Question

The density of acetic acid vapor at $300 \,K$ and $1$ atm is $5\, mg\, cm^{-3}$. The number of acetic acid molecules in the cluster that is formed in the gas phase is closest to

• A. 5
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (B)

Given,
density of acetic acid = $5 \,mg\, cm^{-3}$
Pressure = $1\, atm$
Temperature = $300\, K$
We know that
$pV = RT,$
(when, $n = 1$)
Also,$V=\frac{m}{p}$
$\therefore pM=pRT$
$M=\frac{5\times0.0821\times300}{1}=123.15g$
Molar mass of acetic acid, $CH_{3} COOH$
$= 12\times1+ 1\times3+ 12\times1+ 16\times2 + 1= 60\,g$
$\therefore $ Number of molecules of acetic acid
$=\frac{123.15}{60}\approx 2$