In this explainer, we will learn how to calculate the percentage composition of a substance using chemical formulas or the masses of constituent elements.

There are several ways to represent the chemical makeup of a compound. Let us consider a molecule of glucose.

We can represent the chemical makeup of glucose with the chemical formula . This chemical formula indicates that each molecule of glucose contains six carbon atoms, twelve hydrogen atoms, and six oxygen atoms.

We can also represent the chemical makeup of glucose by stating that glucose is carbon, hydrogen, and oxygen by mass. These values are the percentage composition by mass of glucose and are often referred to as percentage composition or mass percent.

### Definition: Percentage Composition

Percentage composition is the percentage by mass of each element in a compound or sample.

The percentage composition by mass of each element in a compound can be determined from the chemical formula by dividing the total relative mass of each element in one molecule or formula unit by the relative formula mass.

### Equation: Percentage Composition

The following equation can be used to determine the percentage composition by mass of an element in a compound given the chemical formula: where is the number of atoms of the element in one molecule or formula unit, is the relative atomic mass of the element, and is the total relative mass of the element in one molecule or formula unit.

The relative formula mass of a molecule or ionic compound is the sum of the relative atomic masses of the constituent atoms in any one molecule or formula unit.

### Definition: Relative Formula Mass

Relative formula mass is the mass of one molecule or formula unit found by adding the relative atomic masses of the constituent atoms.

We can use the percentage composition by mass equation to calculate the percentage composition of carbon, hydrogen, and oxygen in a molecule of glucose (). First, we add together the relative atomic masses for six carbon atoms, twelve hydrogen atoms, and six oxygen atoms to determine the relative formula mass of glucose:

Then, we can complete the percentage composition by mass equation for each element, filling in the appropriate number of atoms and relative atomic masses.

For carbon,

For hydrogen,

For oxygen,

The sum of the percentage composition by mass of each element in a compound should be equal to .

### Example 1: Calculating the Percentage Composition of Ethanol

Ethanol has the chemical formula . [ = 1 g/mol, = 12 g/mol, = 16 g/mol]

- As a percentage by mass, what is the oxygen content of the ethanol molecule, to the nearest whole number?
- As a percentage by mass, what is the carbon content of the ethanol molecule, to the nearest whole number?
- As a percentage by mass, what is the hydrogen content of the ethanol molecule, to the nearest whole number?

### Answer

**Part 1**

The percentage by mass of oxygen in ethanol, or the percentage composition by mass of oxygen, can be calculated using the formula where is the number of atoms in one molecule of ethanol and is the relative atomic mass.

The relative formula mass of ethanol can be calculated by summing the relative atomic masses of the constituent atoms in one molecule of ethanol:

We can then substitute of , of , and the relative formula mass of ethanol into the percentage composition equation:

Next, we determine the mass percentage of oxygen in ethanol to be . Rounding the answer to the nearest whole number, the percentage by mass of oxygen is determined to be .

**Part 2**

The percentage by mass of carbon in ethanol can be calculated using the same equation as in part 1, except that we will use the number of atoms of carbon and the relative atomic mass of carbon instead of oxygen:

As we have already determined the relative formula mass of ethanol in part 1, we can substitute of , of , and the relative formula mass of ethanol into the equation and determine the mass percentage of carbon:

Rounding the answer to the nearest whole number, the percentage by mass of carbon is determined to be .

**Part 3**

We can determine the percentage by mass of hydrogen in ethanol by repeating the same steps from parts 1 and 2, except that we will use the number of atoms of hydrogen and the relative atomic mass of hydrogen:

Rounding the answer to the nearest whole number, the percentage by mass of hydrogen is determined to be .

The following table shows us how information can be logically organized so that it is easier to solve problems involving percentage composition by mass.

In order to determine the percentage composition by mass of carbon, hydrogen, and oxygen in a molecule of glucose (), we can begin by completing the first three rows of the table.

To determine the total relative mass of each element in the molecule, we multiply the number of atoms of each element by the respective relative atomic mass.

To determine the relative formula mass, we sum the total relative masses.

The percentage composition by mass of each element can then be determined by dividing the total relative mass of each element by the relative formula mass and multiplying by :

### Example 2: Calculating the Percentage Composition of a Ternary Compound

What is the percentage composition of calcium carbonate ()? State percentages to 1 decimal place. [ = 12 g/mol, = 16 g/mol, = 40 g/mol]

### Answer

To determine the percentage composition or percentage composition by mass of each element in calcium carbonate, we can begin by constructing the following table.

