Question

The rate constant for the first-order decomposition of N2O5 by the reaction
2 N2O5 (g)  4 NO2(g) + O2(g) is k, = 3.38 x 10-5 s
-1 at 25 C. What is the half-life of N2O5?
What will be the partial pressure, initially 500 Torr, at ( a) 50 s; (b) 20 min, (c) 2 hr
after initiation of the reaction?

Answer 1

For the unit of k which is second ^-1 we can depict that this a first order reaction

for the first order reaction t1/2 = 0.693/k = 0.693 /3.38 X 10^-5 = 0.205 x 10^5 s or 2.05 X 10^4 s

As we know for first order reation A = Ao e^-kt

therefore P = Po e^-kt after 50 sec

P = 500 torr e^-3.38X 10^-5 x 50 = 499.155 torr

After 20 min = 20X60 = 1200sec

P = 500 e^-3.38X10^-5X1200 = 480.125 torr

After 2 hr = 2 X60 X60 x60 = 7200 sec

P = 500 e^-3.38 X10 ^-5 X7200 = 391 torr