscript 4 superscript 2 negative sign ( a q ) plus 4 h superscript plus sing ( a q ) plus 2 e superscript negative sign yields P b S O subscript 4 ( g ) plus 2 H subscript 2 O ( l ); M n O subscript 4 superscript negative sing ( a q ) plus 8 H superscript plus sign ( a q ) plus 5 e superscript negative sign yield M n superscript 2 positive sign ( a q ) plus 4 H subscript 2 O ( l ); A u superscript 3 positive sign ( a q ) plus 3 e superscript negative sign yields A u ( s ); C l subscript 2 ( g ) plus 2 e superscript negative sign yields 2 C l superscript negative sign ( a q ); O subscript 2 ( g ) plus 4 h superscript positive sign ( a q ) plus 4 e superscript negative sign yields 2 H subscript 2 O ( l ); P t superscript 2 positive sign ( a q ) plus 2 e superscript negative sign yields P t ( s ); B r subscript 2 ( l ) plus 2 e superscript negative sign yields 2 B r superscript negative sign ( a q ); A g superscript positive sign ( a q ) plus e superscript negative sign yields A g ( s ); H g subscript 2 superscript 2 positive sign ( a q ) plus 2 e superscript negative sing yields F e superscript 2 plus ( a q ); M n O subscript 4 superscript negative sign ( a q ) plus 2 H subscript 2 O ( l ) plus 3 e superscript negative sign yields M n O subscript 2 ( s ) plus 4 O H superscript negative sign ( a q ); I subscript 2 ( g ) plus 2 e superscript negative sign yields 2 I superscript negative sign ( a q ); N i O subscript 2 ( s ) plus 2 H subscript 2 O ( l ) plus 2 e superscript negative sign yields N i ( O H ) subscript 2 ( s ) plus 2 O H superscript negative sign ( a q ); C u superscript 2 positive sign ( a q ) plus 2 e superscript negative sign yields C u ( s ); H g subscript 2 C l subscript 2 ( s ) plus 2 e superscript negative sign yields 2 H g ( l ) plus 2 C l superscript negative sign ( a q ); A g C l ( s ) plus 2 e superscript negative sign yields A g ( s ) plus C l superscript negative sign ( a q ); S n superscript 4 positive sign ( a q ) plus 2 e superscript negative sign yields Sn superscript 2 positive sing ( a q ); 2 H superscript positive sign ( a q ) plus 2 e superscript negative sign yields H subscript 2 ( g ); P b superscript 2 positive sign ( a q ) plus 2 e superscript negative sign yields P b ( s ); S n superscript two positive sign ( a q ) plus 2 e superscript negative sing yields S n ( s ); N i superscript 2 positive sign ( a q ) plus 2 e superscript negative sign yields S n ( s ); N I superscript 2 positive sign ( a q ) plus 2 e superscript negative sign yields N I ( s ); C o superscript 2 positive sign ( a q ) plus 2 e superscript negative sign C o ( s ); P b S O subscript 4 ( s ) plus 2 e superscript negative sing yields P b ( s ) plus S O subscript 4 superscript two negative ( a q ); C d superscript 2 positive sign ( a q ) plus 2 e superscript negative sign yields C d ( s ); F e superscript 2 positive sign ( a q ) plus 2 e superscript negative sign yields F e ( s ); C r superscript 3 positive sign ( a q ) plus 3 e superscript negative sing yields C r ( s ); M n superscript 2 positive sign ( a q ) plus 2 e superscript negative sing yields M n ( s ); Z n ( O H ) subscript 2 ( s ) plus 2 e superscript negative sing yields Z n ( s ) plus 2 O H superscript negative sign ( a q ); Z n superscript 2 positive sign ( a q ) plus 2 e superscript negative sign yields Z n ( s ); A l superscript 3 positive sign ( a q ) plus 3 e superscript negative sign yields A l ( s ); M g superscript 2 ( a q ) plus 2 e superscript negative sign yields M g ( s ); N a superscript positive sign ( a q ) plus e superscript negative sign yields