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For the gas-phase thermal decomposition: CH3CHO(g) → CO(g) + CH4(g), the initial pressure is 80 mmHg and the total pressure after 20 minutes is 120 mmHg. Assuming first-order kinetics and given ln 2 = 0.693, the rate constant is:

1. 3.465 * 10⁻² min⁻¹
2. 34.65 min⁻¹
3. 3.465 min⁻¹
4. 0.3465 min⁻¹

Correct answer: 3.465 * 10⁻² min⁻¹

Solution

Initial: P(CH3CHO) = 80 mmHg, total = 80 mmHg. After time t: let x = pressure of CH3CHO decomposed. Pressure of CH3CHO remaining = 80 - x. Pressure of CO = x, pressure of CH4 = x. Total = (80 - x) + x + x = 80 + x = 120, so x = 40. Remaining pressure of CH3CHO = 80 - 40 = 40 mmHg. For first order: k = (1/t) * ln(P0 / Pₜ) = (1/20) * ln(80/40) = (1/20) * ln 2 = 0.693/20 = 0.03465 min⁻¹ = 3.465 * 10⁻² min⁻¹.

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