Question

The vapour pressure of water at 20 °C is 17.5 torr. What will be the no. of moles of water present in one litre of air at 20 °C and 40% relative humidity. (R =0.082 L atm/mol-k)

• (A) 4.2 × 10^–4 mole
• (B) 4.2 × 10^–6 mole
• (C) 3.82 × 10^–4 mole
• (D) 3.82 × 10^–6 mole

Answer 1

The Correct Option is C

Explanation:
Relative humidity (RH) = $\frac{\text{ Partial pressure of }{\mathrm{H}}_2\mathrm{O}\text{ in air }}{\text{ Vapour pressure of }{\mathrm{H}}_2\mathrm{O}}$$\therefore$ Partial pressure of ${\mathrm{H}}_2\mathrm{O}=\mathrm{RH}\times$ Vapour pressure of ${\mathrm{H}}_2\mathrm{O}$$=$$\frac{40}{100}\times 17.5$$=7$ torr$=$$\frac{7}{760}$ atm$=0.0092\mathrm{atm}$Now $\mathrm{PV}=\mathrm{nRT}$$\therefore$$n=\frac{PV}{RT}=\frac{0.0092\times 1}{0.082\times 293}$$=0.000382$ mole$=3.82\times {10}^{-4}\mathrm{mole}$