Question

What is the density of wet air with 75% relative humidity at 1 atm and 300 K? Given vapour pressure of $H_{2}O$ is 30 torr and average molar mass of air is $29gmo{l}^{-}$

• A. 1.815 g/L
• B. 1.165 g/L
• C. 1.365 g/L
• D. 2.165 g/L

Answer 1

The correct option is B 1.165 g/L

% Relative humidity $=\frac{\text{Partial pressure of}{H}_{2}O}{\text{Relative pressure of}{H}_{2}O}\times 100$

$\begin{array}{cc}75& =\frac{P_{\text{H2O}}}{30}\times 100\\ P_{{\dot{H}}_{2}O}& =22.5torr\end{array}$

% of $H_{2}O$ vapour in $air=\frac{22\cdot 5}{760}\times 100=2096$

molar mass of wet air

$\begin{array}{c}=\frac{29\times 97.04+2.96\times 18}{100}\\ =28.67\end{array}$

density of wet air $=\frac{PM}{RT}=\frac{1\times 28.67}{0.0821\times 300}$

$=1.1659/L$

Correct Answer - B