CIE A Level Physics (9702) 2019-2021

Revision Notes

16.1.2 Ideal Gas Equation

Ideal Gas Equation

  • The equation of state for an ideal gas (or the ideal gas equation) can be expressed as:

pV = nRT

  • The ideal gas equation can also be written in the form:

pV = NkT

  • An ideal gas is therefore defined as:

A gas which obeys the equation of state pV = nRT at all pressures, volumes and temperatures

Worked example

Ideal_Gas_Equation_Worked_Example_-_Ideal_Gas_Equation_Question, downloadable AS & A Level Physics revision notes

Step 1:            Write down the ideal gas equation

Since the number of moles (n) is required, use the equation:

pV = nRT

Step 2:            Rearrange for the number of moles n

Ideal Gas Equation equation 1

Step 3:            Substitute in values

V = 8.3 × 103 cm3 = 8.3 × 103 × 10-6 = 8.3 × 10-3 m3

T = 15 oC + 273.15 = 288.15 K

Ideal Gas Equation equation 2

Exam Tip

Don’t worry about remembering the values of R and k, they will both be given in the equation sheet in your exam.

The Boltzmann Constant

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

The Boltzmann Constant equation 1

  • Where:
    • R = molar gas constant
    • NA = Avogadro’s constant
  • Boltzmann’s constant therefore has a value of

The Boltzmann Constant equation 2

  • 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

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