Intermolecular Forces and Gas Laws: Quick Revision

A brief note on Intermolecular Forces and Gas Laws. Read it before a test. Try each question at the end before you open its answer.

Forces and states

• A gas has thermal energy $RT$ larger than the attraction between its particles. A liquid or a solid has an attraction that wins.
• Intermolecular forces: London dispersion (all molecules, grows with the number of electrons), dipole-dipole, hydrogen bonds (H on N, O or F) and ion-dipole.
• Boiling breaks forces between molecules. It does not break bonds inside them.
• Water boils far above $\text{H}_2\text{S}$ because of hydrogen bonds.

The gas laws

• Boyle: $P_1V_1 = P_2V_2$ at constant $T$ and $n$.
• Charles: $V_1/T_1 = V_2/T_2$ at constant $P$ and $n$. Gay-Lussac: $P_1/T_1 = P_2/T_2$ at constant $V$ and $n$.
• Avogadro: $V \propto n$, so equal volumes of gases at the same $T$ and $P$ have the same number of molecules.
• Temperature is always in kelvin: $T = t + 273.15$.

The ideal gas equation

• $PV = nRT$. Choose $R$ to match the units: $8.314\ \text{kPa L K}^{-1}\ \text{mol}^{-1}$, $0.08314\ \text{L bar K}^{-1}\ \text{mol}^{-1}$ or $0.08206\ \text{L atm K}^{-1}\ \text{mol}^{-1}$.
• Density: $d = \dfrac{PM}{RT}$. Molar mass: $M = \dfrac{dRT}{P}$.
• Molar volume: $22.71\ \text{L}$ at $273.15\ \text{K}$ and $1\ \text{bar}$, $22.41\ \text{L}$ at $1\ \text{atm}$, and $24.79\ \text{L}$ at $298.15\ \text{K}$ and $1\ \text{bar}$.

Mixtures and diffusion

• Dalton: $P_i = x_iP_{\text{total}}$, and $P_{\text{total}} = \sum P_i$ for gases that do not react.
• Gas over water: $P_{\text{gas}} = P_{\text{atm}} - P_{\text{water}}$.
• Graham: $\dfrac{r_1}{r_2} = \sqrt{\dfrac{M_2}{M_1}}$ at the same $T$ and $P$. The lighter gas is faster.

A worked example

A $2.5\ \text{L}$ flask holds $0.18\ \text{mol}$ of a gas at $330\ \text{K}$. Find the pressure in bar, and the pressure when the gas is cooled to $275\ \text{K}$.

1. The pressure at $330\ \text{K}$. $P = \dfrac{nRT}{V} = \dfrac{0.18 \times 0.08314 \times 330}{2.5} = 1.98\ \text{bar}$.
2. The cooling. The volume and the amount do not change, so $P \propto T$.
3. The new pressure. $P_2 = 1.98\ \text{bar} \times \dfrac{275}{330} = 1.65\ \text{bar}$.

Practice with new numbers

A program to try

The program finds the molar volume under three standards and the density of two gases.

Mistakes to avoid

• Temperature in Celsius in a gas law. Use kelvin.
• A wrong $R$. The units of $R$ must match $P$ and $V$.
• Forgetting water vapour when a gas is collected over water.
• Turning Graham's law upside down. The lighter gas is faster.
• Saying that boiling breaks covalent bonds. It breaks intermolecular forces.

Check yourself

1. A gas fills $5.0\ \text{L}$ at $2.0\ \text{bar}$. It is pushed into $2.0\ \text{L}$ at the same temperature. What is the new pressure?

2. Why does $\text{HF}$ boil at a higher temperature than $\text{HCl}$?

3. Which is faster through a pinhole, $\text{CH}_4$ or $\text{O}_2$, and by what factor?

Sources

• OpenStax, Chemistry 2e, Chapters 9 and 10.
• IUPAC Gold Book, entry on standard pressure.