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A straight glass tube has two inlets x a...

A straight glass tube has two inlets `x` and `y` at 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 flames first appear at a point `P` inside the tube. Find the distance of `P` from `x`.

Text Solution

Verified by Experts


Mass of the `HCl (g) = 1 + 35.5 = 36.5 g`
Molar mass of `NH_(3) (g) = 14 + 3 xx 1 = 17.0 g`
Accroding to Graham's law of diffusion,
`("Rate of diffusion of HCl (g)")/("Rate of diffusion of" NH_(2) (g)) = sqrt(((M_(NH_(3)))/(M_(HCl)))) = sqrt((17.0)/(36.5)) = 0.6824`
Let the distance between the points X and P = d cm
`:.` Distance between te point `Y` and `P = (200 - d) cm`
The distance travelled by the vapours of gas is directly proportional to rate of diffusion `:. (d)/(200 - d) = ("Rate of diffusion of" HCl (g))/("Rate of diffusion of" NH_(3)(g)) = 0.6824`
or `d = 0.6824 xx 200 - 0.6824d`
or `d + 0.6824 = 0.6824 xx 200 = 136.48`
or `1.6824 d = 136.48` or `d = (136.48)/(1.6824) = 81.12`
Thus, the distance between points P and X `= 81.12 cm`
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