Question

At the start of an experiment, one end of a U-tube of 6 mm glass tubing is immersed in concentrated ammonia solution and the other end in concentrated hydrochloric acid. At the point in the tube where vapour of ammonia and hydrochloric acid meet, white cloud is formed. At what fraction of the distance along the tube from the ammonia solution, the white cloud is first formed?

• A. 0.682
• B. 0.534
• C. 0.466
• D. 0.595

Answer 1

The correct option is D 0.595

$\frac{\text{Rate}\left(N{H}_3\right)}{\text{Rate}\left(HCl\right)}=\sqrt{\frac{M\left(HCl\right)}{M\left(N{H}_3\right)}}=\sqrt{\frac{36.5}{17}}=1.4653$


Thus $N{H}_3$ gas moves faster than $HCl$. Hence, white fumes (of $N{H}_{4}Cl$) are formed away from the $N{H}_3$ end. Total length of the tube $=AB+BC$
$AB=$ distance covered by $N{H}_3$ in time $t$
$BC=$ distance covered by $HCl$ in time $t$
$r_{N{H}_3}=\frac{AB}{t},r_{HCl}=\frac{BC}{t}$
$\frac{r_{N{H}_3}}{r_{HCl}}=\frac{AB}{BC}=1.4653$
$\frac{BC}{AB}=\frac{1}{1.4653}\Rightarrow \frac{BC}{AB}+1=\frac{1}{1.4653}+1$
$\frac{BC+AB}{AB}=\frac{2.4653}{1.4653}\Rightarrow \frac{AB}{\text{Total length}}=\frac{1.4653}{2.4653}=0.595$