GCSE Chemistry - How to Solve: Relative Formula Mass and Percentage by Mass

How to Solve: Relative Formula Mass and Percentage by Mass

Complete Guide For GCSE/A-Level Chemistry (AQA, Edexcel, OCR, WJEC)

Introduction

"Mastering relative formula mass and percentage by mass lets you calculate drug dosages in medicine, check food labels for hidden sugars, and even predict how much metal you can extract from a rock—worth up to 6 marks in Paper 1 Chemistry, where every mark counts toward your grade!"

WHAT YOU NEED TO KNOW FIRST

1. Atomic mass (Ar): The mass of one atom of an element (found on the periodic table).
2. Moles: The unit for amount of substance (1 mole = 6.02 × 10²³ particles).
3. Balanced chemical equations: How to count atoms in a formula (e.g., H₂O has 2 H and 1 O).

KEY TERMS & FORMULAS

1. Relative Formula Mass (Mr)

Definition: The total mass of all atoms in a formula, compared to 1/12th the mass of a carbon-12 atom. Formula: Mr = Σ (number of atoms × Ar of each element) - Σ = "sum of" - Ar = atomic mass (from periodic table) - MEMORISE THIS – Not given on exam sheets.

Example: Mr of CO₂ = (1 × Ar of C) + (2 × Ar of O) = 12 + (2 × 16) = 44.

2. Percentage by Mass

Definition: The percentage of an element’s mass in a compound. Formula: % by mass = (mass of element in 1 mole ÷ Mr of compound) × 100 - Mass of element = (number of atoms × Ar) - MEMORISE THIS – Not given on exam sheets.

Example: % of O in CO₂ = [(2 × 16) ÷ 44] × 100 = 72.7%.

STEP-BY-STEP METHOD

Step 1: Write the formula

• Copy the chemical formula exactly as given (e.g., H₂SO₄, not HSO₄).

Step 2: Find Ar for each element

• Use the periodic table. Round to 1 decimal place (e.g., Cl = 35.5, not 35.45).

Step 3: Count atoms of each element

• Subscripts tell you how many atoms (e.g., H₂SO₄ has 2 H, 1 S, 4 O).

Step 4: Calculate Mr

• Multiply each Ar by its atom count, then add them up.
• Double-check: Did you count all atoms? Did you use the correct Ar?

Step 5: For % by mass, pick your target element

• Circle the element you’re asked about (e.g., "Find % of S in H₂SO₄").

Step 6: Calculate mass of target element in 1 mole

• Multiply its Ar by its atom count (e.g., S in H₂SO₄ = 1 × 32.1 = 32.1).

Step 7: Divide by Mr and multiply by 100

• % = (mass of element ÷ Mr) × 100.
• Round to 1 decimal place unless the question says otherwise.

Step 8: Check units and sig figs

• % answers must end in "%".
• If the question gives Ar to 1 d.p., your answer should too.

WORKED EXAMPLES

Example 1 – Basic: Mr of NaCl

Question: Calculate the relative formula mass of sodium chloride (NaCl).

Step 1: Formula = NaCl. Step 2: Ar of Na = 23.0, Ar of Cl = 35.5. Step 3: 1 Na, 1 Cl. Step 4: Mr = (1 × 23.0) + (1 × 35.5) = 58.5.

Answer: 58.5.

What we did and why: - We added the masses of 1 Na and 1 Cl atom. No subscripts >1, so no multiplication needed.

Example 2 – Medium: % of O in CaCO₃

Question: Calculate the percentage by mass of oxygen in calcium carbonate (CaCO₃).

Step 1: Formula = CaCO₃. Step 2: Ar of Ca = 40.1, C = 12.0, O = 16.0. Step 3: 1 Ca, 1 C, 3 O. Step 4: Mr = (1 × 40.1) + (1 × 12.0) + (3 × 16.0) = 100.1. Step 5: Target element = O. Step 6: Mass of O = 3 × 16.0 = 48.0. Step 7: % = (48.0 ÷ 100.1) × 100 = 47.95% → 48.0% (1 d.p.).

Answer: 48.0%.

What we did and why: - We counted 3 O atoms, not 1. Forgetting the subscript is a common mistake.

Example 3 – Exam-Style: % of N in (NH₄)₂SO₄

Question: Ammonium sulfate, (NH₄)₂SO₄, is used in fertilizers. Calculate the percentage by mass of nitrogen in this compound.

Step 1: Formula = (NH₄)₂SO₄. Step 2: Ar of N = 14.0, H = 1.0, S = 32.1, O = 16.0. Step 3: 2 N, 8 H, 1 S, 4 O (brackets mean ×2 for everything inside). Step 4: Mr = (2 × 14.0) + (8 × 1.0) + (1 × 32.1) + (4 × 16.0) = 132.1. Step 5: Target element = N. Step 6: Mass of N = 2 × 14.0 = 28.0. Step 7: % = (28.0 ÷ 132.1) × 100 = 21.19% → 21.2% (1 d.p.).

Answer: 21.2%.

What we did and why: - Brackets mean we multiply everything inside by 2. We counted 2 N atoms, not 1.

COMMON MISTAKES

1. MISTAKE: Forgetting subscripts (e.g., O₂ → 1 O instead of 2). WHY IT HAPPENS: Rushing or misreading the formula. CORRECT APPROACH: Circle each element and count atoms before calculating.

2. MISTAKE: Using wrong Ar values (e.g., Cl = 35 instead of 35.5). WHY IT HAPPENS: Not checking the periodic table. CORRECT APPROACH: Always write Ar values next to each element.

3. MISTAKE: Ignoring brackets (e.g., (NH₄)₂ → 1 N instead of 2). WHY IT HAPPENS: Not expanding the formula. CORRECT APPROACH: Write out the full formula (e.g., N₂H₈SO₄).

4. MISTAKE: Rounding too early (e.g., 47.95% → 48% before final answer). WHY IT HAPPENS: Not following sig fig rules. CORRECT APPROACH: Round only at the end, to 1 d.p. unless told otherwise.

5. MISTAKE: Mixing up % by mass with % yield or % error. WHY IT HAPPENS: Not reading the question carefully. CORRECT APPROACH: Highlight the word "mass" in the question.

EXAM TRAPS

1. TRAP: Giving Mr instead of % by mass. HOW TO SPOT IT: The question asks for "%" but you’re calculating Mr. HOW TO AVOID IT: Underline the word "percentage" in the question.

2. TRAP: Using the wrong formula (e.g., NaClO instead of NaClO₃). HOW TO SPOT IT: The question shows a diagram or name (e.g., "sodium chlorate(V)"). HOW TO AVOID IT: Write the formula from the name first (chlorate(V) = ClO₃⁻).

3. TRAP: Forgetting to multiply by 100 for %. HOW TO SPOT IT: Your answer is a decimal (e.g., 0.727 instead of 72.7%). HOW TO AVOID IT: Write "% = ( ) × 100" in your working.

1-MINUTE RECAP

"Here’s the night-before cheat sheet:
1. Mr = sum of (atoms × Ar). Count every atom, even in brackets.
2. % by mass = (mass of element ÷ Mr) × 100. Pick the right element!
3. Check your Ar values—Cl is 35.5, not 35.
4. Round to 1 decimal place unless the question says otherwise.
5. Underline key words—if it says ‘percentage’, don’t just give Mr. You’ve got this. Now go ace that exam!"