N a ( s ); C a superscript 2 positive sign ( a q ) plus 2 e superscript negative sign yields C a ( s ); B a superscript 2 positive sing ( a q ) plus 2 e superscript negative sing yields B a ( s ); K superscript positive sign ( a q ) plus e superscript negative sign yields K ( s ); and L i superscript positive sign ( a q ) plus e superscript negative sign yields L I ( s ). Under the column \u201cE degree symbol ( V )\u201d are the following values: positive 2.866, positive 1.69, positive 1.507, positive 1.498, positive 1.35827, positive 1.229, positive 1.20, positive 1.0873, positive 0.7996, positive 0.7973, positive 0.771, positive 0.558, positive 0.558, positive 0.5355, positive 0.49, positive 0.337, positive 0.26808, positive 0.22233, positive 0.151, 0.00 (which appears bold), negative 0.126, negative 0.1262, negative 0.257, negative 0.28, negative 0.3505, negative 0.4030, negative 0.447, negative 0.744, negative 1.185, negative 1.245, negative 0.7618, negative 1.662, negative 2.372, negative 2.71, ne\">\n<thead>\n<tr>\n<th colspan=\"2\">Table\u00a01. Selected Standard Reduction Potentials at 25 \u00b0C<\/th>\n<\/tr>\n<tr valign=\"top\">\n<th>Half-Reaction<\/th>\n<th><em>E<\/em>\u00b0 (V)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>[latex]{\\text{F}}_{2}\\left(g\\right)+{\\text{2e}}^{-}\\longrightarrow {\\text{2F}}^{-}\\left(aq\\right)[\/latex]<\/td>\n<td>+2.866<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{PbO}}_{2}\\left(s\\right)+{\\text{SO}}_{4}{}^{2-}\\left(aq\\right)+{\\text{4H}}^{\\text{+}}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow {\\text{PbSO}}_{4}\\left(s\\right)+{\\text{2H}}_{2}\\text{O}\\left(l\\right)[\/latex]<\/td>\n<td>+1.69<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{MnO}}_{4}{}^{-}\\left(aq\\right)+{\\text{8H}}^{\\text{+}}\\left(aq\\right)+{\\text{5e}}^{-}\\longrightarrow {\\text{Mn}}^{2+}\\left(aq\\right)+{\\text{4H}}_{2}\\text{O}\\left(l\\right)[\/latex]<\/td>\n<td>+1.507<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{Au}}^{3+}\\left(aq\\right)+{\\text{3e}}^{-}\\longrightarrow \\text{Au}\\left(s\\right)[\/latex]<\/td>\n<td>+1.498<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{Cl}}_{2}\\left(g\\right)+{\\text{2e}}^{-}\\longrightarrow {\\text{2Cl}}^{-}\\left(aq\\right)[\/latex]<\/td>\n<td>+1.35827<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{O}}_{2}\\left(g\\right)+{\\text{4H}}^{\\text{+}}\\left(aq\\right)+{\\text{4e}}^{-}\\longrightarrow {\\text{2H}}_{2}\\text{O}\\left(l\\right)[\/latex]<\/td>\n<td>+1.229<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{Pt}}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{Pt}\\left(s\\right)[\/latex]<\/td>\n<td>+1.20<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{Br}}_{2}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow {\\text{2Br}}^{-}\\left(aq\\right)[\/latex]<\/td>\n<td>+1.0873<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{Ag}}^{\\text{+}}\\left(aq\\right)+{\\text{e}}^{-}\\longrightarrow \\text{Ag}\\left(s\\right)[\/latex]<\/td>\n<td>+0.7996<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{Hg}}_{2}{}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{2Hg}\\left(l\\right)[\/latex]<\/td>\n<td>+0.7973<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{Fe}}^{3+}\\left(aq\\right)+{\\text{e}}^{-}\\longrightarrow {\\text{Fe}}^{2+}\\left(aq\\right)[\/latex]<\/td>\n<td>+0.771<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{MnO}}_{4}{}^{-}\\left(aq\\right)+{\\text{2H}}_{2}\\text{O}\\left(l\\right)+{\\text{3e}}^{-}\\longrightarrow {\\text{MnO}}_{2}\\left(s\\right)+{\\text{4OH}}^{-}\\left(aq\\right)[\/latex]<\/td>\n<td>+0.558<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{I}}_{2}\\left(s\\right)+{\\text{2e}}^{-}\\longrightarrow {\\text{2I}}^{-}\\left(aq\\right)[\/latex]<\/td>\n<td>+0.5355<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{NiO}}_{2}\\left(s\\right)+{\\text{2H}}_{2}\\text{O}\\left(l\\right)+{\\text{2e}}^{-}\\longrightarrow {\\text{Ni(OH)}}_{2}\\left(s\\right)+{\\text{2OH}}^{-}\\left(aq\\right)[\/latex]<\/td>\n<td>+0.49<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{Cu}}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{Cu}\\left(s\\right)[\/latex]<\/td>\n<td>+0.337<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{Hg}}_{2}{\\text{Cl}}_{2}\\left(s\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{2Hg}\\left(l\\right)+{\\text{2Cl}}^{-}\\left(aq\\right)[\/latex]<\/td>\n<td>+0.26808<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]\\text{AgCl}\\left(s\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{Ag}\\left(s\\right)+{\\text{Cl}}^{-}\\left(aq\\right)[\/latex]<\/td>\n<td>+0.22233<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{Sn}}^{4+}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow {\\text{Sn}}^{2+}\\left(aq\\right)[\/latex]<\/td>\n<td>+0.151<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{2H}}^{\\text{+}}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow {\\text{H}}_{2}\\left(g\\right)[\/latex]<\/td>\n<td>0.00<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{Pb}}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{Pb}\\left(s\\right)[\/latex]<\/td>\n<td>\u22120.126<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{Sn}}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{Sn}\\left(s\\right)[\/latex]<\/td>\n<td>\u22120.1262<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{Ni}}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{Ni}\\left(s\\right)[\/latex]<\/td>\n<td>\u22120.257<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{Co}}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{Co}\\left(s\\right)[\/latex]<\/td>\n<td>\u22120.28<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{PbSO}}_{4}\\left(s\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{Pb}\\left(s\\right)+{\\text{SO}}_{4}{}^{2-}\\left(aq\\right)[\/latex]<\/td>\n<td>\u22120.3505<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{Cd}}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{Cd}\\left(s\\right)[\/latex]<\/td>\n<td>\u22120.4030<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{Fe}}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{Fe}\\left(s\\right)[\/latex]<\/td>\n<td>\u22120.447<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{Cr}}^{3+}\\left(aq\\right)+{\\text{3e}}^{-}\\longrightarrow \\text{Cr}\\left(s\\right)[\/latex]<\/td>\n<td>\u22120.744<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{Mn}}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{Mn}\\left(s\\right)[\/latex]<\/td>\n<td>\u22121.185<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{Zn(OH)}}_{2}\\left(s\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{Zn}\\left(s\\right)+{\\text{2OH}}^{-}\\left(aq\\right)[\/latex]<\/td>\n<td>\u22121.245<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{Zn}}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{Zn}\\left(s\\right)[\/latex]<\/td>\n<td>\u22120.7618<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{Al}}^{3+}\\left(aq\\right)+{\\text{3e}}^{-}\\longrightarrow \\text{Al}\\left(s\\right)[\/latex]<\/td>\n<td>\u22121.662<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{Mg}}^{2}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{Mg}\\left(s\\right)[\/latex]<\/td>\n<td>\u22122.372<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{Na}}^{\\text{+}}\\left(aq\\right)+{\\text{e}}^{-}\\longrightarrow \\text{Na}\\left(s\\right)[\/latex]<\/td>\n<td>\u22122.71<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{Ca}}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{Ca}\\left(s\\right)[\/latex]<\/td>\n<td>\u22122.868<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{Ba}}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\longrightarrow \\text{Ba}\\left(s\\right)[\/latex]<\/td>\n<td>\u22122.912<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{K}}^{\\text{+}}\\left(aq\\right)+{\\text{e}}^{-}\\longrightarrow \\text{K}\\left(s\\right)[\/latex]<\/td>\n<td>\u22122.931<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]{\\text{Li}}^{\\text{+}}\\left(aq\\right)+{\\text{e}}^{-}\\longrightarrow \\text{Li}\\left(s\\right)[\/latex]<\/td>\n<td>\u22123.04<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Tables like this make it possible to determine the standard cell potential for many oxidation-reduction reactions.<\/p>\n<div class=\"textbox examples\">\n<h3>Example 1:\u00a0Cell Potentials from Standard Reduction Potentials<\/h3>\n<p>What is the standard cell potential for a galvanic cell that consists of Au<sup>3+<\/sup>\/Au and Ni<sup>2+<\/sup>\/Ni half-cells? Identify the oxidizing and reducing agents.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q735792\">Show Answer<\/span><\/p>\n<div id=\"q735792\" class=\"hidden-answer\" style=\"display: none\">\n<p>Using Table\u00a01, the reactions involved in the galvanic cell, both written as reductions, are<\/p>\n<p style=\"text-align: center;\">[latex]{\\text{Au}}^{3+}\\left(aq\\right)+3{\\text{e}}^{-}\\longrightarrow \\text{Au}\\left(s\\right)\\,\\,\\,\\,\\,\\,\\,{E}_{{\\text{Au}}^{3+}\\text{\/Au}}^{\\circ }=\\text{+1.498 V}[\/latex]<br \/>\n[latex]{\\text{Ni}}^{2+}\\left(aq\\right)+2{\\text{e}}^{-}\\longrightarrow \\text{Ni}\\left(s\\right)\\,\\,\\,\\,\\,\\,\\,{E}_{{\\text{Ni}}^{2+}\\text{\/Ni}}^{\\circ }=-\\text{0.257 V}[\/latex]<\/p>\n<p>Galvanic cells have positive cell potentials, and all the reduction reactions are reversible. The reaction at the anode will be the half-reaction with the smaller or more negative standard reduction potential. Reversing the reaction at the anode (to show the oxidation) but <em>not<\/em> its standard reduction potential gives:<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{rl}{}\\text{Anode (oxidation):}&\\text{Ni}\\left(s\\right)\\longrightarrow {\\text{Ni}}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\,\\,\\,\\,\\,\\,\\,{E}_{\\text{anode}}^{\\circ }={E}_{{\\text{Ni}}^{2+}\\text{\/Ni}}^{\\circ }=-\\text{0.257 V}\\\\ \\text{Cathode (reduction):}&\\text{Au}^{3+}\\left(aq\\right)+{\\text{3e}}^{-}\\longrightarrow \\text{Au}\\left(s\\right)\\,\\,\\,\\,\\,\\,\\,{E}_{\\text{cathode}}^{\\circ }={E}_{{\\text{Au}}^{3+}\\text{\/Au}}^{\\circ }=+1.498 V\\end{array}[\/latex]<\/p>\n<p>The least common factor is six, so the overall reaction is<\/p>\n<p style=\"text-align: center;\">[latex]\\text{3Ni}\\left(s\\right)+{\\text{2Au}}^{3+}\\left(aq\\right)\\longrightarrow {\\text{3Ni}}^{2+}\\left(aq\\right)+\\text{2Au}\\left(s\\right)[\/latex]<\/p>\n<p>The reduction potentials are <em>not<\/em> scaled by the stoichiometric coefficients when calculating the cell potential, and the unmodified standard reduction potentials must be used.