Thermodynamics and Rate Processes
Thermodynamics and Rate Processes tests whether you can decide if a reaction is feasible, how far it proceeds, and how fast it gets there. It combines solution thermodynamics, Ellingham diagrams, electrochemistry, reaction kinetics, diffusion, and transport.
Core rules
- ΔG=ΔH−TΔS; at equilibrium ΔG=0 and ΔG°=−RT ln K.
- Activity is referenced to a defined standard state; Raoult for solvent, Henry for dilute solute.
- Ellingham lines plot ΔG° per mole O2; slope is −ΔS°, so phase changes produce breaks. The lowest line at a temperature is the stronger reductant.
- Electrochemical free energy: ΔG=−nFE. A positive cell emf means spontaneous discharge.
- Fick's first law J=−D dC/dx; second law ∂C/∂t=D ∂²C/∂x² for constant D. Arrhenius: k=k0 exp(−Q/RT).
- In gas-solid reactions, shrinking-core models distinguish chemical reaction control from ash diffusion control by their time dependence.
Worked example
For a reaction with ΔG°=−200,000+50T J/mol at 1000 K: ΔG°=−200,000+50,000=−150,000 J/mol. Then ln K=−ΔG°/(RT)=150,000/(8.314×1000)=18.04, so K≈6.8×10^7. The large K means products are strongly favoured at this temperature; it does not by itself give the reaction rate.
Traps
- Using ΔG instead of ΔG° when calculating K.
- Mixing standard states, especially pure solid vs 1 wt% solution.
- Reversing the sign in ΔG=−nFE.
- Assuming a favourable ΔG means fast kinetics.
- Applying steady-state diffusion equations to transient problems.