3.2 Percentage Composition

Introduction

When chemists study a compound, they often want to know how much of each element is present in it. For example, in water (H₂O), what percentage of the mass is hydrogen, and what percentage is oxygen?

This information is called the percentage composition of a compound. It tells us the relative amounts of each element in a compound, expressed as a percentage by mass.

Percentage composition is important in many areas:

• Industry — to know the composition of raw materials and products
• Agriculture — to determine the nutrient content of fertilizers
• Pharmaceuticals — to ensure the correct composition of medicines
• Environmental science — to analyze pollutants and their composition

Definition

Percentage Composition: The relative amounts of each element in a compound, expressed as a percentage by mass.

In simple words: Percentage composition tells you what fraction of a compound's mass comes from each element, expressed as a percentage.

Main Idea

• Percentage composition tells us the mass percentage of each element in a compound.
• To find it, we need:
• The sum of all percentages in a compound must be 100%.

Core Concept

The percentage of an element in a compound is calculated by:

\%\ of an element = mass of element in 1 mole of compoundmolar mass of compound × 100

Simple explanation: If you know how much an element weighs in one mole of a compound, and you know the total mass of one mole of the compound, you can find what percentage of the total mass that element contributes.

Detailed Explanation

Steps to Determine Percentage Composition

To determine the percentage composition of a known compound:

Step 1: Calculate the molar mass of the compound.

Step 2: Calculate the percentage of each element in one mole of the compound.

- This is done by dividing the mass of each element in one mole of the compound by the molar mass, then multiplying by 100.

Formula:

\%\ of an element = mass of element in 1 mole of compoundmolar mass of compound × 100

Step 3: Check that the sum of all percentages equals 100%.

Example: Percentage Composition of MgO

The source gives an example of MgO (magnesium oxide).

Step 1: Calculate the molar mass of MgO.

Molar mass of MgO = 24 + 16 = 40\ g/mol

Step 2: Calculate the percentage of each element.

Percentage of Mg:

\%\ Mg = 2440 × 100 = 60\%

Percentage of O:

\%\ O = 1640 × 100 = 40\%

Step 3: Check the sum.

60\% + 40\% = 100\%

Conclusion: MgO is 60% magnesium and 40% oxygen by mass.

More Examples

The source lists several compounds for which percentage composition can be calculated:

• Water (H₂O)
• Sulphuric acid (H₂SO₄)
• Glucose (C₆H₁₂O₆)
• Ammonium nitrate (NH₄NO₃)

Let's work through one of these examples in detail.

Worked Example: Percentage Composition of Water (H₂O)

Step 1: Calculate the molar mass of H₂O.

Molar mass of H₂O = (2 × 1) + (1 × 16) = 2 + 16 = 18\ g/mol

Step 2: Calculate the percentage of each element.

Percentage of H:

\%\ H = 218 × 100 = 11.11\%

Percentage of O:

\%\ O = 1618 × 100 = 88.89\%

Step 3: Check the sum.

11.11\% + 88.89\% = 100\%

Conclusion: Water is 11.11% hydrogen and 88.89% oxygen by mass.

Worked Example: Percentage Composition of Sulphuric Acid (H₂SO₄)

Step 1: Calculate the molar mass of H₂SO₄.

Molar mass of H₂SO₄ = (2 × 1) + (1 × 32) + (4 × 16) \] \[ = 2 + 32 + 64 = 98\ g/mol

Step 2: Calculate the percentage of each element.

Percentage of H:

\%\ H = 298 × 100 = 2.04\%

Percentage of S:

\%\ S = 3298 × 100 = 32.65\%

Percentage of O:

\%\ O = 6498 × 100 = 65.31\%

Step 3: Check the sum.

2.04\% + 32.65\% + 65.31\% = 100\%

Conclusion: Sulphuric acid is 2.04% hydrogen, 32.65% sulphur, and 65.31% oxygen by mass.

Worked Example: Percentage Composition of Glucose (C₆H₁₂O₆)

Step 1: Calculate the molar mass of C₆H₁₂O₆.

Molar mass of C₆H₁₂O₆ = (6 × 12) + (12 × 1) + (6 × 16) \] \[ = 72 + 12 + 96 = 180\ g/mol

Step 2: Calculate the percentage of each element.