<\/p>\n<p style=\"text-align: center;\">[latex]{E}_{\\text{cell}}^{\\circ }={E}_{\\text{cathode}}^{\\circ }-{E}_{\\text{anode}}^{\\circ }=\\text{1.498 V}-\\left(-0.2\\text{57 V}\\right)=1.7\\text{55 V}[\/latex]<\/p>\n<p>From the half-reactions, Ni is oxidized, so it is the reducing agent, and Au<sup>3+<\/sup> is reduced, so it is the oxidizing agent.<\/p>\n<\/div>\n<\/div>\n<h4 id=\"fs-idp264094080\">Check Your Learning<\/h4>\n<p>A galvanic cell consists of a Mg electrode in 1 <em>M<\/em> Mg(NO<sub>3<\/sub>)<sub>2<\/sub> solution and a Ag electrode in 1 <em>M<\/em> AgNO<sub>3<\/sub> solution. Calculate the standard cell potential at 25 \u00b0C.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q206910\">Show Answer<\/span><\/p>\n<div id=\"q206910\" class=\"hidden-answer\" style=\"display: none\">[latex]\\text{Mg}\\left(s\\right)+2{\\text{Ag}}^{\\text{+}}\\left(aq\\right)\\longrightarrow {\\text{Mg}}^{2+}\\left(aq\\right)+2\\text{Ag}\\left(s\\right)\\,\\,\\,\\,\\,\\,\\,{E}_{\\text{cell}}^{\\circ }=0.7\\text{996 V}-\\left(-2.3\\text{72 V}\\right)=3.17\\text{2 V}[\/latex]<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Key Concepts and Summary<\/h3>\n<p>Assigning the potential of the standard hydrogen electrode (SHE) as zero volts allows the determination of standard reduction potentials, <em>E\u00b0<\/em>, for half-reactions in electrochemical cells. As the name implies, standard reduction potentials use standard states (1 bar or 1 atm for gases; 1 <em>M<\/em> for solutes, often at 298.15 K) and are written as reductions (where electrons appear on the left side of the equation). The reduction reactions are reversible, so standard cell potentials can be calculated by subtracting the standard reduction potential for the reaction at the anode from the standard reduction for the reaction at the cathode. When calculating the standard cell potential, the standard reduction potentials are <em>not<\/em> scaled by the stoichiometric coefficients in the balanced overall equation.<\/p>\n<h4>Key Equations<\/h4>\n<ul>\n<li>[latex]{E}_{\\text{cell}}^{\\circ }={E}_{\\text{cathode}}^{\\circ }-{E}_{\\text{anode}}^{\\circ }[\/latex]<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Exercises<\/h3>\n<ol>\n<li id=\"fs-idm41082448\">For each reaction listed, determine its standard cell potential at 25 \u00b0C and whether the reaction is spontaneous at standard conditions.\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]\\text{Mg}\\left(s\\right)+{\\text{Ni}}^{2+}\\left(aq\\right)\\longrightarrow {\\text{Mg}}^{2+}\\left(aq\\right)+\\text{Ni}\\left(s\\right)[\/latex]<\/li>\n<li>[latex]2{\\text{Ag}}^{\\text{+}}\\left(aq\\right)+\\text{Cu}\\left(s\\right)\\longrightarrow {\\text{Cu}}^{2+}\\left(aq\\right)+\\text{2Ag}\\left(s\\right)[\/latex]<\/li>\n<li>[latex]\\text{Mn}\\left(s\\right)+{\\text{Sn(NO}}_{3}{)}_{2}\\left(aq\\right)\\longrightarrow {\\text{Mn(NO}}_{3}{)}_{2}\\left(aq\\right)+\\text{Sn}\\left(s\\right)[\/latex]<\/li>\n<li>[latex]3{\\text{Fe(NO}}_{3}{)}_{2}\\left(aq\\right)+{\\text{Au(NO}}_{3}{)}_{3}\\left(aq\\right)\\longrightarrow {\\text{3Fe(NO}}_{3}{)}_{3}\\left(aq\\right)+\\text{Au}\\left(s\\right)[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>For each reaction listed, determine its standard cell potential at 25 \u00b0C and whether the reaction is spontaneous at standard conditions.