{"id":663,"date":"2018-03-20T15:17:25","date_gmt":"2018-03-20T15:17:25","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/suny-orgbiochemistry\/?post_type=chapter&p=663"},"modified":"2018-08-13T01:32:06","modified_gmt":"2018-08-13T01:32:06","slug":"6-1-the-mole","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-monroecc-orgbiochemistry\/chapter\/6-1-the-mole\/","title":{"raw":"6.1 The Mole","rendered":"6.1 The Mole"},"content":{"raw":"
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Learning Objective<\/h3>\r\n
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  1. Define the mole unit.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n

    Figure 6.1 \"Water Molecules\"<\/a> shows that we need 2 hydrogen atoms and 1 oxygen atom to make 1 water molecule. If we want to make 2 water molecules, we will need 4 hydrogen atoms and 2 oxygen atoms. If we want to make 5 molecules of water, we need 10 hydrogen atoms and 5 oxygen atoms. The ratio of atoms we will need to make any number of water molecules is the same: 2 hydrogen atoms to 1 oxygen atom.<\/span><\/h3>\r\n<\/div>\r\n
    \r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"2535\"]\"image\" Figure 6.1 Water Molecules.<\/em> The ratio of hydrogen atoms to oxygen atoms used to make water molecules is always 2:1, no matter how many water molecules are being made.[\/caption]\r\n

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    One problem we have, however, is that it is extremely difficult, if not impossible, to organize atoms one at a time. As stated in the introduction, we deal with billions of atoms at a time. How can we keep track of so many atoms (and molecules) at a time? We do it by using mass rather than by counting individual atoms.<\/p>\r\n

    A hydrogen atom has a mass of approximately 1 u. An oxygen atom has a mass of approximately 16 u. The ratio of the mass of an oxygen atom to the mass of a hydrogen atom is therefore approximately 16:1.<\/p>\r\n

    If we have 2 atoms of each element, the ratio of their masses is approximately 32:2, which reduces to 16:1\u2014the same ratio. If we have 12 atoms of each element, the ratio of their total masses is approximately (12 \u00d7 16):(12 \u00d7 1), or 192:12, which also reduces to 16:1. If we have 100 atoms of each element, the ratio of the masses is approximately 1,600:100, which again reduces to 16:1. As long as we have equal numbers of hydrogen and oxygen atoms, the ratio of the masses will always be 16:1.<\/p>\r\n

    The same consistency is seen when ratios of the masses of other elements are compared. For example, the ratio of the masses of silicon atoms to equal numbers of hydrogen atoms is always approximately 28:1, while the ratio of the masses of calcium atoms to equal numbers of lithium atoms is approximately 40:7.<\/p>\r\n

    So we have established that the masses of atoms are constant with respect to each other, as long as we have the same number of each type of atom. Consider a more macroscopic example. If a sample contains 40 g of Ca, this sample has the same number of atoms as there are in a sample of 7 g of Li. What we need, then, is a number that represents a convenient quantity of atoms so we can relate macroscopic quantities of substances. Clearly even 12 atoms are too few because atoms themselves are so small. We need a number that represents billions and billions of atoms.<\/p>\r\n

    Chemists use the term mole<\/span><\/strong><\/span>\u00a0to represent a large number of atoms or molecules. Just as a dozen implies 12 things, a mole (mol) represents 6.022 \u00d7 1023<\/sup> things. The number 6.022 \u00d7 1023<\/sup>, called Avogadro\u2019s number<\/span><\/strong><\/span>\u00a0after the 19th-century chemist Amedeo Avogadro, is the number we use in chemistry to represent macroscopic amounts of atoms and molecules. Thus, if we have 6.022 \u00d7 1023<\/sup> O atoms, we say we have 1 mol of O atoms. If we have 2 mol of Na atoms, we have 2 \u00d7 (6.022 \u00d7 1023<\/sup>) Na atoms, or 1.2044 \u00d7 1024<\/sup> Na atoms. Similarly, if we have 0.5 mol of benzene (C6<\/sub>H6<\/sub>) molecules, we have 0.5 \u00d7 (6.022 \u00d7 1023<\/sup>) C6<\/sub>H6<\/sub> molecules, or 3.011 \u00d7 1023<\/sup> C6<\/sub>H6<\/sub> molecules.<\/p>\r\n\r\n

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    Notes<\/h3>\r\n

    A mole represents a very large number! If 1 mol of quarters were stacked in a column, it could stretch back and forth between Earth and the sun 6.8 billion<\/em> times.<\/p>\r\n \r\n\r\n<\/div>\r\n<\/div>\r\n

    Notice that we are applying the mole unit to different types of chemical entities. In these examples, we cited moles of atoms and<\/em> moles of molecules. The word mole<\/em> represents a number of things\u20146.022 \u00d7 1023<\/sup> of them\u2014but does not by itself specify what \u201cthey\u201d are. They can be atoms, formula units (of ionic compounds), or molecules. That information still needs to be specified.<\/p>\r\n

    Because 1 H2<\/sub> molecule contains 2 H atoms, 1 mol of H2<\/sub> molecules (6.022 \u00d7 1023<\/sup> molecules) has 2 mol of H atoms. Using formulas to indicate how many atoms of each element we have in a substance, we can relate the number of moles of molecules to the number of moles of atoms. For example, in 1 mol of ethanol (C2<\/sub>H6<\/sub>O), we can construct the following relationships (Table 6.1 \"Molecular Relationships\"<\/a>):<\/p>\r\n\r\n