Percentage of C:

\%\ C = 72180 × 100 = 40.00\%

Percentage of H:

\%\ H = 12180 × 100 = 6.67\%

Percentage of O:

\%\ O = 96180 × 100 = 53.33\%

Step 3: Check the sum.

40.00\% + 6.67\% + 53.33\% = 100\%

Conclusion: Glucose is 40.00% carbon, 6.67% hydrogen, and 53.33% oxygen by mass.

Worked Example: Percentage Composition of Ammonium Nitrate (NH₄NO₃)

Step 1: Calculate the molar mass of NH₄NO₃.

Molar mass of NH₄NO₃ = (2 × 14) + (4 × 1) + (3 × 16) \] \[ = 28 + 4 + 48 = 80\ g/mol

Step 2: Calculate the percentage of each element.

Percentage of N:

\%\ N = 2880 × 100 = 35.00\%

Percentage of H:

\%\ H = 480 × 100 = 5.00\%

Percentage of O:

\%\ O = 4880 × 100 = 60.00\%

Step 3: Check the sum.

35.00\% + 5.00\% + 60.00\% = 100\%

Conclusion: Ammonium nitrate is 35.00% nitrogen, 5.00% hydrogen, and 60.00% oxygen by mass.

Summary Table

Intermediate Level

Steps for calculating percentage composition:

• Write the formula of the compound.
• Calculate the molar mass by adding the atomic masses of all atoms.
• Calculate the mass of each element in one mole of the compound.
• Divide the mass of each element by the molar mass.
• Multiply by 100 to get the percentage.
• Check that the sum of all percentages equals 100%.

Example: For H₂SO₄:

• Molar mass = 98 g/mol
• Mass of H = 2 g → 2.04%
• Mass of S = 32 g → 32.65%
• Mass of O = 64 g → 65.31%
• Sum = 100%

Formula / Mathematical Form

\%\ of an element = mass of element in 1 mole of compoundmolar mass of compound × 100

Important Points

• - Percentage composition = relative amounts of each element in a compound, expressed as a percentage by mass.
• - Formula:
• \%\ of an element = mass of element in 1 mole of compoundmolar mass of compound × 100
• - The sum of all percentages in a compound must equal 100%.
• - To find percentage composition, you need the molar mass of the compound and the mass of each element in one mole.
• - Examples:
• - MgO: Mg = 60%, O = 40%
• - H₂O: H = 11.11%, O = 88.89%
• - H₂SO₄: H = 2.04%, S = 32.65%, O = 65.31%
• - C₆H₁₂O₆: C = 40.00%, H = 6.67%, O = 53.33%
• - NH₄NO₃: N = 35.00%, H = 5.00%, O = 60.00%

Remember

• - Percentage composition = mass % of each element.
• - Formula: (mass of element / molar mass) × 100.
• - Sum of percentages = 100%.
• - Need molar mass and mass of each element.
• - MgO: Mg = 60%, O = 40%.
• - H₂O: H = 11.11%, O = 88.89%.
• - H₂SO₄: H = 2.04%, S = 32.65%, O = 65.31%.
• - C₆H₁₂O₆: C = 40.00%, H = 6.67%, O = 53.33%.
• - NH₄NO₃: N = 35.00%, H = 5.00%, O = 60.00%.
• - Percentage composition → empirical formula.

Common Mistakes

Quick Revision

• Percentage Composition:
• The relative amounts of each element in a compound are expressed as the percentage composition.

Formula:

• \%\ of an element = mass of element in 1 mole of compoundmolar mass of compound × 100

Steps:

• Calculate the molar mass of the compound.
• Calculate the percentage of each element in one mole of the compound.
• Check that the sum of all percentages equals 100%.

Examples:

• Key point:
• The sum of percentages of all elements in a compound must be equal to 100%.

60-Second Revision

• Percentage composition = mass % of each element in a compound.
• Formula: (mass of element / molar mass) × 100.
• Sum of all percentages = **100%**.
• MgO: Mg = 60%, O = 40%.
• H₂O: H = 11.11%, O = 88.89%.
• H₂SO₄: H = 2.04%, S = 32.65%, O = 65.31%.
• C₆H₁₂O₆: C = 40.00%, H = 6.67%, O = 53.33%.
• NH₄NO₃: N = 35.00%, H = 5.00%, O = 60.00%.
• ⚠️ Warning: always check that the percentages add up to 100%.