Question

Arsine produces hydrogen gas on heating. The pressure of produced hydrogen was measured, at consant volume and temperature, as follows:

Time (hours)	0	5.5	6.5	8
Pressure (atm)	0.965	1.060	1.076	1.100

Calculate the specific rate and half-life peroid of reaction assuming the reaction to be of first-order.

Answer 1

Specific rate $=$ rate when concentration is unity

$=$ rate constant $k$

Now, $k=\frac{1}{k}ln\frac{P_0}{P_t}$

$k=\frac{1}{5.5}ln\frac{0.965}{1.060-0.965}$

$=\frac{1}{5.5}ln\frac{0.965}{0.095}$

$k=0.42h{r}^{-1}$

$t_{1/2}=\frac{ln2}{k}=\frac{0.693}{0.42}=1.65$ hrs