Looking at the chemical formula of calcium carbonate and the given relative atomic masses, we can complete the first three rows of the table.

To determine the total relative mass of each element, we multiply the relative atomic mass by the number of atoms in one formula unit for each element.

Summing the total relative masses of all elements gives us the relative formula mass of .

To determine the percentage composition by mass of each element, we can use the following equation:

Written to one decimal place, the percentage composition of calcium carbonate is calcium, carbon, and oxygen.

The percentage composition by mass of an element in a compound is always the same regardless of the sample size, so long as the sample is pure.

Suppose we have a 400-gram sample of glucose. The percentage composition of glucose indicates that of the total mass of the sample is carbon (160.00 g), of the mass is hydrogen (26.68 g), and of the mass is oxygen (213.32 g).

We can use experimental mass data to determine the percentage composition of elements in a compound. In the laboratory, we work with masses in grams or kilograms rather than relative atomic masses or formula masses. Therefore, we can adjust the percentage composition equation to reflect this difference:

### Example 3: Calculating the Percentage Composition of a Theoretical Binary Compound

A compound contains only the elements and . A sample of the compound with a mass of 12.5 g is found to contain 6.50 g of . What is the percentage composition of the compound?

### Answer

This question is asking us to find the percentage composition or percentage composition by mass of elements and in a compound. To do this, we can use the following percentage composition by mass equation:

We know that the total mass of the sample containing the compound is 12.5 g and that the sample contains 6.50 g of . Therefore, we can substitute these values into the equation, and determine the percentage composition by mass of to be .

As the compound contains only elements and , the sum of the percentage composition by mass of elements and must be equal to :

We can substitute the percentage composition by mass of into the equation, and determine the percentage composition by mass of to be . Therefore, the percentage composition of the compound is and by mass.

### Example 4: Calculating the Mass of Calcium Chloride That Contains a Given Mass of Chlorine

How many grams of contain 15.0 g of chlorine? Give your answer to 1 decimal place. [ = 35.5 g/mol, = 40 g/mol]

### Answer

In order to determine how many grams of calcium chloride () contain 15.0 g of chlorine, we must first determine the percentage composition by mass of chlorine in the compound. The percentage composition by mass of chlorine in can be determined using the equation where is the number of atoms in one formula unit of and is the relative atomic mass.

The relative formula mass of calcium chloride can be calculated by summing the relative atomic masses of the constituent atoms in one formula unit of calcium chloride:

We can then substitute of , of , and the relative formula mass of calcium chloride into the percentage composition equation, and determine the mass percentage of chlorine in calcium chloride to be .

The percentage composition by mass of an element in a compound is the same regardless of the sample size, so long as the sample is pure. Here, we have a sample of calcium chloride that contains 15.0 g of chlorine. These 15.0 g of chlorine must represent of the total mass of the sample. We can adjust the variables of the percentage composition equation in order to solve for the total mass of :

We can then substitute the percentage composition of chlorine and total mass of chlorine into the equation, and rearrange to solve for the total mass of the sample,

Writing the mass to one decimal place, 23.5 g of will contain 15.0 g of chlorine.

### Example 5: Determining the Number of Atoms of Vanadium in a Vanadium Oxide from the Percentage Composition

A vanadium compound has the molecular formula , where is a whole number. If the percentage by mass of in is , what is the value of ? [ = 16 g/mol, = 51 g/mol]

### Answer

The percentage by mass equation for vanadium in an unknown vanadium oxide is where is the number of vanadium atoms in one molecule of and is the relative atomic mass. Both the percentage by mass and the relative atomic mass of vanadium are given in the question. Hence, can be substituted with the variable , the number of vanadium atoms in :

The relative formula mass of can be calculated by summing the relative atomic masses of the constituent atoms in one molecule of :

Then, the relative formula mass can be substituted into the percentage composition equation:

We can then rearrange the equation to solve for , the number of vanadium atoms:

Therefore, the value of in is 2.

### Key Points

- Percentage composition by mass is a way to represent the chemical makeup of a compound.
- The general equation for the percentage composition by mass is
- The percentage composition equation can be used when determining the percentage composition of a single molecule/formula unit or a mass of a large sample:
- The percentage composition does not change regardless of the amount of compound present.
- The sum of the percentage composition of a compound should be equal to .