The second-order reaction $2 A (g) 2 B (g) + C (g)$ starts with pure A at 100 kPa in a rigid vessel, and the total pressure is 112.5 kPa after 200 s. Calculate the rate constant (in pressure units) in $1 0^{- 5} kP a^{- 1} s^{- 1}$ to two decimal places.

Numerical answer type, answer in 10^-5 kPa^-1 s^-1, tolerance 0.03.

Answer: 1.67 10^-5 kPa^-1 s^-1

If A reacts by

p

P_{t} = P_{0} - p + p + p /2 = P_{0} + p /2

, so

p = 2 (112.5 - 100) = 25

kPa and

p_{A} = 75

kPa. For second order

k = \frac{1}{t} (\frac{1}{p _{A}} - \frac{1}{P _{0}}) = \frac{1}{200} (\frac{1}{75} - \frac{1}{100}) = 1.67 \times 1 0^{- 5} kP a^{- 1} s^{- 1}