Thermodynamics - Quick Revision
System, surroundings and state
- Universe = system + surroundings. Open (exchanges matter + energy), closed (energy only), isolated (neither).
- State functions (U, H, S, G, p, V, T) depend only on the state, not the path. Path functions: q (heat), w (work).
- Adiabatic process: q = 0. Isothermal: T constant.
First law (energy conservation)
- DU = q + w. IUPAC signs: q positive when heat enters system; w positive when work done ON system.
- PV work (constant pex): w = -pex DV. Reversible isothermal: w = -2.303 nRT log(Vf/Vi).
- Constant volume: w = 0, DU = qV. Free expansion into vacuum: w = 0, q = 0, DU = 0.
Enthalpy
- H = U + pV (state function). At constant pressure DH = qp.
- DH = DU + Dng RT (Dng = moles of gaseous products - reactants).
- Exothermic: DH < 0. Endothermic: DH > 0.
- Cp - CV = R for an ideal gas. q = C DT.
Enthalpy changes & calorimetry
- Bomb calorimeter -> constant volume -> qV = DU. Constant-pressure calorimeter -> qp = DH.
- Types: formation (DfH, element reference state = 0), combustion (DcH, exothermic), fusion/vaporisation/sublimation (all positive), neutralisation, solution, lattice (Born-Haber).
- Hess's law: DH path-independent; DrH = sum of step enthalpies.
- Gas phase: DrH = (bond enthalpies of reactants) - (bond enthalpies of products).
Spontaneity, entropy and Gibbs energy
- Enthalpy decrease alone does NOT decide spontaneity (some endothermic reactions are spontaneous).
- Entropy S = measure of disorder; gas > liquid > solid. DS = qrev/T.
- Second law: spontaneous => DStotal = DSsys + DSsurr > 0. At equilibrium DS = 0.
- Third law: entropy of a perfect crystal = 0 at 0 K.
- Gibbs energy G = H - TS; DG = DH - TDS. DG < 0 spontaneous, > 0 non-spontaneous, = 0 equilibrium.
- DrG = -RT ln K = -2.303 RT log K. Strongly exothermic -> large K; strongly endothermic -> K << 1.
Temperature effect on spontaneity (DG = DH - TDS)
- DH-, DS+ -> spontaneous at all T. DH+, DS- -> never spontaneous.
- DH-, DS- -> spontaneous at low T. DH+, DS+ -> spontaneous at high T.
Common traps
- q and w are NOT state functions; DU is.
- Use w = q + DU with correct IUPAC signs (work BY system is negative).
- All enthalpies of fusion, vaporisation and sublimation are positive.
- DfH of an element in its reference state is zero, not unity.