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 `29 g mol^(-1)`.

Options

A. 1.614 g/L
B. 0.96 g/L
C. 1.06 g/L
D. 1.164 g/L

Answer

D

Explanation

% of Relative humidity = `("Partial pressure of " H_(2) O)/("Vapour pressure of" H_(2) O) xx 100`
`75 = (P_(H_2O))/(30) xx 100 implies p_(H_(2) O) = 22.5` torr , % of `H_(2) O` vapour in air `= ((22.5))/(760) xx 100 = 2.96`
Molar mass of wet air = `(29 xx 97.04 + 2.96 xx 18)/(100) = (2814 + 53.28)/(100)= 28.67`
Density of wet air = `(PM)/(RT) = (1 xx 28.67)/(0.0821 xx 300) = 1.164` g/L