>> View the other Key Equations and Concepts in this chapter

Working with Moles

>> Parts of this equation/concept include:

A -	Moles, Molecules, and Atoms
B -	Molar Mass
C -	Converting Between Grams and Moles

Moles not only are the SI base unit for amount, but also are a central unit used in many chemical calculations. In general, converting to moles is a first step for most calculations. A mole is simply a large group of things. It is normally used in the context of molecules and atoms, since it is too big of a group to be applied to anything larger.

The symbol for mole is mol. Many students get in the very bad habit of using m to represent mole. This is a bad idea, since m is also used as the symbol for meter and is a concentration unit (Chapter 5) molality. It might also be tempting to use m to represent molecules (proper symbol = molec), but that would allow confusion with meters and molality and, also, possibly with moles. Using the proper symbol avoids confusion and is a good habit overall.

Avogadro's number, 6.022 x 10²³, is how many things are in a mole. When you count that high, your number is not exact. This value has four significant figures. It is possible to find values for Avogadro's number that have more significant figures, but four is normally plenty. Although you can have Avogadro's number (a mole) of anything, it is usually used as follows:

1 mole = 6.022 x 10²³ atoms
1 mole = 6.022 x 10²³ molecules

This can be applied to any type of atom or molecule.

>> Example 1

How many moles of copper are 5.44 x 10²² atoms of copper?

Solution:

5.44 x 1022 atoms

1 mol 6.0221023 atoms

=

0.0903 mol Cu

Three significant figures are the fewest from atoms of copper.

>> Example 2

How many molecules of HCl are in 0.97 mol HCl?

Solution:

0.97 mol

6.022 x 1023 molec 1 mol

=

5.8 x 1023 molecules

The chemical formula allows you to relate the number of atoms to the whole molecule. The formula is the ratio of atoms, so it applies equally to atoms and molecules or moles of atoms and moles of molecules.

>> Example 3

How many atoms of oxygen are in one molecule of sulfuric acid? How many moles of oxygen are in one mole of sulfuric acid?

Solution:

Sulfuric acid has the formula of H₂SO₄. There are four atoms of oxygen in one molecule of H₂SO₄. There are also four moles of oxygen in 1 mole of sulfuric acid. These values are exact (infinite significant figures).

>> Example 4

How many atoms of hydrogen are in 0.5129 mol water?

Solution:

Note that two changes are required in this question—a change from moles to atoms and a change from water molecules to hydrogen atoms.

0.5129 mol H2O

2 mol H 1 mol H2O

6.022 x 1023 atoms 1 mol H

=

6.177 x 1023 atoms H

Or equally correct:

0.5129 mol H2O

6.022 x 1023 molec 1 mol

2 atoms H 1 molec H2O

=

6.177 x 1023 atoms H

Note that you change units and type of substance as separate steps. It is a good idea to keep track of both as you do these types of calculations. The starting number had four significant figures, Avogadro's number had 4 significant figures, and the atom-to-molecule ratio has infinite significant figures. Thus the answer has four significant figures.

  >> back to the Top of the Page

It is not a coincidence that the mass of an atom n atomic mass units (amu) is the same value as a mass of a mole of that atom in grams. Since a mole contains so many atoms, it is appropriate to use the weighted average of all the isotopes of that atom. This value is listed on the periodic table. For example, one atom of fluorine (F) weighs 19 amu and 1 mol of atoms of fluorine weighs 19.00 g. Another way to say this is that the molar mass of fluorine is 19.00 g/mol. Because of differences in rounding and geographical distribution of isotopes, it is not uncommon for different periodic tables to have slightly different values. The values are rarely different enough to affect the results.

Ions are formed by gain or loss of electrons. Since the mass of an electron is about zero compared with the rest of the atom, the charge will not affect molar mass.

Since masses are additive, the mass of a molecule is the sum of each atom in the molecule. The molar mass of a molecule is the sum of the molar mass of each atom in the molecule.

Since molar masses are determined by addition, significant figures are determined by the value with the fewest decimal places. It is generally a good practice to use a minimum of two decimal places for molar mass values. The unit for molar mass is g/mol (grams per mole).

>> Example 5

What is the molar mass of the following compounds?

1. FeCl₃
2. Zn(NO₃)₂
3. N₂O
4. CH₄

Solution:

1. There are one iron atom, molar mass = 55.845, and three chlorine atoms, molar mass = 35.453 each.

   molar mass of FeCl₃ = 55.845 + 3(35.453) = 162.204 g/mol

2. There are one zinc, two nitrogens, and six oxygens, so

   molar mass = 65.39 + 2(14.01) + 6(16.00) = 189.41 g/mol

3. Two nitrogens and one oxygen

   molar mass = 2(14.01) + 16.00 = 44.02 g/mol

4. One carbon and four hydrogens

   molar mass = 12.01 + 4(1.008) = 16.04 g/mol

  >> back to the Top of the Page

Molar mass is used to convert grams to moles and the reverse. It can be used as a conversion factor, just as centimeters and meters can be converted to one another. The key is to use the molar mass of the appropriate substance. In mole problems both grams and substance might change, but only one at a time! If you need to change substance, it is usually easiest to do so with a constant unit of moles.

>> Example 6

How many moles are in 0.355 g of FeCl₃?

Solution:

The molar mass of FeCl₃ is 162.204 g/mol (above). Therefore 1 mol FeCl₃ = 162.204 g.

0.355 g

1 mol 162.204 g

=

2.18 x 10–3 mol FeCl3

>> Example 7

How many grams are 0.0608 mol of nickel(II) iodide?

Solution:

The formula for nickel(II) iodide is NiI₂. Its molar mass is 58.69 + 2(126.90) = 312.49 g/mol.

0.0608 mol NiI2

312.49 g 1 mol

=

18.999392 g

=

19.0 g

>> Example 8

How many grams of oxygen are in 0.1926 mol of barium hydroxide?

Solution:

The formula for barium hydroxide is Ba(OH)₂. The molar mass of barium hydroxide is 171.35 g/mol. The molar mass of oxygen (O) is 16.00 g/mol. The relationship between barium hydroxide and oxygen is either

1 molecule Ba(OH)₂ = 2 atom oxygen

or

1 mol Ba(OH)₂ = 2 mol oxygen

0.1926 mol Ba(OH)2

2 mol oxygen 1 mol Ba(OH)2

16.00 g O 1 mol O

=

6.163 g

The molar mass of barium hydroxide was not needed, since barium hydroxide was already in units of moles and moles were the proper unit to change substances.

>> Example 9

How many moles of nitrogen are in 0.18 g of dinitrogen tetraoxide?

Solution:

Dinitrogen tetraoxide is N₂O₄. Its molar mass is 2(14.01) + 4(16.00) = 92.02 g/mol.

0.18 g N2O4

1 mol N2O4 92.02 g N2O4

2 mol N 1 mol N2O4

=

3.9 x 10–3 mol

>> Example 10

How many grams of CaSO₄ can be made with 0.742 g calcium?

Solution:

The molar mass of calcium sulfate is 40.08 + 32.07 +  4(16.00) = 136.15 g/mol.

0.742 g Ca

1 mol Ca 40.08 g

1 mol CaSO4 1 mol Ca

136.15 g 1 mol CaSO4

=

2.52 g

>> View the other Key Equations and Concepts in this chapter