Calculating with Ideal Gases

Solving an Ideal Gas Problem

The Method, Step by Step

List the known quantities and convert them into the international system (Pa, m³, K, mol).
Identify the unknown quantity and isolate it in PV = nRT.
Calculate, then convert the result into a convenient unit if needed (for example from m³ to liters).
Check that the order of magnitude is reasonable.

A Concrete Example

We seal n = 2.5 mol of dioxygen in a bottle, at a temperature of 20°C (i.e. T = 293 K). The pressure measured in the bottle is P = 3.0×10^5 Pa. What is the volume of the bottle?

We isolate V in the ideal gas law:

V = n*R*T / P
V = (2.5 * 8.314 * 293) / (3.0e5)
V = 0.0203 m3
V = 20.3 L

(the volume of the bottle is about 20.3 liters)

Checking the Order of Magnitude

We can check with the molar volume at 20°C, 1 atm (about 24.0 L/mol): at this pressure, 2.5 mol would occupy about 2.5 * 24.0 = 60 L. Here, the actual pressure (3.0×10^5 Pa) is about 3 times greater than 1 atm (1.013×10^5 Pa): the volume must therefore be about 3 times smaller, i.e. about 20 L. The result of 20.3 L is consistent.

And to Find a Pressure

The method is identical. For example, for n = 0.20 mol of gas sealed in a volume V = 5.0 L (i.e. 5.0×10^-3 m³) at T = 300 K, we isolate P:

P = n*R*T / V

Common Mistake