Chemical Kinetics Question 40
Question: The rate constant k, for the reaction $ N_2O_5(g)\to $
$ 2NO_2(g)+\frac{1}{2}0_2(g) $ is $ 2.3\times {10^{-2}}{s^{-1}} $ . Which equation given below describes the change of $ [N_2O_5] $ with time- $ {{[N_2O_5]}_0} $ and $ {{[N_2O_5]} _{t}} $ correspond to concentration of $ N_2O_5 $ initially and at time, t [AIIMS 2004]
Options:
A) $ {{[N_2O_5]} _{t}}={{[N_2O_5]}_0}+kt $
B) $ {{[N_2O_5]}_0}={{[N_2O_5]} _{t}}e^{kt} $
C) $ {\log _{10}}{{[N_2O_5]} _{t}}={\log _{10}}{{[N_2O_5]}_0}-kt $
D) $ In\frac{{{[{N_2}O_5]}_0}}{{{[{N_2}O_5]} _{t}}}=kt $
Show Answer
Answer:
Correct Answer: D
Solution:
Rate constant $ =2.3\times {10^{-2}}{{\sec }^{-1}} $ It means it is a first order reaction (because unit of rate constant is sec-1) For first order reaction $ K=\frac{1}{t}\ln \frac{a}{a-x} $
$ Kt=\ln \frac{a}{a-x}=\ln \frac{{{[N_2O_5]}_0}}{{{[N_2O_5]} _{t}}} $
