A vessel contains 8gm of a gas at a pressure P and temperature 500K. The gas leaves through a small hole. The mass of the gas leaked out when the pressure is P/2 and temperature is 400K is 

Given that $m_1=8, P_1=P,T_1=500k$

$and P_2=\frac{P}{2} ,T_2=400k$

From equation PV=mRT

$P_1{V}_1=m_{1}R{T}_1$

$P{V}_1=8\times R\times 500 .....\left(1\right)$

$P_2{V}_2=m_{2}R{T}_2$

$\frac{P}{2}{V}_2=m_{2}R\times 400 .....\left(2\right)$

From (1) and (2)

$2=\frac{8\times 5}{m_2\times 4}$

$m_2=5$

 The mass of the gas leaked out is

$∆m=m_1-m_2=8-5=3gm$