Chemical Kinetics

 32) 6.82 x 10^-3 s^-1          n = 0.0250 mol N₂O₅          V = 2.0 L

       N₂O₅(g) 2NO₂(g) + O₂(g)

       (a) Δt = 2.5 min x 60 s/min = 150 s

             ln[A]_t = -kt + ln[A]₀

             ln[N₂O₅]_t = -kt + ln[N₂O₅]₀ = -kt + ln[n/V]₀

             ln[N₂O₅]_t = -6.82 x 10^-3 s^-1 x 150 s + ln[0.0250/2.0]₀

             ln[N₂O₅]_t = -5.41

             [N₂O₅]_t = e^-5.41 = 4.5 x 10^-3 M

             [N₂O₅] = n/V

             n_N2O5 = 4.5 x 10^-3 mol N₂O/L x 2.0 L = 9.0 x 10^-3 mol N₂O₅

       (b) n_N2O5 = 0.010 mol N₂O₅

             [N₂O₅]_t = n/V = 0.010 mol N₂O₅/2.0 L = 0.0050 M

             ln[N₂O₅]_t = -kt + ln[N₂O₅]₀

             ln(0.0050) = -6.82 x 10^-3 s^-1 x Δt + ln(0.0125)

              ln(0.0050/0.0125) = -6.82 x 10^-3 s^-1 x Δt

             Δt = 130 s

       (c) [N₂O₅]₀ = n/V = 0.0250 mol N₂O₅/2.0 L = 0.0125 M

            [N₂O₅]_t1/2 = 1/2[N₂O₅]₀

            ln[N₂O₅]_t = -kt + ln[N₂O₅]₀

            ln(1/2 x [N₂O₅]₀/[N₂O₅]₀) = -6.82 x 10^-3 s^-1 x Δt

            Δt = 102 s