Ideal gas equation

This is a mathematical relationship between the pressure, volume, temperature and number of moles of a gas. The word ideal is an indication that it is an approximation. Real gases obey the ideal gas equation to a greater or lesser extent, and there are alternative equations which give more accurate results. However, the ideal gas equation gives useful results:

pV = nRT

where p = pressure in N m^-2, V = volume in m³, n = number of moles in mol, T = absolute temperature in K and R is the gas constant (8.314 J mol^-1 K^-1).

It can be used to calculate the molar mass of a compound if we know the mass of substance and the other variables.

These calculations are not required on most specifications.

Example

0.164 g of a liquid was vaporized in gas syringe at 100°C and standard atmospheric pressure of 101 kPa. The volume occupied by the vapour was 86.6 cm³. What is the molar mass of the compound?

kPa is a kilopascal = 10³ N m^-2, so p = 101 kPa = 1.01 × 10⁵ N m^-2

V = 86.6 cm³ = 86.6 × 10^-6 m³

n = ?

R = 8.314 J mol^-1 K^-1

T = 100°C = 373 K

We need to rearrange the equation to give n = pV/RT

n = 1.01 × 10⁵ × 86.6 × 10^-6 /(8.314 × 373) = 0.00282 mol

mass of one mole = mass of substance ÷ number of moles

mass of one mole = 0.164/0.00282 = 58 g mol^-1

Exercise

1. 0.112 g of a liquid was vaporized in gas syringe at 100°C and atmospheric pressure of 98 kPa. The volume occupied by the vapour was 76.9 cm³. What is the molar mass of the compound? Answer

2. Use the ideal gas equation to estimate the mass of air present in a typical-sized room of dimensions 4 m × 4 m × 3 m. Assume room temperature and pressure. Answer