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

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