Question

The half life of decomposition of $N_2{O}_5$ is a first order reaction represented by
$N_2{O}_5\to N_2{O}_4+1/2O_2$
After 15 min the volume of $O_2$ produced is 9mL and at the end of the reaction 35 mL. The rate constant is equal to:

• A. $\frac{1}{15}ln\frac{35}{26}$
• B. $\frac{1}{15}log\frac{44}{26}$
• C. $\frac{1}{15}log\frac{35}{36}$
• D. None of the above

Answer 1

The correct option is A $\frac{1}{15}ln\frac{35}{26}$

$k=\frac{2.303}{t}log\frac{V_{\infty }}{V_{\infty }-V_t}$
$k=\frac{1}{t}ln\frac{V_{\infty }}{V_{\infty }-V_t}$
$k=\frac{1}{15}ln\frac{35mL}{(35-9)mL}=\frac{1}{15}ln\frac{35}{26}$