{"id":7336,"date":"2021-06-08T21:55:47","date_gmt":"2021-06-08T21:55:47","guid":{"rendered":"https:\/\/opentextbc.ca\/introductorychemistry\/chapter\/the-mole\/"},"modified":"2021-09-23T21:15:51","modified_gmt":"2021-09-23T21:15:51","slug":"the-mole","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/introductorychemistry\/chapter\/the-mole\/","title":{"raw":"The Mole","rendered":"The Mole"},"content":{"raw":"[latexpage]\r\n
\r\n

Learning Objectives<\/p>\r\n\r\n<\/header>\r\n

\r\n
    \r\n \t
  1. Describe the unit mole<\/em>.<\/li>\r\n \t
  2. Relate the mole quantity of substance to its mass.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\nSo far, we have been talking about chemical substances in terms of individual atoms and molecules. Yet we don\u2019t typically deal with substances an atom or a molecule at a time; we work with millions, billions, and trillions of atoms and molecules at a time. What we need is a way to deal with macroscopic, rather than microscopic, amounts of matter. We need a unit of amount that relates quantities of substances on a scale that we can interact with.\r\n\r\nChemistry uses a unit called mole. A [pb_glossary id=\"8164\"]mole[\/pb_glossary]\u00a0(mol) is a number of things equal to the number of atoms in exactly 12 g of carbon-12. Experimental measurements have determined that this number is very large:\r\n

    1 mol = 6.02214179 \u00d7 1023<\/sup> things<\/p>\r\nUnderstand that a mole means a number of things, just like a dozen means a certain number of things\u2014twelve, in the case of a dozen. But a mole is a much larger number of things. These things can be atoms, or molecules, or eggs; however, in chemistry, we usually use the mole to refer to the amounts of atoms or molecules. Although the number of things in a mole is known to eight decimal places, it is usually fine to use only two or three decimal places in calculations. The numerical value of things in a mole is often called Avogadro's number<\/i> (N<\/i>A<\/sub>), which is also known as the Avogadro constant<\/i>, after Amadeo Avogadro, an Italian chemist who first proposed its importance.\r\n

    \r\n

    Example 5.3<\/p>\r\n\r\n<\/header>\r\n

    \r\n

    Problem<\/h1>\r\nHow many molecules are present in 2.76 mol of H2<\/sub>O? How many atoms is this?\r\n

    Solution<\/h2>\r\nThe definition of a mole is an equality that can be used to construct a conversion factor. Also, because we know that there are three atoms in each molecule of H2<\/sub>O, we can also determine the number of atoms in the sample.\r\n

    [latex]2.76 \\cancel{\\text{ mol }\\ce{H2O }} \\times \\dfrac{6.022 \\times 10^{23}\\text{ molecules }\\ce{H2O}}{\\cancel{\\text{mol }\\ce{H2O}}}}=1.66 \\times 10^{24}\\text{ molecules }\\ce{H2O}[\/latex]<\/p>\r\nTo determine the total number of atoms, we have:\r\n

    [latex]1.66 \\times 10^{24} \\cancel{\\text{ molecules }\\ce{H2O}}\\times \\dfrac{3\\text{ atoms}}{1\\text{ \\cancel{molecule}}}=4.99 \\times 10^{24}\\text{ atoms}[\/latex]<\/p>\r\n\r\n

    Test Yourself<\/h1>\r\nHow many molecules are present in 4.61 \u00d7 10\u22122<\/sup> mol of O2<\/sub>?\r\n

    Answer<\/h2>\r\n2.78 \u00d7 1022<\/sup> molecules\r\n\r\n<\/div>\r\n<\/div>\r\nHow big is a mole? It is very large. Suppose you had a mole of dollar bills that need to be counted. If everyone on earth (about 6 billion people) counted one bill per second, it would take about 3.2 million years to count all the bills. A mole of sand would fill a cube about 32 km on a side. A mole of pennies stacked on top of each other would have about the same diameter as our galaxy, the Milky Way. A mole is a lot of things\u2014but atoms and molecules are very tiny. One mole of carbon atoms would make a cube that is 1.74 cm on a side, small enough to carry in your pocket.\r\n\r\nWhy is the mole unit so important? It represents the link between the microscopic and the macroscopic, especially in terms of mass. A mole of a substance has the same mass in grams as one unit (atom or molecules) has in atomic mass units<\/i>. The mole unit allows us to express amounts of atoms and molecules in visible amounts that we can understand.\r\n\r\nFor example, we already know that, by definition, a mole of carbon has a mass of exactly 12 g. This means that exactly 12 g of C has 6.022 \u00d7 1023<\/sup> atoms:\r\n

    12 g C = 6.022 \u00d7 1023<\/sup> atoms C<\/p>\r\nWe can use this equality as a conversion factor between the number of atoms of carbon and the number of grams of carbon. How many grams are there, say, in 1.50 \u00d7 1025<\/sup> atoms of carbon? This is a one-step conversion:\r\n

    [latex]1.50 \\times 10^{25}\\cancel{\\text{ atoms C}}\\times \\dfrac{12.0000\\text{ g C}}{6.022\\times 10^{23}\\cancel{\\text{ atoms C}}}=299\\text{ g C}[\/latex]<\/p>\r\nBut it also goes beyond carbon. Previously we defined atomic and molecular masses as the number of atomic mass units per atom or molecule. Now we can do so in terms of grams. The atomic mass of an element is the number of grams in 1 mol of atoms of that element, while the molecular mass of a compound is the number of grams in 1 mol of molecules of that compound. Sometimes these masses are called [pb_glossary id=\"8003\"]molar masses[\/pb_glossary]\u00a0to emphasize the fact that they are the mass for 1 mol of things. (The term molar<\/i> is the adjective form of mole and has nothing to do with teeth.)\r\n\r\nHere are some examples:\r\n