In a container m g of a gas is placed . After some time some gas is allowed to escape from container.The pressure of the gas becomes half and it`s absolute temperature 2/3 rd .The amount of gas escaped is?

Let the molecular mass of the gas be M.So moles of gas be m/M.Let P1,T1,ni be the initial pressure , temperature ,moles of the gas respectively.And P1,T2,n2 be the final pressure, temperature and moles of the gas.P1=P ,T1=T,n1=m/MP1=P /2,T2=2T/3,n2=nApplying P1/T1×n1=P1/T2×n2.We get n2=3/4n1Let m1 be the mass of gas left.m1/M =3/4m/MWe get m1=3/4m.Therefore 1/4 of the initial amount of gas has escaped.

P V = nRT

Initial pressure = P
Final = P/2
Initial Tem = T
Final is 2/3T

P1/P2 = n1.T1/n2.T2

P1/(P/2) = n1.T/n2.2/3T

2=3n1/2n2

n2=3/4n1

using n = W/M

n = m/M

m2/M = 3/4 . m1/M

M is getting canceled

m2 = 3/4 m1

Final answer = 75% of m