The rate constant k , for the reaction N_ 2 O_ 5( g) arrow2 NO_ 2( g) +1 / 2 O_ 2( g) is 2.3 ×10^ -2 s^ -1 . Which equation given below describes the change of [N_2 O_5] with time? [N_2 O_5]_0 and [N_2 O_5]_t correspond

Correct answer: D. [N_2 O_5]_0 [~N_2 O_5]_t =k t aligned & k=(1)/(t) a( initial ) a-x( after time t) & k t= [N_2 O_5]_0 [~N_2 O_5]_t aligned

AIIMS 2004

AIIMS 2004 · Chemistry · Chemical Kinetics

The rate constant k , for the reaction N_ 2 O_ 5( g) arrow2 NO_ 2(...

The rate constant

k

, for the reaction

\mathrm{N}_{2} \mathrm{O}_{5(\mathrm{ g})} \rightarrow2 \mathrm{NO}_{2(\mathrm{ g})}+1 / 2 \mathrm{O}_{2(\mathrm{ g})}is 2.3 \times10^{-2} \mathrm{ s}^{-1}. Which equation given below describes the change of \left[\mathrm{N}_2 \mathrm{O}_5\right] with time? \left[\mathrm{N}_2 \mathrm{O}_5\right]_0 and \left[\mathrm{N}_2 \mathrm{O}_5\right]_t correspond to concentration of \mathrm{N}_2 \mathrm{O}_5 initially and at time

.

A $\left[\mathrm{N}_2 \mathrm{O}_5\right]_t=\left[\mathrm{N}_2 \mathrm{O}_5\right]_0+k t$
B $\left[\mathrm{N}_2 \mathrm{O}_5\right]_t=\left[\mathrm{N}_2 \mathrm{O}_5\right]_0 e^{k t}$
C $\log \left[\mathrm{N}_2 \mathrm{O}_5\right]_t=\log \left[\mathrm{N}_2 \mathrm{O}_5\right]_0+k t$
D $\ln \frac{\left[\mathrm{N}_2 \mathrm{O}_5\right]_0}{\left[\mathrm{~N}_2 \mathrm{O}_5\right]_t}=k t$

D. $\ln \frac{\left[\mathrm{N}_2 \mathrm{O}_5\right]_0}{\left[\mathrm{~N}_2 \mathrm{O}_5\right]_t}=k t$

\begin{aligned}& k=\frac{1}{t} \ln \frac{a(\text{ initial })}{a-x(\text{ after time } t)}\\ & k t=\ln \frac{\left[\mathrm{N}_2 \mathrm{O}_5\right]_0}{\left[\mathrm{~N}_2 \mathrm{O}_5\right]_t} \end{aligned}