Question

Hydrogen gas is filled in a vessel at $20^{\circ }C$ at a certain pressure. Some gas is allowed to escape from the vessel and the temperature of the vessel is then raised to $40^{\circ }C$ to obtain the same pressure. Then the fraction of the gas allowed to escape is -

Answer 1

Answer: 0.06

Initially temperature of hydrogen gas molecules $T=293K$
Pressure $=P$ (let), volume $=V$ (let)
$n_i=\frac{PV}{RT}=\frac{PV}{293R}$....(1)
Let finally $n_f$ moles of $H_2$ are left in the vessel
Final temperature $=40^{\circ }C=313K$
Final pressure $=P$
$n_f=\frac{PV}{313R}$....(2)
Fraction of gas allowed to escape
$=\frac{n_i-n_f}{n_i}$
$=\frac{\frac{PV}{293R}-\frac{PV}{313R}}{\frac{PV}{293R}}$
$=\frac{(313-293)}{313\times 293}\times 293=\frac{20}{393}$
$=0.068$