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_3gas 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.

A straight glass tube has two inlets X and Y at the two ends. The leng

1.	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_3gas 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.
Answer» Solution :This PROBLEM can easily be understood with the help of the following figure. White fumes appear at point P due to the formation of `NH_4Cl`according to the equation `NH_3 (g) + HCl(g) to NH_4 CI(g)` At point P, HCl gas and `NH_3` gas meet together and react to form fumes of `NH_4 CL`. SUPPOSE the distance of point P from the inlet X is x cm. `:.`The distance travelled by HCl gas = x cm and, the distance travelled by `NH_3 " gas " = (200 - x) cm`. The time TAKEN by HCl gas to reach point P will be the same as the time taken by `NH_3` to reach point P. Let this time be equal to t. Rate of diffusion of HCl gas `(r_1) = (" distance travelled ")/("time") =X/t` Rate of diffusion of `NH_3 " gas " (r_2) (200-x)/t` MOLECULAR mass of `HCl (M_1) = 36.5` Molecular mass of `NH_3 (M_2) = 17` According to Graham.s law of diffusion, `r_1/r_1 =sqrt(M_2/M_1)` `:.(x//t)/((200 - x)//t)= sqrt(17/(36.5))` or `x/(200-x) = 0.6825 " or " x = 81.13 cm` Hence, white fumes appear at a distance of 81.13 cm from the inlet X.