How many moles of H$_2$SO4 are there in 50 cm$^3$ of 0.108 mol dm$^3$ solution of the acid?

Analyze the question: You are asked for the number of moles of H₂SO₄ in 50 cm³ of a 0.108 mol/dm³ solution.

Concept: Moles = concentration (mol/dm³) × volume (dm³)

Since concentration is in mol/dm³, the volume must be converted from cm³ to dm³ first: 1 dm³ = 1000 cm³

Solution:

1. Convert the volume: 50 cm³ = 50 ÷ 1000 = 0.050 dm³

2. Apply the formula: n = C × V n = 0.108 × 0.050 n = 0.0054 mol

3. Write in standard form: 0.0054 = 5.4 × 10⁻³ mol

Check against the options:

• A. 5.4 × 10 = 54 (too large)
• B. 5.4 × 10⁻³ = 0.0054 ✔
• C. 5.4 × 10⁻² = 0.054 (this comes from a decimal slip)
• D. 5.4 × 10⁻¹ = 0.54 (too large)

Exam tip: Always convert cm³ to dm³ by dividing by 1000 before using n = C × V. A quick shortcut: moles = (C × V in cm³) ÷ 1000, so 0.108 × 50 = 5.4, then 5.4 ÷ 1000 = 5.4 × 10⁻³. Also, the 2 in H₂SO₄ doesn't matter here, because you are counting moles of the acid itself, not moles of H⁺ ions.