In these lessons, we will learn

- how to calculate the relative formula mass or relative molecular mass,
- how to use the relative molecular mass to calculate the percent mass of an element in a compound,
- how to use the relative molecular mass to calculate the percent mass of water in a compound.

**Related Pages**

Mole Calculation

Stoichiometry Lessons

Chemistry Lessons

The following diagram shows how to calculate the relative molecular mass or relative formula mass. Scroll down the page for more examples and solutions.

**What is relative formula mass and relative molecular mass?**

The **relative formula mass** of a substance is the sum of the relative
atomic masses of the elements present in a formula unit. The symbol for relative formula mass is M_{r}.

If the substance is made of simple molecules, this mass may also be called the
**relative molecular mass**.

**How to calculate the relative formula mass?**

**Example:**

What is the relative mass formula of hydrogen gas? (Relative atomic mass: H = 1)

**Solution:**

The formula for hydrogen gas is H_{2}. Each molecule contains 2 hydrogen atoms.

The relative mass formula of hydrogen gas is

M_{r}(H_{2}) = 2 × A_{r}(H) = 2 × 1 = 2

**Example:**

What is the relative mass formula of water? (Relative atomic masses: H = 1, O = 16)

**Solution:**

The formula for water is H_{2}O. Each molecule contains 2 hydrogen atoms and 1 oxygen atom.

The relative mass formula of water is

M_{r}(H_{2}O) = 2 × A_{r}(H) + A_{r}(O) = 2 × 1 + 16 = 18

**Example:**

What is the relative mass formula of sodium chloride? (Relative atomic masses: Na = 23, Cl = 35.5)

**Solution:**

Sodium Chloride is an ionic solid with the formula Na^{+}Cl^{-}.

The relative mass formula of sodium chloride is

M_{r}(NaCl) = A_{r}(Na) + A_{r}(Cl) = 23 + 35.5 = 58.5

**How to find the Percent Mass of Elements in a compound?**

How to use M_{r} to calculate the **percent mass of an element**
in a compound?

**Example:**

What percentage of the mass of ammonium nitrate is nitrogen? (The formula for ammonium nitrate is NH_{4}NO_{3}, Relative atomic masses: H = 1, O = 16, N = 14)

**Solution:**

M_{r}(NH_{4}NO_{3}) = (2 × 14) + (4 × 1) + (3 × 16) = 28 + 4 + 48 = 80

Mass of nitrogen in the formula = 28

Mass of nitrogen as a fraction of the total = <imgloading=“lazy” src="/image-files/chem37.gif" width=“24” height=“41” align=“absmiddle”>

Mass of nitrogen as percentage of total mass

**Example:**

What percentage of the mass of O in NaNO_{3}? (Relative atomic masses: Na = 23, O = 16, N = 14)

**Solution:**

M_{r}(NaNO_{3}) = 23 + 14 + (3 × 16) = 23 + 14 + 48 = 85

Mass of O in the formula = 48

Mass of O as a fraction of the total =

Mass of O as percentage of total mass

**How to find percent by mass and percent composition?**

**Example:**

Find the percent composition by mass of potassium dichromate (K_{2}Cr_{2}O_{7})

Step 1: Find the molar mass of the compound.

Step 2: Divide the total mass of each element by the molar mass and multiply by 100 to find the % mass.

**How find the percent of an element in a compound?**

Finding the percent by mass means finding the mass of the elements in the compound and adding the masses for the total mass.

**Example:**

You have a 7364 milligrams sample of SO_{2}. How many grams of sulfur are in the sample?

**How to calculate the Mass Percent of an Element in a Compound?**

Mass Percent Composition of an Element in a Compound

To calculate the mass percent composition (or simply, the mass percent) of an element in a compound,
we divide the mass of the element in 1 mol of the compound with the mass of 1 mol of the compound and
multiply by 100%.

**Examples:**

- What is the mass percent of carbon in carbon dioxide?
- What is the mass percent of oxygen in carbon dioxide?

**How to find the Percent Mass of Water in a compound?**

How to use M_{r} to calculate the **percent mass of water**
in a compound?

**Example:**

What percentage of the mass of magnesium sulfate is water? (Given that the formula for magnesium
sulfate is MgSO_{4}•7H_{2}O, Relative atomic masses: H = 1, O = 16, S = 32, Mg = 24)

**Solution:**

M_{r}(MgSO_{4}•7H_{2}O) = 24 + 32 + (4 × 16) + (7 × 18) = 246

M_{r}(H_{2}O) = 2 × A_{r}(H) + A_{r}(O) = 2 × 1 + 16 = 18

Mass of water in the formula = 18 × 7 = 126

Mass of water as a fraction of the total =

Mass of hydrogen as percentage of total mass

**How to calculate the Water of Crystallization?**

This video outlines how to determine the percent, by mass, of water trapped in a hydrate’s crystal lattice.

**Example:**

What is the percent of water, by mass, in the hydrate CuSO_{4}2H_{2}O

**How to calculate the percentage of water in the formula of a hydrated compound?**

**Example:**

Determine the % water in the following hydrates:

a) CuSO_{4}5H_{2}O

b) CaCl_{2}2H_{2}O

c) KAl(SO_{4})_{2}12H_{2}O

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