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Only gas A is introduced into a closed rigid container at constant temperature and reacts following first-order kinetics according to: 2A(g) --> 2B(g) + C(g). The total pressure of the gas mixture is recorded at two times: - At t = 10 min: P_total = 1.3 atm - At t = infinity: P_total = 1.5 atm What is the approximate rate constant for the disappearance of A? (Use ln 5 = 1.6, ln 2 = 0.7)

1. 0.03 min^(-1)
2. 0.045 min^(-1)
3. 0.09 min^(-1)
4. 0.058 min^(-1)

Correct answer: 0.09 min^(-1)

Solution

From P_inf = 1.5 = (3/2)P0, we get P0 = 1.0 atm. At t = 10 min: 1.3 = 1.0 + x/2, so x = 0.6 atm. Pressure of A at t=10 is P0 - x = 0.4 atm. For first-order: k = (1/t) ln(P0/P_A) = (1/10) ln(1.0/0.4) = (1/10) ln(2.5).

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