Consider the following first order gas phase reaction at constant temperature A(g) 2B(g) + C(g) If the total pressure of the gases is found to be 200 torr after 23 sec. and 300 torr upon the complete decomposition of A after a very long time, then the rate constant of the given reaction is 10-2 s-1 (nearest integer) [Given : 10(2) = 0.301]
Answer
3
Solution
A(g) 2B(g) + C(g)
Pressures: t = 0: P0, 0, 0; at t: P0 - x, 2x, x, so Pt = P0 + 2x; at t = ∞: P = 3P0
Since 3P0 = 300, P0 = 100 torr. The pressure of A left at time t is P0 - x = P - Pt2, while P0 = P - P02, so for a first order reaction
k = 2.303t P0P0 - x = 2.303t P - P0P - Pt
= 2.30323 300 - 100300 - 200 = 2.303 0.30123
= 0.0301 s-1 = 3.01 10-2 s-1 3 10-2 s-1
Answer: 3