If a sample gas is collected over water. The atmospheric pressure is 778 mm and the temperature is 30°C. If the vapor pressure of water at 30 C is 31.8 mm, what is the pressure of the gas?

P = 746.2 mmHg or 0.9818 atm

Explanation:

First, we have a sample gas (This can be hydrogen, argon, nitrogen or any other gas) that was collected with a pressure of 778 mmHg. We also know the vapor pressure which is 31.8 mmHg. To get the pressure that the gas is exerting, we can assume that the atmospherical pressure is the total pressure of the whole system. Therefore we can use the following expression:

Pt = Pw + Pg   (1)

Where:

Pt: total pressure

Pw: water pressure

Pg: gas pressure

From (1) we can solve for the gas pressure and have:

Pg = Pt - Pw

Replacing the data we have:

Pg = 778 - 31.8

If you want this value in atm, you should divide it by 760 mmHg (Conversion from mmHg to atm):

Pg = 746.2 / 760