A mixture of 0.5 mole of `CO` and 0.5 mole of `CO_(2)` is taken in a vessel and allowed to effuse out through a pinhole into another vessel which has vacuum If a total of A mole has effused out in time t show that `M_(1)A +M_(2) (1-A) =36` where `M_(1)` and `M_(2)` are mean molar masses of the mixture that has effused out and the mixture still remaining in vessel respectively .

Explanation

Before diffusion ltbr gtMole of `CO =0.5`
Mole of `CO_(2) =0.5`
Total mole diffused out `=A`
Let mole of `CO` diffused `=a`
and Mole of `CO_(2)` diffused `=b`
Then `a + b= A`
Now, `M_(1)` Mean molar mass of diffused portion
`M_(1) = (a xx28 + 44 xx b)/((a +b)) = (28a +44b)/(A)`
Also `M_(2)` = Mean molar mass of left portion
`=((0.5 -a) xx 28+(0.5 -b)xx44)/((0.5 -a) + (0.5 -b))`
`=(14-28a +22-44b)/(1-(a+b))`
`=(36 - 28a -44b)/(1-A)`
`M_(2) = (36)/(1-A) - (28a +44b)/(1 -A)`
`M_(2) = (36)/(1-A) - (M_(1)A)/(1-A)`
`:. M_(2) (1-A) = 36 -M_(1) A`
or `M_(1) A +M_(2) (1-A) = 36` .