A dilute solution of sulphuric acid is electrolysed using a current of 0.10 A for 2 hours to produce hydrogen and oxygen gas. The total volume of gases produced a STP is _____________ cm³. (Nearest integer)
[Given : Faraday constant F = 96500 C mol⁻¹ at STP, molar volume of an ideal gas is 22.7 L mol⁻¹]

Solution

Chemistry ma’am · 4 steps

Find the moles of electrons first, then see how many moles of gas each electron makes at each electrode.

1. Charge passed. Q = It = 0.10 A × 7200 s = 720 C. So the moles of electrons are 720/96500 = 7.46 × 10⁻³ mol.
2. Electrode reactions. At the cathode, 2H⁺ + 2e⁻ → H₂, so each mole of H₂ needs 2 mol of electrons. At the anode, 2H₂O → O₂ + 4H⁺ + 4e⁻, so each mole of O₂ needs 4 mol of electrons.

   n_(gas) = nₑ/2 + nₑ/4 = 3/4nₑ = 3/4 × 7.46 × 10⁻³ = 5.60 × 10⁻³ mol

3. Convert to volume. V = 5.596 × 10⁻³ mol × 22700 cm³ mol⁻¹ = 127.0 cm³.
4. So. The total volume of hydrogen and oxygen at STP is about 127.0 cm³, which rounds to 127.

The common slip: 85. Counting only the hydrogen and leaving out the oxygen from the anode gives about 85, not 127.

The idea to keep. In electrolysis, convert charge into moles of electrons first. Then divide by the electrons each product needs: 2 for H₂ and 4 for O₂.

Answer from the NTA final answer key. Solution by PrepWiser.