Question

A sample of hydrogen fluoride gas (only $HF$ molecules) is collected in a vessel and left for some time. Then, a constant molar mass of the sample is experimentally determined as $34gmo{l}^{-1}$. Assume that this abnormal molar mass is due to dimerization as well as trimerization of some $HF$ molecules (no molecules in any other polymeric forms) and the mole ratio of monomeric and trimeric forms of hydrogen fluoride molecules present is 4 : 1. What percentage of hydrogen fluoride molecules is dimerized?

• A. $50$
• B. $58.8$
• C. $76.47$
• D. $17.65$

Answer 1

The correct option is B $58.8$

According to the question:
Initial concentration of $HF$ = $a$
Dimerised concentration of $HF$ = $x$ and Trimerised concentration of $HF$ = $y$
Reaction for the dimerisation of $HF$
$2HF$ $\to$ $H_2{F}_2$
$a–(2x+3y)$ $x$
Reaction for the trimerisation of $HF$
$3HF$ $\to$ $H_3{F}_3$
$a–(3y+2x)$ $y$
From question, $\frac{y}{(a-(2x+3y\left)\right)}=\frac{1}{4}$ … (1)
and $a–(2x+3y)+x+(y\times 34)$ = $a\times 20$ … (2)
Where $34gmo{l}^{-1}$ = molar mass of sample and $20gmo{l}^{-1}$ = molar mass of $HF$
From $\left(1\right)$ and $\left(2\right)$: $a=17y=\frac{17}{5}\times x$

Percentage of $HF$ molecules dimerized
= $\frac{2x}{a}\times 100$ = $58.82\%$