The decomposition of N_20_5 is represented below. Its half-life is independent o

Question

The decomposition of N_20_5 is represented below. Its half-life is independent of concentration and the rate constant is 5.21 times10^'5 s^-1 at a temperature of 28.0 degreeC. The activation energy is 46.2 kJ/mol. 2 N_2O_s(g) rightarrow 4 NO_2(g) + O_2(g) Calculate the concentration of N0_2(g) produced after 35 minutes if the reaction starts with 0.110 M N_2O_s(g) at 28.0 degreeC. "a" in the integrated rate law equals 2 in this case. Calculate the rate constant for the reaction at 55.0 degreeC. Fully explain why the rate constant at 55.0 degreeC differs from the rate constant at 28.0 degreeC.

Explanation / Answer

Since half-life is independent of concentration, this is a first order reaction.

Given rate constant, k = 5.21x10-5 s-1

(a): Given time, t = 35 min = 35 min x (60 s / 1 min) = 2100 s

initial concentration, [N2O5]0 = 0.110 M

For first order reaction, the concentration of the reactant after time, t, [N2O5]t is given by

[N2O5]t = [N2O5]0 x (exp)-kt = 0.110 M x (exp)^ (- 5.21x10-5 s-1 x 2100 s) = 0.0986 M

----------------- 2N2O5(g) -------> 4NO2(g) + O2(g)

init.con: 0.110 M ------------ 0 M ------- 0 M

change: - 2y ------------------ + 4y ------- +y

After 35 min: (0.110 - 2y)M, 4y M, ---- y M

Hence [N2O5]t = (0.110 - 2y)M = 0.0986 M

=> 2y = 0.110 M - 0.0986 M

=> y = 0.0057 M

Hence concentration of NO2(g) after 35 min = 4y = 4 x 0.0057 M = 0.0228 M (answer)

(b):

Rate constant varies with temperature through Arrheniusequation which is

ln(k2 / k1) = (Ea / R) x (1/T1 - 1/T2)

where T1 = 28.0 C = 301 K , k1 = 5.21x10-5 s-1

T2 = 55.0 C = 328 K, k2 = ?

=> ln(k2 / 5.21x10-5 s-1 ) = (46200 J.mol-1 / 8.314 J.mol-1K-1) x (1/301K - 1/328K)

=>  ln(k2 / 5.21x10-5 s-1 ) = 1.5197

=> k2 = 2.38 x 10-4 s-1 (answer)

(c): Rate constant increases with temperature and it almost doubles for every 10 DegC rise in temperature. The temperature dependence of rate constant can be calculated from Arrhenius equation. Hence the rate constant at 55.0 DegC is more that the rate conatant at 28 DegC

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