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 $35mL$. The rate constant is equal to :

• A. $\frac{1}{15}log\frac{35}{26}$
• 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 $\frac{1}{15}log\frac{35}{26}$

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