Relative Molecular Mass & Relative Formula Mass

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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 H₂. Each molecule contains 2 hydrogen atoms.
The relative mass formula of hydrogen gas is
M_r(H₂) = 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 H₂O. Each molecule contains 2 hydrogen atoms and 1 oxygen atom.
The relative mass formula of water is
M_r(H₂O) = 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 NH₄NO₃, Relative atomic masses: H = 1, O = 16, N = 14)

Solution:
M_r(NH₄NO₃) = (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 NaNO₃? (Relative atomic masses: Na = 23, O = 16, N = 14)

Solution:
M_r(NaNO₃) = 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 (K₂Cr₂O₇)
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.

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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 SO₂. How many grams of sulfur are in the sample?

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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:

1. What is the mass percent of carbon in carbon dioxide?
2. What is the mass percent of oxygen in carbon dioxide?

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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 MgSO₄•7H₂O, Relative atomic masses: H = 1, O = 16, S = 32, Mg = 24)

Solution:
M_r(MgSO₄•7H₂O) = 24 + 32 + (4 × 16) + (7 × 18) = 246
M_r(H₂O) = 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 CuSO₄•2H₂O

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

Example:
Determine the % water in the following hydrates:
a) CuSO₄•5H₂O
b) CaCl₂•2H₂O
c) KAl(SO₄)₂•12H₂O

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