the rates of diffusion of 2 gases are in the ratio 1:4. if the ratio of their masses present in the mixture effused is 2:3, calculate the ratio of their mole fraction.

please explain briefly!!!

We have,

So putting the values we get ,

= 1/4

So,  M₂ /M₁ = 1/ 16

Now we have weight ratio of the gases : W₁ /W₂ = 2/3

So, mole fraction of gase 1, x₁ =  n₁/n₁+n₂  and  x₂ =  n₂/n₁+n₂

Now , n₁ =W₁ /M₁ , and  n₂ =W₂ /M₂ ,

So, putting the values and solving we get,  

 x₁/x₁= W₁ x M₂ /W₂ x M₁ =2 x 1/ 3 x 16 = 2/48 = 1/24

So ratio of mole fractions  x₁: x₁= 1:24

I hope it is clear now!