States of Matter and Thermodynamics
Domain 4: States of Matter and Thermodynamics
This domain tests gas-law calculations and the energy bookkeeping of physical and chemical change: first law, enthalpy, Hess's law, entropy, and Gibbs energy.
Core rules
- Ideal gas: PV=nRT; use kelvin. Dalton's law: P_total=Σp_i; mole fraction gives partial pressure. Graham's law: r ∝ 1/√M. The van der Waals equation corrects for finite volume (b) and attraction (a).
- First law: ΔU=q+w; work done on the system is positive in this convention. At constant volume, q_v=ΔU; at constant pressure, q_p=ΔH. ΔH=ΔU+Δn_gRT.
- Hess's law: enthalpy is a state function, so the route is irrelevant. Standard enthalpy of formation of an element in its standard state is zero.
- ΔG=ΔH−TΔS. Spontaneity requires ΔG<0; ΔH negative and ΔS positive always favour spontaneity. At equilibrium ΔG=0.
- Calorimetry: q=mcΔT; for a reaction, q_reaction=−q_calorimeter, so sign matters.
Worked example
2 mol ideal gas expands isothermally and reversibly at 300 K from 10 L to 20 L. w=−nRT ln(V2/V1)=−2 x 8.314 x 300 x ln2=−3.46 x 10^3 J. ΔU=0 for an ideal gas at constant T, so q=+3.46 x 10^3 J. The gas does work, so w is negative and heat is absorbed.
Traps
- Inserting Celsius into PV=nRT or ΔG equations.
- Reversing q and w sign conventions.
- Using ΔH=ΔU without the Δn_gRT correction.
- Thinking a spontaneous reaction must be fast.
- Ignoring that standard states specify 1 bar (or older 1 atm), not 1 M for gases.