# Percent Composition Formula

## What is the Percent Composition Formula?

Any chemical compound is composed of different constituent elements. Sometimes in calculations about chemical reactions you need to identify the amount of an element in a given compound. Or in order to understand the contribution of a particular element in any of the stoichiometric calculations of a chemical compound of which the element is part of, it is necessary to know the amount of the given element in the compound. This can be known by knowing the percentage composition of the element in a given compound which is obtained from the percent composition formula.

### Properties of Percent Composition Formula

Percent composition chemistry relies on the formula of percent composition by mass. The formula percentage composition or the formula for mass percentage is obtained as a ratio of the amount of each element present in the compound to the total sum of the individual elements of the compound, multiplied by 100 in order to obtain the percentage. In simple terms, the formula for mass percentage of an element or the percent composition by mass is given as:

Percent Composition by Mass = (Mass of element / Molecular weight of compound) * 100

Typically, the mass or weight of the elements and the compound is taken in grams. As can be seen from the above given formula, it is clear that the percentage composition of a compound can be expressed in terms of each of the individual elements present in the compound.

Mathematically to calculate the percentage by mass of an element in a compound the following formula is used:

%CE = (gE/gT) * 100; where CE is just a representation of the percentage composition of an element, gE is the total amount of element, gT is the total weight of the compound.

The ratio when multiplied by 100 gives the percentage composition formula.

It is also possible to obtain the molecular formula from percent composition of an element for a given compound. This can be easily obtained as the ratio is of the molecular weight of an element to the molecular weight of the compound. Thus, the formula for mass percentage is also useful in obtaining the molecular formula, especially in cases of unknown chemical formula of a newly discovered chemical compound.

### Some Simple Examples

Example 1: Calculate the percentage by mass of calcium and oxygen in calcium hydroxide compound.

Solution 1: The chemical formula of calcium hydroxide is given as = Ca(OH)$_{2}$ Based on the molecular formula of calcium hydroxide, the formula mass can be calculated by getting the sum of molar mass of each of the constituent elements.

The molar mass of each of the constituent elements is given as:

Calcium, Ca = 40 g/mol.

Oxygen, O = 16 g/mol.

Hydrogen, H = 1 g/mol.

Thus, the total molar mass of the compound = mass of Ca + 2*(mass of O) + 2*(mass of H)

= 40 + 2*16 + 2*1  = 40 + 32 + 2

= 74 g/mol.

From the available information, the percentage by mass of calcium in calcium hydroxide is calculated as,

%Ca = (40/74)*100 = 54.05%.

Similarly, the percentage by mass of oxygen can be calculated as,

%O = (16/74)*100 = 21.62%.

Example 2: Calculate the percentage by mass of each of the elements of water.

Solution 2: The molecular formula of water molecules is H$_{2}$O.

The molar mass of each of the elements is given below:

Hydrogen, H = 1 g/mol.

Oxygen, O = 16 g/mol.

The total molecular weight of water from the given molar mass of the elements is

= 2*(mass of H) + mass of O.

= 2*1 + 16 = 2 + 16 = 18 g/mol.

Hence, from the given available information, the percent composition by mass of Hydrogen in water is,

%H = (1/18) = 11.11%.

Similarly, the percent by composition by mass of oxygen is given as,

%O = (16/18) = 88.89%.