\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]\\text{Mn}\\left(s\\right)+{\\text{Ni}}^{2+}\\left(aq\\right)\\longrightarrow {\\text{Mn}}^{2+}\\left(aq\\right)+\\text{Ni}\\left(s\\right)[\/latex]<\/li>\n<li>[latex]3{\\text{Cu}}^{2+}\\left(aq\\right)+\\text{2Al}\\left(s\\right)\\longrightarrow {\\text{2Al}}^{3+}\\left(aq\\right)+\\text{2Cu}\\left(s\\right)[\/latex]<\/li>\n<li>[latex]\\text{Na}\\left(s\\right)+{\\text{LiNO}}_{3}\\left(aq\\right)\\longrightarrow {\\text{NaNO}}_{3}\\left(aq\\right)+\\text{Li}\\left(s\\right)[\/latex]<\/li>\n<li>[latex]{\\text{Ca(NO}}_{3}{)}_{2}\\left(aq\\right)+\\text{Ba}\\left(s\\right)\\longrightarrow {\\text{Ba(NO}}_{3}{)}_{2}\\left(aq\\right)+\\text{Ca}\\left(s\\right)[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>Determine the overall reaction and its standard cell potential at 25 \u00b0C for this reaction. Is the reaction spontaneous at standard conditions?<br \/>\n[latex]\\text{Cu}\\left(s\\right)\\mid {\\text{Cu}}^{2+}\\left(aq\\right)\\parallel {\\text{Au}}^{3+}\\left(aq\\right)\\mid \\text{Au}\\left(s\\right)[\/latex]<\/li>\n<li>Determine the overall reaction and its standard cell potential at 25 \u00b0C for the reaction involving the galvanic cell made from a half-cell consisting of a silver electrode in 1 <em>M<\/em> silver nitrate solution and a half-cell consisting of a zinc electrode in 1 <em>M<\/em> zinc nitrate. Is the reaction spontaneous at standard conditions?<\/li>\n<li>Determine the overall reaction and its standard cell potential at 25 \u00b0C for the reaction involving the galvanic cell in which cadmium metal is oxidized to 1 <em>M<\/em> cadmium(II) ion and a half-cell consisting of an aluminum electrode in 1 <em>M<\/em> aluminum nitrate solution. Is the reaction spontaneous at standard conditions?<\/li>\n<li>Determine the overall reaction and its standard cell potential at 25 \u00b0C for these reactions. Is the reaction spontaneous at standard conditions? Assume the standard reduction for Br<sub>2<\/sub>(<em>l<\/em>) is the same as for Br<sub>2<\/sub>(<em>aq<\/em>).[latex]\\text{Pt}\\left(s\\right)\\mid {\\text{H}}_{2}\\left(g\\right)\\mid {\\text{H}}^{\\text{+}}\\left(aq\\right)\\parallel {\\text{Br}}_{2}\\left(aq\\right)\\mid {\\text{Br}}^{-}\\left(aq\\right)\\mid \\text{Pt}\\left(s\\right)[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q802553\">Show Selected Answers<\/span><\/p>\n<div id=\"q802553\" class=\"hidden-answer\" style=\"display: none\">\n<p>1. The answers are as follows:<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]{E}_{\\text{cell}}^{\\circ }={E}_{\\text{cathode}}^{\\circ }-{E}_{\\text{anode}}^{\\circ }=-\\text{0.257 V}-\\left(-\\text{2.372 V}\\right)=\\text{+2.115 V (spontaneous)}[\/latex]<\/li>\n<li>[latex]{E}_{\\text{cell}}^{\\circ }={E}_{\\text{cathode}}^{\\circ }-{E}_{\\text{anode}}^{\\circ }=\\text{0.7996 V}-\\left(\\text{+0.337 V}\\right)=\\text{+0.4626 V (spontaneous)}[\/latex]<\/li>\n<li>[latex]{E}_{\\text{cell}}^{\\circ }={E}_{\\text{cathode}}^{\\circ }-{E}_{\\text{anode}}^{\\circ }=-\\text{0.1262 V}-\\left(-\\text{1.185 V}\\right)=\\text{+1.0589 V (spontaneous)}[\/latex]<\/li>\n<li>[latex]{E}_{\\text{cell}}^{\\circ }={E}_{\\text{cathode}}^{\\circ }-{E}_{\\text{anode}}^{\\circ }=\\text{1.498 V}-\\left(\\text{+0.771 V}\\right)=\\text{+0.727 V (spontaneous)}[\/latex]<\/li>\n<\/ol>\n<p>3. The reaction occurs as follows:<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{rl}\\text{anode:}&3\\times \\left(\\text{Cu}\\left(s\\right)\\longrightarrow {\\text{Cu}}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\right){E}_{{\\text{Cu}}^{2+}\\text{\/Cu}}^{\\circ }\\\\ \\text{cathode:}&2\\times \\left({\\text{Au}}^{3+}\\left(aq\\right)+{\\text{3e}}^{-}\\longrightarrow \\text{Au}\\left(s\\right)\\right)\\\\ \\\\ \\text{overall:}&^3\\text{Cu}\\left(s\\right)+{\\text{2Au}}^{3+}\\left(aq\\right)\\longrightarrow {\\text{3Cu}}^{2+}\\left(aq\\right)+\\text{2Au}\\left(s\\right)\\end{array}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]{E}_{\\text{cell}}^{\\circ }={E}_{\\text{cathode}}^{\\circ }-{E}_{\\text{anode}}^{\\circ }=1.4\\text{98 V}-\\left(\\text{+0.34 V}\\right)=\\text{+1.16 V}\\left(\\text{spontaneous}\\right)[\/latex]<\/p>\n<p>5.