Question

The density of acetic acid vapor at $300K$ and $1$ atm is $5mgc{m}^{-3}$. 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 = $5mgc{m}^{-3}$
Pressure = $1atm$
Temperature = $300K$
We know that
$pV=RT,$
(when, $n=1$)
Also,$V=\frac{m}{p}$
$\therefore pM=pRT$
$M=\frac{5\times 0.0821\times 300}{1}=123.15g$
Molar mass of acetic acid, $C{H}_{3}COOH$
$=12\times 1+1\times 3+12\times 1+16\times 2+1=60g$
$\therefore$ Number of molecules of acetic acid
$=\frac{123.15}{60}\approx 2$