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A first-order gas-phase reaction A(g) -> B(g) + C(g) + D(s) is carried out at constant temperature and pressure. Initially only A was present and the container volume was 100 L. After 13.86 minutes the volume was found to be 150 L. Find the rate constant. (Use ln 2 = 0.693.)
- 5 * 10⁻² per minute
- 2 * 10⁻² per second
- 5 * 10⁻² per second
- 4 * 10⁻² per minute
Correct answer: 5 * 10⁻² per minute
Solution
V/V0 = 150/100 = 1.5, so 1+x = 1.5, giving x = 0.5. Using the first-order rate law: k = (1/t)*ln(1/(1-x)) = (1/13.86)*ln 2 = 0.693/13.86 = 0.05 min⁻¹ = 5*10⁻² per minute.
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