At 25°C, 50 g of iron reacts with HCl to form FeCl₂. The evolved hydrogen gas expands against a constant pressure of 1 bar. The work done by the gas during this expansion is _________ J. (Round off to the Nearest Integer).
[Given : R = 8.314 J mol⁻¹ K⁻¹. Assume, hydrogen is an ideal gas] [Atomic mass of Fe is 55.85 u]

Solution

Chemistry ma’am · 4 steps

Each mole of Fe gives one mole of H2, and at constant pressure the work done by that gas is just nRT.

1. Write the reaction. Fe + 2HCl → FeCl₂ + H₂. One mole of iron releases one mole of hydrogen gas, so n_(H₂) = n_(Fe).
2. Moles of gas. n_(Fe) = 50/55.85 = 0.8953 mol, so 0.8953 mol of H₂ is formed.
3. Work at constant pressure. The gas starts from essentially zero volume and pushes back the surroundings at a fixed pressure. For an ideal gas pΔ V = nRT, so the pressure value is not needed.

   W = pΔ V = nRT = 0.8953 × 8.314 × 298 ≈ 2218 J

4. So. The work done by the hydrogen gas is about 2218 J. With the sign convention for work done on the system, this is w = -2218 J.

The common slip: 186. Using T = 25 instead of 298 K gives 186 J, not 2218 J. Convert from °C to kelvin before using nRT.

The idea to keep. When a reaction produces gas at constant pressure, the expansion work is Δ n_g RT. Find the moles of gas from the equation and always use the temperature in kelvin.

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