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Ideal Gas Equation (Edexcel International A Level Physics)

Revision Note

Lindsay Gilmour

Last updated

Ideal Gas Equation

  • When calculating for gases, assume that the gas is an ideal gas

  • The three gas laws (explained below) can be combined to create one equation in terms of pressure, volume, temperature and amount of gas. 

Ideal gas equation 2

The Boltzmann Constant, k

  • The Boltzmann constant k is used in the ideal gas equation and is defined as:

k equals R over N subscript A

  • Where:

    • R = molar gas constant

    • NA = Avogadro’s constant

  • Boltzmann’s constant therefore has a value of

k space equals space fraction numerator 8.31 over denominator 6.02 space cross times space 10 to the power of 23 end fraction space equals space 1.38 space cross times space 10 to the power of negative 23 space end exponent J space K to the power of negative 1 end exponent

  • The Boltzmann constant relates the properties of microscopic particles (e.g. kinetic energy of gas molecules) to their macroscopic properties (e.g. temperature)

    • This is why the units are J K-1

  • Its value is very small because the increase in kinetic energy of a molecule is very small for every incremental increase in temperature

The Gas Laws

  • The ideal gas laws are the experimental relationships between pressure (P), volume (V) and temperature (T) of an ideal gas

  • The mass and the number of molecules of the gas is assumed to be constant for each of these quantities

Boyle’s Law

  • If the temperature T of an ideal gas is constant, then Boyle’s Law is given by:

Boyle's Law_2

  • This means the pressure is inversely proportional to the volume of a gas

Gas Volumes at Low Temperatures & High Pressures

Pressure increases when a gas is compressed

  • The relationship between the pressure and volume for a fixed mass of gas at constant temperature can also be written as:

P1V1 = P2V2

  • Where:

    • P1 = initial pressure (Pa)

    • P2 = final pressure (Pa)

    • V1 = initial volume (m3)

    • V2 = final volume (m3)

Charles's Law

  • If the pressure P of an ideal gas is constant, then Charles’s law is given by:

V ∝ T

  • This means the volume is proportional to the temperature of a gas

    • The relationship between the volume and thermodynamic temperature for a fixed mass of gas at constant pressure can also be written as:

    Charles's Law

  • Where:

    • V1 = initial volume (m3)

    • V2 = final volume (m3)

    • T1 = initial temperature (K)

    • T2 = final temperature (K)

9-7-charles_-law_edexcel-al-physics-rn

Pressure Law

  • If the volume V of an ideal gas is constant, the Pressure law is given by:

P ∝ T

  • This means the pressure is proportional to the temperature

    • The relationship between the pressure and thermodynamic temperature for a fixed mass of gas at constant volume can also be written as:

Pressure Law

  • Where:

    • P1 = initial pressure (Pa)

    • P2 = final pressure (Pa)

    • T1 = initial temperature (K)

    • T2 = final temperature (K)

9-7-pressure-law_edexcel-al-physics-rn

Worked Example

A storage cylinder of an ideal gas has a volume of 8.3 × 103 cm3. The gas is at a temperature of 15oC and a pressure of 4.5 × 107 Pa. Calculate the number of molecules of gas in the cylinder.

Answer:

Step 1: Write down the ideal gas equation

p V space equals space N k T

Step 2: Rearrange the equation for the number of molecules, N

N space equals space fraction numerator p V over denominator k T end fraction

Step 3: Substitute in values

V space equals space 8.3 space cross times space 10 cubed space c m cubed space equals space left parenthesis 8.3 space cross times space 10 cubed right parenthesis space cross times space 10 to the power of negative 6 space end exponent equals space 8.3 space cross times space 10 to the power of negative 3 end exponent space m cubed

T space equals space 15 space C presuperscript o space plus space 273.15 space equals space 288.15 space K

N space equals space fraction numerator left parenthesis 4.5 space cross times space 10 to the power of 7 right parenthesis space cross times space left parenthesis 8.3 space cross times space 10 to the power of negative 3 end exponent right parenthesis over denominator open parentheses 1.38 space cross times space 10 to the power of negative 23 end exponent close parentheses space cross times space 288.15 end fraction space equals space 9.4 space cross times space 10 to the power of 25 space end exponent molecules space left parenthesis 2 space s f right parenthesis

Examiner Tips and Tricks

After you solve a problem using any of the gas laws (or all of them combined), always check whether your final result makes physical sense - e.g. if you are asked to calculate the final pressure of a fixed mass of gas being heated at constant volume, your result must be greater than the initial pressure given in the problem (since Gay- Lussac's law states that pressure and absolute temperature are directly proportional at constant volume).

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    Lindsay Gilmour

    Author: Lindsay Gilmour

    Expertise: Physics

    Lindsay graduated with First Class Honours from the University of Greenwich and earned her Science Communication MSc at Imperial College London. Now with many years’ experience as a Head of Physics and Examiner for A Level and IGCSE Physics (and Biology!), her love of communicating, educating and Physics has brought her to Save My Exams where she hopes to help as many students as possible on their next steps.