Question

The decomposition of dinitrogen pentoxide $\left(N_2{O}_5\right)$ follows first order rate law. Calculate the rate constant from the given data:
$t=800$ sec $\left[N_2{O}_5\right]=1.45$ $mol$ $L^{-1}=\left[A_1\right]$
$t=1600$ sec $\left[N_2{O}_5\right]=0.88$ $mol$ $L^{-1}=\left[A_2\right]$

Answer 1

Applying the formula,
$k=\frac{2.303}{(t_2-t_1)}{\log }_{10}\frac{\left[A_1\right]}{\left[A_2\right]}$
$=\frac{2.303}{(1600-800)}{\log }_{10}\frac{1.45}{0.88}$
$=\frac{2.303}{800}\times 0.2169=6.24\times {10}^{-4}{sec}^{-1}$