Ideal gas model assumptions

• An ideal gas is modelled as moving particles whose individual volumes are negligible.

• There are no intermolecular forces between the particles.

• All collisions between particles and with container walls are elastic.

• In an elastic collision, the particles’ total kinetic energy is conserved.

The diagram represents gas particles in motion and collisions with the container walls. The ideal-gas model additionally assumes negligible particle volume, no intermolecular forces and elastic collisions. Source

Molar volume

• Molar volume is the volume occupied by one mole of gas at a specified temperature and pressure.

• For an ideal gas, molar volume is constant when temperature and pressure are fixed.

• Use $n = \dfrac{V}{V_m}$ when the molar volume at the stated conditions is provided.

• The ideal-gas molar volume at standard temperature and pressure (STP) is given in the data booklet.

Temperature–volume relationship

• For a fixed amount of ideal gas at constant pressure, volume increases as absolute temperature increases.

• The relationship is $V \propto T$.

• Therefore, $\dfrac{V}{T} = \text{constant}$ when pressure and amount of gas remain unchanged.

• A graph of $V$ against $T$ in kelvin is a straight line through the origin for an ideal gas.

• Always use absolute temperature in kelvin when analysing or calculating this relationship.

Combined gas law

• For a fixed amount of ideal gas, use $\dfrac{P_1V_1}{T_1} = \dfrac{P_2V_2}{T_2}$.

• Subscripts $1$ and $2$ represent the initial and final conditions.

• Convert all temperatures to kelvin before substitution.

• Use SI units for pressure and volume as required by the syllabus.

• Rearrange the equation first when solving for an unknown pressure, volume or temperature.

Real gases and model limitations

• Real gases do not behave exactly like the ideal-gas model.

• Deviation is greatest at low temperature and high pressure.

• At low temperature, intermolecular attractions become more significant, contradicting the assumption of no intermolecular forces.

• At high pressure, particles are closer together, so their actual particle volume can no longer be considered negligible.

• The ideal-gas model therefore becomes less accurate when its simplifying assumptions become significant.

Pressure–volume relationship

• For a fixed amount of ideal gas at constant temperature, pressure increases as volume decreases.

• The relationship is $P \propto \dfrac{1}{V}$.

• Therefore, $PV = \text{constant}$ when temperature and amount of gas remain unchanged.

• A graph of $P$ against $V$ is a decreasing curve.

• A graph of $P$ against $\dfrac{1}{V}$ is a straight line through the origin.

For a fixed amount of gas at constant $T$, increasing $V$ causes $P$ to decrease. The curved $P$ against $V$ relationship is consistent with $P \propto \dfrac{1}{V}$. Source

Pressure–temperature relationship

• For a fixed amount of ideal gas at constant volume, pressure increases as absolute temperature increases.

• The relationship is $P \propto T$.

• Therefore, $\dfrac{P}{T} = \text{constant}$ when volume and amount of gas remain unchanged.

• A graph of $P$ against $T$ in kelvin is a straight line through the origin for an ideal gas.

• Identify which variable is held constant before interpreting any pressure, volume and temperature graph.

Ideal gas equation and molar mass

• Use the ideal gas equation $PV = nRT$ to relate pressure, volume, amount and temperature.

• Use $P$ in pascals, $V$ in $m^3$, $n$ in moles and $T$ in kelvin.

• The gas constant $R$ and the ideal gas equation are provided in the data booklet.

• Rearrange $PV = nRT$ before substituting numerical values.

• For a gas sample of mass $m$ and molar mass $M$, use $n = \dfrac{m}{M}$.

• Combining the equations gives $M = \dfrac{mRT}{PV}$, allowing molar mass to be determined from experimental gas data.v