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 s $\left[N_2{O}_5\right]=1.45\text{mol}{L}^{-1}=\left[A_1\right]$
t = 1600 s $\left[N_2{O}_5\right]=0.88\text{mol}{L}^{-1}=\left[A_2\right]$

Take:
$lo{g}_{10}\frac{\left[1.45\right]}{\left[0.88\right]}=0.217$

• A. $3.12\times {10}^{-1}{s}^{-1}$
• B. $6.24\times {10}^{-5}{s}^{-1}$
• C. $6.24\times {10}^{-4}{s}^{-1}$
• D. $3.12\times {10}^{-4}{s}^{-1}$

Answer 1

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

Applying the formula,
$k=\frac{2.303}{(t_2-t_1)}lo{g}_{10}\frac{\left[A_1\right]}{\left[A_2\right]}$
$=\frac{2.303}{(1600-800)}lo{g}_{10}\frac{\left[1.45\right]}{\left[0.88\right]}$
$=\frac{2.303}{800}\times 0.217=6.24\times {10}^{-4}{s}^{-1}$