Question

A straight glass tube as shown has 2 inlets $X$ and $Y$ at the two ends of $200\text{cm}$ long tube. $HCl$ gas through inlet $X$ and $N{H}_3$ gas through inlet $Y$ are allowd to enter in the tube at the same time and under the identical conditions. At a point $P$ inside the tube both the gases meet first. The distance of point $P$ from $X$ is:

• A. $118.9\text{cm}$
• B. $81.1\text{cm}$
• C. $91.1\text{cm}$
• D. $108.9\text{cm}$

Answer 1

The correct option is B $81.1\text{cm}$

Rate α $\frac{1}{M.W}$​ (Graham's law of diffusion)
More rate means more distance is covered. So rate α distance.
So,$\frac{r_{HCl}}{r_{N{H}_3}}=\sqrt{\frac{M.W_{N{H}_3}}{M.W_{HCl}}}=\sqrt{\frac{17}{36.5}}$
$\Rightarrow \frac{x}{(200-x)}=\sqrt{\frac{17}{36.5}}$
$\Rightarrow \frac{x}{200-x}=\sqrt{\frac{17}{36.5}}\Rightarrow x=81.13\text{cm}$