This is "Unit 9", section 9.1 from the book General Chemistry (v. 1.0).

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9.1 The Mole

Learning Objective

  1. To calculate the molecular mass of a covalent compound and the formula mass of an ionic compound and to calculate the number of atoms, molecules, or formula units in a sample of a substance.

So far, we have been talking about chemical substances in terms of individual atoms and molecules. Yet chemists, and people in general, don't 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 with which we can interact.

Chemistry uses a unit called mole. A moleThe number of things equal to the number of atoms in exactly 12 g of carbon-12; equals 6.022×1023 things. (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:

1 mol = 6.02214179 × 1023 things

Understand that a mole means a number of things, just like a dozen means a certain number of things, specifically twelve. 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 (NA), which is also known as the Avogadro constant, after Amadeo Avogadro, an Italian chemist who first proposed its importance.

Example 3

How many molecules are present in 2.76 mol of H2O? How many atoms is this?

Solution

The 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 H2O, we can also determine the number of atoms in the sample.

( 2.76 mol H 2 O ) ( 6.02 × 10 23 molecules mol H 2 O ) = 1.66 × 10 24

To determine the total number of atoms, we have

( 1.66 × 10 24 molecules H 2 O ) ( 3 atoms 1 molecule H 2 O ) = 4.99 × 10 24

Test Yourself

How many molecules are present in 4.61 × 10-2 mol of O2?

Answer

2.78 × 1022 molecules

To appreciate the magnitude of Avogadro’s number, consider a mole of pennies. Stacked vertically, a mole of pennies would be 4.5 × 1017 mi high, or almost six times the diameter of the Milky Way galaxy. If a mole of pennies were distributed equally among the entire population on Earth, each person would get more than one trillion dollars. Clearly, the mole is so large that it is useful only for measuring very small objects, such as atoms.

Note the Pattern

One mole always has the same number of objects: 6.022 × 1023.

Summary

The mole is a unit used to measure the number of atoms, molecules, or (in the case of ionic compounds) formula units in a given mass of a substance. The mole is defined as the amount of substance that contains the number of carbon atoms in exactly 12 g of carbon-12 and consists of Avogadro’s number (6.022 × 1023) of atoms of carbon-12.

Numerical Problems

  1. Give the number of molecules or formula units in each sample.

    1. 1.30 × 10−2 mol of SCl2
    2. 1.03 mol of N2O5
    3. 0.265 mol of Ag2Cr2O7

  2. Give the number of moles in each sample.

    1. 9.58 × 1026 molecules of Cl2
    2. 3.62 × 1027 formula units of KCl
    3. 6.94 × 1028 formula units of Fe(OH)2

  3. What is the total number of atoms in each sample?

    1. 0.431 mol of Li
    2. 2.783 mol of methanol (CH3OH)
    3. 0.0361 mol of CoCO3
    4. 1.002 mol of SeBr2O

  4. What is the total number of atoms in each sample?

    1. 0.980 mol of Na
    2. 2.35 mol of O2
    3. 1.83 mol of Ag2S
    4. 1.23 mol of propane (C3H8)

  5. Decide whether each statement is true or false and explain your reasoning.

    1. There are more molecules in 0.5 mol of Cl2 than in 0.5 mol of H2.
    2. One mole of H2 has 6.022 × 1023 hydrogen atoms.

  6. How many atoms are present in 4.55 mol of Fe?

  7. How many atoms are present in 0.0665 mol of K?

  8. How many molecules are present in 2.509 mol of H2S?

  9. How many molecules are present in 0.336 mol of acetylene (C2H2)?

  10. How many moles are present in 3.55 × 1024 Pb atoms?

  11. How many moles are present in 2.09 × 1022 Ti atoms?

  12. How many moles are present in 1.00 × 1023 PF3 molecules?

  13. How many moles are present in 5.52 × 1025 penicillin molecules?

Answers

    1. 7.83 × 1021 molecules
    2. 6.20 × 1023 molecules
    3. 1.60 × 1023 molecules
    1. 2.59 × 1023 atoms
    2. 1.006 × 1025 atoms
    3. 1.09 × 1023 atoms
    4. 2.41 × 1024 atoms

    1. False. 0.5 mol of Cl2 contains exactly the same number of molecules as 0.5 mol of H2. If the number of moles of molecules is the same, the number of molecules is the same, regardless of the identity of the substance.
    2. False. One mole of H2 has 12.044 × 1023 hydrogen atoms.

  6. 2.74 × 1024 atoms

  8. 1.511 × 1024 molecules

  10. 5.90 mol

  12. 0.166 mol