4PH1

Ideal Gases

Solids, Liquids & Gases · 1 question type

Practise

Exam Frequency Analysis

Past paper frequency (2018 to 2024)

This topic accounts for approximately 7% of your exam marks.

stable
Low
Stable7%

Gas law calculations (Boyle's Law, pressure-temperature) and kinetic theory explanations appear regularly.

Statement

  • At constant volume and for a fixed amount of an ideal gas:

P ∝ T (in kelvin)

  • Equivalently, if subscript 1 marks the initial state and subscript 2 marks a later state:

p₁ / T₁ = p₂ / T₂

  • where:
    • p₁, p₂ = pressures in Pa (any consistent unit, as long as both are the same)
    • T₁, T₂ = absolute temperatures in kelvin (always, never °C)
Two containers of the same fixed volume: heating the gas makes the molecules move faster, so they collide with the walls more often and harder, raising the pressure (P ∝ T)
Source: The Pressure Law by Save My Exams

Using the equation

  • Convert any Celsius readings to kelvin first by adding 273. Forgetting to do this is one of the most common exam mistakes
  • Rearranging for p₂: p₂ = p₁ × (T₂ / T₁)
  • Rearranging for T₂: T₂ = T₁ × (p₂ / p₁)
Worked example

Pressure law calculation

A gas in a sealed container has a pressure of 80 kPa at a temperature of 27 °C. The container is heated until the temperature reaches 127 °C. Calculate the new pressure. (Volume stays constant.)

Solution:

  • Convert both temperatures to kelvin: T₁ = 27 + 273 = 300 K, T₂ = 127 + 273 = 400 K
  • Substitute into p₁/T₁ = p₂/T₂: 80/300 = p₂/400
  • Rearrange: p₂ = 80 × 400/300
  • p₂ = 107 kPa (to 3 s.f.)