Ideal Gas Equation (AQA A Level Physics): Revision Note

Ideal Gas Equation

• An ideal gas is a specific type of gas which:

  • Has molecules with negligible volume

  • Collisions which are elastic

  • Cannot be liquified

  • Has no interactions between the molecules (except during collisions)

  • Obeys the (ideal) gas laws (Boyles law, Charles’ law and Pressure law)

• All of these can occur at any temperature or pressure

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

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

• An ideal gas is therefore defined as:

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

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

$\mathrm{n}=\frac{\mathit{p}\mathit{V}}{\mathit{R}\mathit{T}}$

Step 3: Substitute in values

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

T = 15 °C + 273.15 = 288.15 K

$\mathrm{n}=\frac{4.5\times {10}^7\times 8.3\times {10}^{-3}}{8.31\times 288.15}=155.98=160\mathrm{mol}\left(2\mathrm{s}.\mathrm{f}.\right)$