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Characteristics of Equilibrium Constant

What is the d...

Question

What is the density of wet air with $75 %$ relative humidity at $1 a t m$ and $300 K$ ? Given : vapour pressure of $H_{2} O$ is $30 t o r r$ and average molar mass of air is $29 g / m o l$ .

1.614 g / L

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0.96 g / L

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1.06 g / L

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1.164 g / L

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Solution

The correct option is D $1.164 g / L$
$%$ Relative humidity $= \frac{P a r t i a l p r e s s u r e o f H_{2} O}{V a p o u r p r e s s u r e o f H_{2} O} \times 100$
$75 = \frac{P_{H_{2} O}}{30} \times 100$
$P_{H_{2} O} = 22.5 t o r r$
$% o f H_{2} O$ vapour in air $= \frac{(22.5)}{760} \times 100 = 2.96$
Molar mass of wet air $= \frac{29 \times 97.04 + 2.96 \times 18}{100}$
$= \frac{2814.16 + 53.28}{100} = 28.67$
Density of wet air $= \frac{P M}{R T} = \frac{1 \times 28.67}{0.0821 \times 300}$
$= 1.164 g / L$

Option D is correct.

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What is the density of wet air with 75% relative humidity at 1atm and 300K? Given : vapour pressure of H2O is 30torr and average molar mass of air is 29g/mol.

What is the density of wet air with $75 %$ relative humidity at $1 a t m$ and $300 K$ ? Given : vapour pressure of $H_{2} O$ is $30 t o r r$ and average molar mass of air is $29 g / m o l$ .