The decomposition of N_2O_5 is represented below. Its half-life is independent o

Question

The decomposition of N_2O_5 is represented below. Its half-life is independent of concentration and the rate constant is 5.21 Times 10^5 s^-1 at a temperature of 28.0 degreeC. The activation energy is 46.2 kJ/mol. 2 N_2O_5(g) rightarrow 4 NO_2(g) + O_2(g) a) Calculate the concentration of NO_2(g) produced after 35 minutes if the reaction starts with 0.110 M N_2O_5(g) at 28.0 degreeC. b) Calculate the rate constant for the reaction at 55.0 degreeC. c) Fully explain why the rate constant at 55.0 degreeC differs from the rate constant at 28.0 degreeC.

Explanation / Answer

a)

For a reaction aA + bB -------> cC + dD

r = -dA/adt = - dB/bdt = dC/cdt = dD/ddt

For the given reaction r = k[N2O5] is a first order reaction (see units of k)

Let [N2O5]t=35 = x and  [N2O5]i = 0.11 M and dt = 35 minutes or 2100 s

So r = -d[N2O5]/2dt

2*k*x = (0.11-x)/2100

4200*5.21*10-5*x = 0.11-x

x = 0.09 M

b) K = Ae-Ea/RT So lnK = lnA - Ea/RT -------- (I)

T1 = 28oC or 301K, K1 = 5.21*10-5

T2 = 55oC or 328K, K2 = K and Ea = 46.2 KJ/mol

Putting values of K1 and K2 in (1) and subtracting we get

ln(K1/ K2) = Ea/R (1/T2 - 1/T1)

ln(5.21*10-5/k) = 46.2*103/8.314(1/328 - 1/301) = 905.35 s-1

c) Clearly since the rate constant value depends on temperature it changes with the change in temperature

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