A 4: 1 molar mixture of He and CH4 is contained in a vessel at 20 bar pressure. Due to a hole in the vessel, the gas mixture leaks out. What is the composition of the mixture effusing out initially?

A 4: 1 molar mixture of He and CH4 is contained in a vessel at 20 bar

1.	A 4: 1 molar mixture of He and CH4 is contained in a vessel at 20 bar pressure. Due to a hole in the vessel, the gas mixture leaks out. What is the composition of the mixture effusing out initially?
Answer» Solution :Total PRESSURE of the mixture = 20 bar Since He and `CH_4` are PRESENT in the molar RATIO 4:1, we have partial pressure of Help `He(P_(He)) = 4/5xx 20 = 16` bar and partial pressure of `CH4(P_(Ch_4)) = 1/5 xx 20 = 4` bar If t is the time taken in effusion, rate of diffusion of `He(r_(He)) = (""^nHe)/t` and rate of diffusion of `CH_4(r_(CH_4)) =(""^nCH_4)/t` where `n""^Heand n""^CH_4` are respectively the number of moles of He and `CH_4` effused initially. According to Graham.s law of diffusion, for two gases at ifferent pressures, we have `r_(He)/r_(CH_4)=sqrt(M_(CH_4)/M_(He))xxP_1/P_2` `:. ""(""^nHe//t)/(""^nCH_4//t)=sqrt(16/4)xx16/4` or`(""^nHe)/(""^nCH_4)=8/1` Hence, the initially effused mixture contains the moles of helium and methane in the ratio 8: 1