Question

A 500 mL gas sample is collected over water at a pressure of 740mmHg and 25 degrees C. What is the volume of the dry gas at STP?

Answer 1

Answer:

The volume of the dry gas at STP is = 0.4314 L

Explanation:

We are given:

Total vapor pressure = 740 mmHg

Also, considering Vapor pressure of water = 23.78 mmHg

Vapor pressure of gas = Total vapor pressure - Vapor pressure of water = (740 - 23.78) mmHg = 716.22 mmHg

We use the equation given by ideal gas which follows:

$PV=nRT$

where,

P = pressure of the gas = 716.22 mmHg

V = Volume of the gas = 500 mL = 0.5 L  ( 1 ml = 0.001 L )

T = Temperature of the gas = $25^oC=[25+273]K=298K$

R = Gas constant = $62.3637\text{ L.mmHg }mol^{-1}K^{-1}$

n = number of moles of gas = ?

Putting values in above equation, we get:

$716.22mmHg\times 0.5L=n\times 62.3637\text{ L.mmHg }mol^{-1}K^{-1}\times 298K\\\\n=\frac{716.22\times 0.5}{62.3637\times 298}=0.01926mol$

At STP, 1 mole of gas yields a volume of 22.4 L

So,

0.01926 mole of gas yields volume of $0.01926\times 22.4\ L$

Hence, the volume of the dry gas at STP is = 0.4314 L