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Part of JPC-06 — Chemical Kinetics: Rate Laws & Arrhenius Equation

Gas-Phase Kinetics

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For gas-phase first-order decompositions, pressure replaces concentration. General case: A(g) -> nB(g) (or multiple products with total n moles of gaseous products per mole of A). At t=0: P_A = P_0. At time t: x moles of A decompose. P_A = P_0 - x. Total product pressure = (sum of stoichiometric coefficients of products) * x. P_total = P_0 - x + nx = P_0 + (n-1)x. Therefore: x = (P_t - P_0)/(n-1). P_A = P_0 - x = P_0 - (P_t - P_0)/(n-1) = (nP_0 - P_t)/(n-1). For A -> B + C (n=2): P_A = 2P_0 - P_t. For A -> 3B (n=3): P_A = (3P_0 - P_t)/2. At completion (t -> inf): P_inf = nP_0 (all A converted to products). The rate constant: k = (2.303/t)log(P_0/P_A). This approach is used in JEE problems where pressure data is given instead of concentration data. Common trap: incorrectly accounting for stoichiometry when calculating P_A from P_total.

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