For gas-phase first-order decomposition A(g) -> B(g) + C(g): initial pressure = P_0 (all A). At time t, if x amount decomposes: P_A = P_0 - x, P_B = x, P_C = x. Total pressure P_t = P_0 + x, so x = P_t - P_0. P_A = P_0 - (P_t - P_0) = 2P_0 - P_t. k = (2.303/t)log(P_0/(2P_0 - P_t)). At completion (t -> infinity): P_infinity = 2P_0 (for A -> B + C). General: if A -> nB (n products from 1 reactant), P_infinity = nP_0, and k = (2.303/t)log((n-1)P_0/((n)P_0 - P_t)). This gaseous decomposition approach is frequently tested in JEE.
Part of JPC-06 — Chemical Kinetics: Rate Laws & Arrhenius Equation
First Order Kinetics with Gases
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