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For the first-order gas-phase reaction A(g) -> 2B(g) + C(g), the following pressure data is recorded: Time (min): 0 100 infinity Total pressure (mmHg): 100 190 280 What is the half-life of the reaction?
- 50 min
- 120 min
- 70 min
- Cannot be predicted
Correct answer: 120 min
Solution
From the pressure data: at t=100 min, total pressure = 190 = 100 + 2x, giving x=45 and p_A=55 mmHg. Using k = (1/t)*ln(P0/p_A) = (1/100)*ln(100/55) ≈ 0.00596 min^(-1), the half-life = ln(2)/k ≈ 116 min ≈ 120 min.
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