C1. (6) The following data were obtained from the decomposition study of nitroge

Question

C1. (6) The following data were obtained from the decomposition study of nitrogen dioxide: 2NO2(g) -> 2N0(g) + O2(g) Temperature Initial Initial Rate of Decomposition NO2], M of NO2 (mol/L.s) 600 600 700 0.010 0.025 0.025 5.0 x 10-5 3.1 x 10-4 7.2 x 10-4 (a) Determine the rate law for the decomposition of NO2 and calculate the rate constants k (with appropriate unit) at 600 K and at 700 K, respectively (b) Calculate the activation energy for this reaction. (c) How long does it take for the concentrations of NO, to decrease from 0.025 M to 0.010 M

Explanation / Answer

a) order w.r.t NO2

R1/R2 = (a1/a2)^x

(5*10^-5/(3.1*10^-4)) = (0.01/0.025)^x

x = 2

rate law, rate = k[NO2]^2

K at 600k = rate/[NO2]^2 = 5*10^-5/0.01^2 = 0.5 M-1.S-1

k at 700k = 7.2*10^-4/0.025^2 = 1.152 M-1.S-1

b) ln(k2/k1) = Ea/R[1/T1-1/T2]

   ln(1.152/0.5) = (x/8.314)((1/600)-(1/700))

Ea = activation energy = 29.144 kj/mol

c) rate = dx/dt

   dt = dx/rate

      = (0.025-0.01)/(3.1*10^-4-(5*10^-5))

      = 57.7 sec

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