Page 115 - Theory and Problems of BEGINNING CHEMISTRY

104 FORMULA CALCULATIONS [CHAP. 7

numerically equal to the number of grams of the element per mole. Consider sodium, with atomic mass 23.0:

23.0 amu 23.0 amu 6.02 × 10 23 Na atoms 1g 23.0g
= =
Na atom Na atom 1 mol Na 6.02 × 10 23 amu mol Na

Avogadro’s number appears in both the numerator and the denominator of this expression; the values reduce to
a factor of 1 (they cancel), and the numeric value in grams per mole is equal to the numeric value of the atomic
mass in amu per atom.

23.0 amu 23.0g
=
Na atom mol Na atoms

A similar argument leads to the conclusion that the formula mass of any element or compound is equal to the
number of grams per mole of the element or compound.

EXAMPLE 7.3. How many feet tall is a stack of a dozen shoe boxes, each 4 in. tall?
4in. 4in. 12 box 1ft 4ft
Ans. = =
box box 1 dozen 12 in. dozen
The same number, but in different units, is obtained because the number of inches in 1 foot is the same as the number in 1
dozen. Compare this process to the one above for grams per mole.

Changing grams to moles and moles to grams is perhaps the most important calculation you will have to
make all year (Fig. 7-2). We use the term molar mass for the mass of 1 mol of any substance. The units are
typically grams per mole.

Molar mass Number of
Mass moles

Fig. 7-2. Molar mass conversions
The mass of a substance can be converted to moles, and vice versa, with the molar mass.

EXAMPLE 7.4. Calculate the mass of 1.000 mol of SCl 2 .
Ans. The formula mass of SCl 2 is given by
S = 32.06 amu
2Cl = 2 × 35.45 amu = 70.90 amu
SCl 2 = total = 102.96 amu
Thus, the mass of 1.000 mol of SCl 2 is 102.96 g.

EXAMPLE 7.5. Calculate the mass of 2.50 mol NaClO 4 .
Ans. The formula mass of NaClO 4 is given by
Na 23.0 amu
Cl 35.5 amu
4 × O 64.0 amu
122.5 amu
NaClO 4
NaClO 4 has a formula mass of 122.5 amu.

122.5 g NaClO 4
2.50 mol NaClO 4 = 306 g NaClO 4
1 mol NaClO 4