Gas laws and the ideal gas equation

Chemistry · Gases. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

Four quantities describe a sample of gas: pressure P, volume V, temperature T and number of moles n. The gas laws tell us how one changes when another is changed and the rest are kept constant.

Temperature must always be on the Kelvin scale. Its zero is absolute zero, about −273 °C (0 K), the temperature at which the volume of an ideal gas would become zero. It is never reached in practice because real gases liquefy first.

Boyle's law, Charles's law and Avogadro's law combine into one equation, the general gas equation PV = nRT. From it we can find any one quantity, and also the molar mass or the density of a gas.

Rules to remember

Common mistake

Students put the temperature in °C into the equations. Add 273 first, and choose the value of R that matches the units of pressure and volume.

Worked example

1.4 g of a gas occupies 1.23 dm3 at 1 atm and 300 K. What is its molar mass? (R = 0.0821 dm3 atm K−1 mol−1)

  1. Use M = mRT ÷ PV. The units are atm, dm3 and K, so R = 0.0821.
  2. RT = 0.0821 × 300 = 24.63.
  3. M = (1.4 × 24.63) ÷ (1 × 1.23) = 34.48 ÷ 1.23 = 28.0.

Answer: About 28 g mol−1, so the gas could be nitrogen, N2.

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