Question

(11 marks) At 65 degree C, the compound N2O5 decomposes in the gas phase to give nitrogen dioxide and oxygen, following first order kinetics. The partial pressure of N2O5 in a flask takes 12.0 minutes to decrease from 0.850 atm to 0.650 atm at this temperature. a. (4 marks) What is the rate constant and half-life for the decomposition of N2O5 at this temperature? b. (3 marks) At what time does the partial pressure of N2O5 in the flask reach 0.350 atm? c. (4 marks) At a temperature of 75 degree C, it takes 8.5 minutes for the partial pressure of N2O5 to decrease from 0.850 atm to 0.650 atm. What is the activation energy for this reaction?

Answer 1

$k\: =\: \frac{2.303}{t}\; log\: \frac{P_{0}}{(2P_{0}-P_{t})}$

$k\: =\: \frac{2.303}{12*60}\; log\: \frac{0.850}{(2*0.850-0.650)}$

$k\: =\: \frac{2.303}{720}\; log\: \frac{0.850}{(1.7-0.650)}$

$k\: =\: 0.003198\; log\: \frac{0.850}{(1.7-1.05)}$

$k\: =\: 0.003198\; log\: \frac{0.850}{(0.65)}$

$k\: =\: 0.003198\; log\: 1.3076$

$k\: =\: 0.003198\; *\: 0.1164$

$k\: =\: 0.0003722\: \; sec^{-1}$

ii) Half life period

$t_{\frac{1}{2}}\; =\: \frac{0.693}{k}$

$t_{\frac{1}{2}}\; =\: \frac{0.693}{0.0003722}$

$t_{\frac{1}{2}}\; =\: 1861.90\: sec^{-1}$