Question

A straight glass tube has 2 inlets $X$ and $Y$ at the two ends of a 200 cm long tube as shown in the figure. $HCl$ gas through inlet $X$ and $N{H}_3$ gas through inlet $Y$ are allowed to enter in the tube at the same time and under 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 cm
• B. 81.1 cm
• C. 150.1 cm
• D. 108.9 cm

Answer 1

The correct option is B 81.1 cm

Let $x$ cm be the distance travelled by the gas from $HCl$ side. So, the distance from $N{H}_3$ side is $(200-x)\text{cm}$. Consider at time 't' both the gases meet.

Rate of diffusion =$\frac{distancetravelled}{timetaken}$
$\frac{r_1}{r_2}=\frac{x}{200-x}$….(i)

Consider $r_1$ to be the rate of diffusion for $HCl$ and $r_2$ to be the rate of diffusion for $N{H}_3$.

So, according to Graham's law of diffusion,
$\frac{r_1}{r_2}$ = $\sqrt{\frac{MolarMassofN{H}_3\left(M_2\right)}{MolarMassofHCl\left(M_1\right)}}..\left(ii\right)$

$\frac{r_1}{r_2}=\sqrt{\frac{17}{36.5}}$
Using (i) and (ii)
$\Rightarrow \frac{x}{200-x}=\sqrt{\frac{17}{36.5}}$
= $1.46x=200-x$
$\Rightarrow x=81.13\text{cm}$