States of Matter and Thermochemistry
Scope
This domain covers gas behavior (ideal and nonideal), kinetic molecular theory, intermolecular forces and phase diagrams, plus calorimetry, Hess's law, enthalpies of formation, and the sign conventions that govern heat flow.
Core rules
- Ideal gas law PV = nRT with T in kelvin; van der Waals corrections account for molecular volume (b) and attraction (a).
- Graham's law: effusion rate ratio = √(M₂/M₁).
- Intermolecular force strength: ion–dipole > hydrogen bonding > dipole–dipole > London dispersion; dispersion grows with polarizability and molecular size.
- Calorimetry: q = mcΔT for a solution, q = CΔT for a bomb calorimeter, and q_reaction = −q_surroundings.
- Hess's law: enthalpy is a state function, so any path summing to the overall reaction gives the same ΔH. ΔH°f = 0 for elements in their standard states.
Worked example
50.0 mL of 0.100 M HCl is mixed with 50.0 mL of 0.100 M NaOH and the temperature rises 6.8 °C. Assume density 1.00 g/mL and c = 4.18 J/g·°C. Total mass = 100.0 g, so q = 100.0 × 4.18 × 6.8 = 2842 J = 2.84 kJ released. Moles of water formed = 0.100 × 0.0500 = 0.00500 mol. ΔH_neutralization = −2.84 kJ / 0.00500 mol = −568 kJ/mol, negative because the mixture warms.
Traps
- Reversing the sign: exothermic reactions have negative ΔH, and q_system = −q_surroundings.
- Using only one solution's mass in a mixing calorimetry problem.
- Putting Celsius into PV = nRT instead of kelvin.
- Forgetting that ΔH°f of an element is zero, or that Hess's law requires flipping signs when reversing equations.