Question

The decomposition of dinitrogen pentoxide $\left(N_2{O}_5\right)$ follows first order rate law. What will be the rate constant from the given data?
At $t=800s,\left[N_2{O}_5\right]=1.45mol{L}^{-1}$
At $t=1600s,\left[N_2{O}_5\right]=0.88mol{L}^{-1}$

• A. $3.12\times {10}^{-4}{s}^{-1}$
• B. $6.24\times {10}^{-4}{s}^{-1}$
• C. $2.84\times {10}^{-4}{s}^{-1}$
• D. $8.14\times {10}^{-4}{s}^{-1}$

Answer 1

The correct option is B $6.24\times {10}^{-4}{s}^{-1}$

From first-order rate law equation:

$k=\frac{2.303}{(t_2-t_1)}\log \frac{\left[A_1\right]}{\left[A_2\right]}$

$k=\frac{2.303}{(1600-800)}\log \frac{1.45}{0.88}=\frac{2.303}{800}\times 0.2169$

$=6.24\times {10}^{-4}{s}^{-1}$.

Hence, the correct answer is option $\text{B}$.