States of Matter, Gases and Solutions
This domain tests the kinetic model of gases, the ideal gas equation applied to real laboratory data, phase behaviour, and the quantitative description of solutions.
The ideal gas equation
pV = nRT with p in Pa, V in m³, T in kelvin and R = 8.314 J K−1 mol−1. Substitute T = θ + 273. Molar mass follows from M = mRT/pV. Dalton's law states that the total pressure of a mixture equals the sum of partial pressures, so a gas collected over water has p(gas) = p(total) − p(water vapour).
Deviations from ideality
Real gases deviate most at high pressure and low temperature, where molecules are close together: attractive forces reduce the observed pressure and molecular volume makes the container effectively smaller. The van der Waals equation corrects for both.
Phase behaviour
A vapour pressure curve rises with temperature and meets the boiling point where vapour pressure equals external pressure. On a phase diagram the triple point is where all three phases coexist and the critical point marks the end of the liquid–vapour boundary. Lowering external pressure lowers the boiling point, which is why vacuum distillation works.
Solutions
Molarity c = n/V (temperature dependent); molality = moles of solute per kg of solvent (temperature independent). Dilution obeys c1V1 = c2V2. Colligative properties - boiling point elevation, freezing point depression, osmotic pressure - depend on the number of dissolved particles, so 1 mol of NaCl gives roughly twice the effect of 1 mol of glucose.
Worked example
2.00 g of a gas occupies 1.12 dm³ at 273 K and 101 kPa. M = mRT/pV = (2.00 × 8.314 × 273)/(101000 × 1.12 × 10⁻³) = 4539/113.1 = 40.1 g mol−1. The gas is argon.
Traps that cost marks
- Using degrees Celsius in pV=nRT; always convert to kelvin.
- Forgetting to subtract the vapour pressure of water for gas collected over water.
- Mixing molarity and molality, or assuming molarity is temperature independent.
- Treating volatile solutes as contributing to colligative effects.
- Using dm³ where the equation needs m³.