$word_{count}$: 200

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 = $\frac{P_t - P_0}{(n-1)}$. $P_A$ = $P_0$ - x = $P_0$ - $\frac{P_t - P_0}{(n-1)}$ = $\frac{nP_0 - P_t}{(n-1)}$. For A -> B + C (n=2): $P_A$ = 2$P_0$ - $P_t$. For A -> 3B (n=3): $P_A$ = $\frac{3P_0 - P_t}{2}$. At completion (t -> inf): $P_{inf}$ = $nP_0$ (all A converted to products). The rate constant: k = $\frac{2.303}{t}$log$\frac{P_0}{P_A}$. 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 $P_{total}$.