Question

The decomposition of an aqueous solution of ammonium nitrite was studied. The volume of nitrogen gas collected at different intervals of time was follows:
$\begin{array}{ccccc}Time\left(minutes\right)& 10& 15& 20& \infty \\ Vol.of{N}_2\left(mL\right)& 6.25& 9.00& 11.40& 35.05\end{array}$
From the above data prove that the reaction is of the first order.

Answer 1

For this reaction:

$K=\frac{1}{t}ln\frac{V_{\infty }}{V_{\infty }-V_t};V_{\infty }=35.05$
Values of K at different times are:-

Time	$V_{\infty }-V_t$	$\frac{1}{t}ln\frac{V_{\infty }}{V_{\infty }-V_t}=k$
10 min	35.05-6.25=28.80	$\frac{1}{10}ln\frac{35.05}{28.80}=0.019{min}^{-1}$
15 min	35.05-9.00=26.05	$\frac{1}{15}ln\frac{35.05}{26.05}=0.019{min}^{-1}$
20 min	35.05-11.40=23.65	$\frac{1}{20}ln\frac{35.05}{23.65}=0.019{min}^{-1}$
25 min	35.05-13.65=21.40	$\frac{1}{25}ln\frac{35.05}{21.40}=0.019{min}^{-1}$

As value of K is constant it shows that it is first order reaction.