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    Table 6.1<\/span> Molecular Relationships<\/strong><\/h5>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    1 Molecule of C2<\/sub>H6<\/sub>O Has<\/th>\r\n1 Mol of C2<\/sub>H6<\/sub>O Has<\/th>\r\nMole Relationships<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
    2 C atoms<\/td>\r\n2 mol of C atoms<\/td>\r\n[latex]\\frac{2\\text{ mol C atoms}}{1\\text{ mol }C_{2}H_{6}O \\text{ molecules}}[\/latex]\u00a0 AND [latex]\\frac{1\\text{ mol }C_{2}H_{6}O \\text{ molecules}}{2\\text{ mol C atoms}}[\/latex]<\/td>\r\n<\/tr>\r\n
    6 H atoms<\/td>\r\n6 mol of H atoms<\/td>\r\n[latex]\\frac{6\\text{ mol H atoms}}{1\\text{ mol }C_{2}H_{6}O \\text{ molecules}}[\/latex]\u00a0 AND [latex]\\frac{1\\text{ mol }C_{2}H_{6}O \\text{ molecules}}{6\\text{ mol H atoms}}[\/latex]\u00a0 <\/span><\/td>\r\n<\/tr>\r\n
    1 O atom<\/td>\r\n1 mol of O atoms<\/td>\r\n[latex]\\frac{1\\text{ mol O atoms}}{1\\text{ mol }C_{2}H_{6}O \\text{ molecules}}[\/latex]\u00a0 AND [latex]\\frac{1\\text{ mol }C_{2}H_{6}O \\text{ molecules}}{1\\text{ mol O atoms}}[\/latex]\u00a0 <\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n

    The following example illustrates how we can use these relationships as conversion factors.<\/p>\r\n\r\n

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    Example 1<\/h3>\r\n

    If a sample consists of 2.5 mol of ethanol (C2<\/sub>H6<\/sub>O), how many moles of carbon atoms, hydrogen atoms, and oxygen atoms does it have?<\/p>\r\n

    Solution<\/p>\r\n[reveal-answer q=\"17203\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"17203\"]\r\n\r\nUsing the relationships in Table 6.1 \"Molecular Relationships\", we apply the appropriate conversion factor for each element:\r\n\r\n\"image\"\r\n\r\nNote how the unit mol C2<\/sub>H6<\/sub>O molecules cancels algebraically. Similar equations can be constructed for determining the number of H and O atoms:\r\n\r\n2.5\u00a0mol\u00a0C2<\/sub>H6<\/sub>O\u00a0molecules \u00d7 [latex]\\frac{6\\text{ mol H atoms}}{1\\text{ mol }C_{2}H_{6}O \\text{ molecules}}[\/latex] <\/span>= 15\u00a0mol\u00a0H\u00a0atoms\r\n\r\n2.5\u00a0mol\u00a0C2H6O\u00a0molecules \u00d7 [latex]\\frac{1\\text{ mol O atoms}}{1\\text{ mol }C_{2}H_{6}O \\text{ molecules}}[\/latex]\u00a0<\/span>= 2.5\u00a0mol\u00a0O\u00a0atoms[\/hidden-answer]\r\n\r\n<\/div>\r\n

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    Skill-Building Exercise<\/h3>\r\n
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      If a sample contains 6.75 mol of Na2<\/sub>SO4<\/sub>, how many moles of sodium atoms, sulfur atoms, and oxygen atoms does it have?<\/p>\r\n\r\n<\/div><\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n

      The fact that 1 mol equals\u00a0[latex]6.022\\times{10^{23}}[\/latex] items can also be used as a conversion factor.\r\n<\/span><\/p>\r\n\r\n<\/div>\r\n

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      Example 2<\/h3>\r\n

      How many formula units are present in 2.34 mol of NaCl? How many ions are in 2.34 mol?<\/p>\r\n

      Solution<\/p>\r\n

      Typically in a problem like this, we start with what we are given and apply the appropriate conversion factor. Here, we are given a quantity of 2.34 mol of NaCl, to which we can apply the definition of a mole as a conversion factor:<\/p>\r\n 2.34\u00a0mol\u00a0NaCl \u00d7 [latex]\\frac{6.022\\times{10^{23}}\\text{ formula units NaCl}}{1 \\text{ mol NaCl}}[\/latex] = 1.41\u00d71024<\/sup>\u00a0NaCl\u00a0units <\/span>\r\n

      Because there are two ions per formula unit, there are<\/p>\r\n 1.41\u00d71024<\/sup>\u00a0NaCl\u00a0units \u00d7\u00a0 [latex]\\frac{2\\text{ ions}}{1\\text{ NaCl unit}}[\/latex] = 2.82\u00d71024<\/sup>\u00a0ions <\/span>\r\n

      in the sample.<\/p>\r\n\r\n<\/div>\r\n

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      Skill-Building Exercise<\/h3>\r\n
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        How many molecules are present in 16.02 mol of C4<\/sub>H10<\/sub>? How many atoms are in 16.02 mol?<\/p>\r\n\r\n<\/div><\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n

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        Concept Review Exercise<\/h3>\r\n
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          What is a mole?<\/p>\r\n\r\n<\/div><\/li>\r\n<\/ol>\r\n<\/div>\r\n

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          Answer<\/h3>\r\n[reveal-answer q=\"473575\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"473575\"]\r\n\r\n1. A mole is 6.022 \u00d7 1023<\/sup> things.[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
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          Key Takeaway<\/h3>\r\n