1.1 What is Chemistry?

10.3. Chemical Formulas http://www.ck12.org

Determining Percent Composition from a Chemical Formula

The percent composition of a compound can also be determined from its chemical formula. The subscripts in the
formula are first used to calculate the mass of each element found in one mole of the compound. That value is then
divided by the molar mass of the compound and multiplied by 100%.

% by mass=mass of element in 1 mol of compoundmolar mass of compound ×100%

The percent composition of a given compound is always the same as long as the compound is pure.

Example 10.15

Dichlorine heptoxide (Cl 2 O 7 ) is a highly reactive compound used in some synthesis reactions. Calculate the percent
composition of dichlorine heptoxide.

Answer:

Determine the mass of each element in one mole of the compound, and find the total molar mass of the compound:

• mass of Cl in 1 mol Cl 2 O 7 = 2 x molar mass of Cl = 70.90 g


• mass of O in 1 mol Cl 2 O 7 = 7 x molar mass of O = 112.00 g


• molar mass of Cl 2 O 7 = 70.90 g/mol + 112.00 g/mol = 182.90 g/mol

Now, calculate the percent by mass of each element by dividing the mass of that element in 1 mole of the compound
by the molar mass of the compound and multiplying by 100%.

% Cl=

70 .90 g Cl

182 .90 g

×100%= 38 .76% Cl

% O=

112 .00 g O

182 .90 g

×100%= 61 .24% O

As expected, the percentages add up to 100%.

Determining Empirical Formulas from Percent Composition

A procedure called elemental analysis allows us to determine the empirical formula of an unknown compound.
Percent composition data can be directly obtained with this technique, and these values can be used to find the molar
ratios of the elements, which gives us the empirical formula. The steps to be taken are outlined below.

1. Assume a 100 g sample of the compound so that the given percentages can be directly converted into grams.


2. Use each element’s molar mass to convert the grams of each element to moles.


3. In order to find a whole-number ratio, divide the moles of each element by the smallest value obtained in step
   2.


4. If all the values at this point are whole numbers (or very close), each number is equal to the subscript of the
   corresponding element in the empirical formula.


5. In some cases, one or more of the values calculated in step 3 will not be whole numbers. Multiply each of
   them by the smallest number that will convert all values into whole numbers (or very close to whole numbers).
   Note that all values must be multiplied by the same number so that the relative ratios are not changed. These
   values can then be used to write the empirical formula.

Example 10.16