A sample of gas occupies 50.0 L at 15.0 Celsius and 640.0 mmHg pressure. What is the volume at STP?

Answer 1

There are multiple approaches to solving this problem. The equation that will always work for comparing an ideal gas in state A to state B is

P₁V₁ ⁄n₁T₁ = P₂V₂ ⁄n₂T₂

I will provide the more conceptually impressive approach. At STP, 1 mole of an ideal gas occupies a volume of 22.4 L; you have, no doubt, been taught this fact before. Thus, if we know the number of moles of ideal gas that we have, we can simply use the above molar-volume at STP to find the volume (note: n₁ = n₂ for an isolated ideal gas).

Rearranging the ideal gas law gives

n = PV ⁄ RT

I'll use R = 0.08206 L·atm ⁄mol·K which requires us to get pressure in unit atm and temperature in unit Kelvin.

T = 15.0°C + 273.15 = 288.15 K

P = 640.0 mmHg × 1 atm ⁄ 760 mmHg = 0.8421 atm

Thus,

n = (0.8421)(50.0) ⁄ (0.08206)(288.15) = 1.78 mol

When this ideal gas is at STP, the volume is

V = 1.78 mol × 22.4 L⁄mol = 39.9 L