Page 117 - Theory and Problems of BEGINNING CHEMISTRY

106 FORMULA CALCULATIONS [CHAP. 7

Number of Chemical formula Number of moles
moles of of element in
compound the compound

Fig. 7-3. Chemical formulas mole ratio
The number of moles of each element in a compound and the number of moles of the compound as a whole are
related by the subscript of that element in the chemical formula.

7.5. PERCENT COMPOSITION OF COMPOUNDS
The term percent means the quantity or number of units out of 100 units total. Percentage is computed by
finding the fraction of the total quantity represented by the quantity under discussion and multiplying by 100%.
For example, if a group of 30 persons includes 6 females, the percent of females in the group is
6
× 100% = 20%
30
In other words, if there were 100 persons in the group and the ratio of females to males were the same, 20 of the
group would be female. Percentage is a familiar concept to anyone who pays sales taxes.
The concept of percentage is often used to describe the composition of compounds. If the formula of a
compound is known, the percent by mass of an element in the compound is determined by computing the
fraction of the formula mass which is made up of that element, and multiplying that fraction by 100%. Thus, an
element X with atomic mass 12.0 amu in a compound XY of formula mass 28.0 amu will be present in
12.0 amu
× 100% = 42.9%
28.0 amu
The chemical formula gives the number of moles of atoms of each element in each mole of the compound; then
the number of grams of each element in the number of grams of compound in 1 mol of the compound can be
directly computed. Knowing the mass of 1 mol of the compound and the mass of each element in that quantity
of compound allows calculations of the percent by mass of each element.

EXAMPLE 7.10. Calculate the percent composition of CaSO 4 , that is, the percent by mass of each element in the
compound.
Ans. One mole of the compound contains 1 mol of calcium, 1 mol of sulfur, and 4 mol of oxygen atoms. The formula
mass is 136.14 amu (Example 7.2); hence, there is 136.14 g/mol CaSO 4 .
One mole of calcium has a mass of 40.08 g. The percent calcium is therefore
40.08gCa
%Ca = × 100% = 29.44% Ca
136.14 g CaSO 4
One mole of sulfur has a mass of 32.06 g. The percent sulfur is given by
32.06gS
%S = × 100% = 23.55% S
136.14 g CaSO 4
Four moles of oxygen has a mass of 4 × 16.00 g. The percent oxygen is given by
4 × 16.00gO
%O = × 100% = 47.01% O
136.14 g CaSO 4
The total of all the percentages in the compound is 100.00%. Within the accuracy of the calculation, the total of all
the percentages must be 100%. This result may be interpreted to mean that if there were 100.00 g of CaSO 4 , then
29.44 g would be calcium, 23.55 g would be sulfur, and 47.01 g would be oxygen.

In laboratory work, the identity of a compound may be established by determining its percent composition
experimentally and then comparing the results with the percent composition calculated from its formula.

EXAMPLE 7.11. A compound was analyzed in the laboratory and found to contain 69.94% iron and 30.06% oxygen. Is
the compound iron(II) oxide, FeO, or iron(III) oxide, Fe 2 O 3 ?