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A solid substance A decomposes as A(s) -> 2B(g) + C(g) by a first-order reaction. The total pressure after 20 min is 150 mmHg and after a very long time is 225 mmHg. Find the rate constant and the total pressure after 40 min.

1. 0.05 ln 1.5 min^(-1), 200 mm
2. 0.5 ln 2 min^(-1), 300 mm
3. 0.05 ln 3 min^(-1), 300 mm
4. 0.05 ln 3 min^(-1), 200 mm

Correct answer: 0.05 ln 3 min^(-1), 200 mm

Solution

At t=inf: 3*alpha_max=225 => alpha_max=75 mmHg. At t=20: 3*alpha=150 => alpha=50 mmHg. Remaining A corresponds to alpha_max - alpha = 25. First-order: k = (1/20)*ln(75/25) = (1/20)*ln3 = 0.05*ln3 min^(-1). At t=40: alpha_max - alpha₄₀ = 75*e^(-40k) = 75*e^(-2*ln3) = 75/9 = 25/3. alpha₄₀ = 75 - 25/3 = 200/3. Total pressure = 3*alpha₄₀ = 200 mmHg.

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