The decomposition of according to the equation: 2(g) -> 4(g) + (g) is a first-order reaction. After — Chemical Kinetics Chemistry Question
Question
The decomposition of $N_2O_5$ according to the equation: 2$N_2O_5$(g) -> 4$NO_2$(g) + $O_2$(g) is a first-order reaction. After 30 min, from the start of the decomposition in a closed vessel, the total pressure developed is found to be 300 mm of Hg and on complete decomposition, the total pressure is 600 mm of Hg. The rate constant of the reaction is (ln 1.2 = 0.18)
💡 Solution & Explanation
The reaction is: $N_2O_5$(g) -> 2$NO_2$(g) + 1/2 $O_2$(g). Let the initial pressure of $N_2O_5$ be P_0. At time t, P_total = P_0 + 1.5x. At t = inf, P_inf = 2.5 P_0 => 600 = 2.5 P_0 => P_0 = 240 mm Hg. At t = 30 min, P_total = 300 mm Hg => 240 + 1.5x = 300 => x = 40 mm Hg. The pressure of remaining $N_2O_5$ at 30 min is P_N2O5 = P_0 - x = 240 - 40 = 200 mm Hg. The rate constant is K = 1/t * ln(P_0/P_N2O5) = 1/30 * ln(240/200) = 1/30 * ln(1.2) = 0.18/30 = 6.0 × 10^-3 min^-1.