Molar Gas Volume (DP IB Chemistry): Revision Note

Molar gas volume

• Gases in a container exert a pressure as the gas molecules are constantly colliding with the walls of the container

A particle model of a gas in a container

Changing gas volume

• Decreasing the volume (at constant temperature) of the container causes the molecules to be squashed together which results in more frequent collisions with the container wall

• The pressure of the gas increases

Gas molecule collision frequency with increasing pressure diagram

• Pressure is inversely proportional to volume (when temperature is constant):

P ∝

PV = a constant

• This is known as Boyle's Law

• We can show a graphical representation of Boyle's Law in three different ways:

  • A graph of pressure of gas plotted against 1 / volume gives a straight line

  • A graph of pressure against volume gives a curve

  • A graph of PV versus P gives a straight line

Sketch graphs of Boyles' Law

Changing gas temperature

• When a gas is heated (at constant pressure) the particles gain more kinetic energy

• This leads to more frequent collisions with the container walls

• To keep the pressure constant, the gas must expand, so the volume increases

• The volume is therefore directly proportional to the temperature in Kelvin (at constant pressure)

V ∝ T

= a constant

• This is known as Charles' Law

• A graph of volume against temperature in Kelvin gives a straight line

Gas molecule collision frequency with increasing temperature diagram

Changing gas pressure

• Increasing the temperature (at constant volume) of the gas causes the molecules to gain more kinetic energy

• The particles move faster and collide more frequently with the container walls

• This leads to an increase in pressure

• Therefore, pressure is directly proportional to temperature (in Kelvin) at constant volume

P ∝ T

= a constant 

• A graph of temperature in Kelvin of a gas plotted against pressure gives a straight line

Gas molecule collision frequency with increasing pressure at constant volume diagram

Pressure, volume and temperature

• Combining these three relationships together:

  • PV = a constant

  • V / T = a constant

  • P / T = a constant

• We can see how the ideal gas equation is constructed

  • PV / T = a constant

  • PV = a constant x T

• This constant is made from two components, the number of moles, n, and the gas constant, R, resulting in the overall equation:

PV = nRT

Changing the conditions of a fixed amount of gas

• When n (moles) and R (gas constant) are constant, the ideal gas law simplifies to:

• Where

  • P₁, V₁ and T₁ are the initial conditions of the gas

  • P₂, V₂ and T₂ are the final conditions of the gas

• The temperature must be in Kelvin