A straight glass tube has two inlets X and Y at the two ends. The length of the tube is 200 cm. HCl gas through inlet X and `NH_3` gas through inlet Y are allowed to enter the tube at the same time. White fumes first appear at a point Pinside the tube. Find the distance of P from X.

Explanation

According to Graham's law of diffusion
`(Rate of diffusion of HCl)/(Rate of diffusion of NH_(3))=sqrt((M_(NH_(3)))/(M_(HCl)))` (`1`)

Let the distance between `P` and `x` be `d cm`.
Then the distance between`P` and `y` will be `(200-d)cm`.
These two gases meet at point `P` in time `t`.
Rate of diffusion`=(Distance)/(Time)`
Rate of diffusion of `HCl=(d)/(t)`
Rate of diffusion of `NH_(3)=(200-d)/(t)`
Putting in equation (`i`), we get
`(d//t)/((200-d)//t)=sqrt((17)/(36.5))`
or `(d)/(200-d)=0.6824`
`:. d=81.12 cm`