\u00a0Oxidation occurs at the anode and reduction at the cathode:<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{rl}{}\\text{anode:}&3\\times \\left(\\text{Cd}\\left(s\\right)\\longrightarrow {\\text{Cd}}^{2+}\\left(aq\\right)+{\\text{2e}}^{-}\\right){E}_{{\\text{Cd}}^{2+}\\text{\/Cd}}^{\\circ }=-\\text{0.4030 V}\\\\ \\text{cathode:}&2\\times \\left({\\text{Al}}^{3+}\\left(aq\\right)+{\\text{3e}}^{-}\\longrightarrow \\text{Al}\\left(s\\right)\\right){E}_{{\\text{Al}}^{3+}\\text{\/Al}}^{\\circ }=-\\text{1.662 V}\\\\ \\\\ \\text{overall:}&3\\text{Cd}\\left(s\\right)+{\\text{2Al}}^{3+}\\left(aq\\right)\\longrightarrow {\\text{3Cd}}^{2+}\\left(aq\\right)+\\text{2Al}\\left(s\\right)\\end{array}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]{E}_{\\text{cell}}^{\\circ }={E}_{\\text{cathode}}^{\\circ }-{E}_{\\text{anode}}^{\\circ }=-\\text{1.662 V}-\\left(-\\text{0.4030 V}\\right)=-\\text{1.259 V}\\left(\\text{nonspontaneous}\\right)[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<h2>Glossary<\/h2>\n<p><b>standard cell potential [latex]\\left({E}_{\\text{cell}}^{\\circ }\\right)[\/latex]: <\/b>the cell potential when all reactants and products are in their standard states (1 bar or 1 atm or gases; 1 <em>M<\/em> for solutes), usually at 298.15 K; can be calculated by subtracting the standard reduction potential for the half-reaction at the anode from the standard reduction potential for the half-reaction occurring at the cathode<\/p>\n<p><b>standard hydrogen electrode (SHE): <\/b>the electrode consists of hydrogen gas bubbling through hydrochloric acid over an inert platinum electrode whose reduction at standard conditions is assigned a value of 0 V; the reference point for standard reduction potentials<\/p>\n<p><b>standard reduction potential (<em>E<\/em>\u00b0): <\/b>the value of the reduction under standard conditions (1 bar or 1 atm for gases; 1 <em>M<\/em> for solutes) usually at 298.15 K; tabulated values used to calculate standard cell potentials<\/p>\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-3639\">\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":17,"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-3639","chapter","type-chapter","status-publish","hentry"],"part":2970,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/pressbooks\/v2\/chapters\/3639","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/wp\/v2\/users\/17"}],"version-history":[{"count":10,"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/pressbooks\/v2\/chapters\/3639\/revisions"}],"predecessor-version":[{"id":6067,"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/pressbooks\/v2\/chapters\/3639\/revisions\/6067"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/pressbooks\/v2\/parts\/2970"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/pressbooks\/v2\/chapters\/3639\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/wp\/v2\/media?parent=3639"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/pressbooks\/v2\/chapter-type?post=3639"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/wp\/v2\/contributor?post=3639"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/wp\/v2\/license?post=3639"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}