Thermodynamics and Kinetics of Metallurgical Processes
This domain tests whether you can decide if a reaction is feasible, how far it proceeds, and how fast. Feasibility comes from ΔG; extent from equilibrium constants and activities; rate from Arrhenius behaviour and transport.
Core rules
- ΔG = ΔH − TΔS; a reaction is feasible when ΔG < 0. At equilibrium ΔG = 0 exactly, which does not mean the reaction stops - it means forward and reverse rates balance.
- ΔG = ΔG° + RT ln Q; at equilibrium ΔG° = −RT ln K.
- Ellingham diagrams plot ΔG° per mole of O2 against temperature. The lower line is the more stable oxide; a metal can reduce any oxide lying above its own line, and line crossings define the temperature where the reducing agent becomes effective.
- Gibbs phase rule: F = C − P + 2 for pressure and temperature variables.
- Activities: Raoult's law for the solvent, Henry's law for dilute solutes; the Henrian (1 wt%) standard state is used for dilute liquid metal solutions.
- Arrhenius: k = A exp(−Ea/RT). Fick's first law J = −D dc/dx (steady state); second law for transient diffusion. Parabolic oxidation or scale growth follows x² = kt.
Worked example
A process rate constant at 800 °C (1073 K) is k1. Find k2 at 850 °C (1123 K) when Ea = 150 kJ/mol. ln(k2/k1) = −(Ea/R)(1/T2 − 1/T1) = −(18,041)(8.9047 × 10⁻⁴ − 9.3197 × 10⁻⁴) = 0.749, so k2/k1 = 2.11. A 50 K rise roughly doubles the rate.
Traps that cost marks
Putting degrees Celsius into an Arrhenius or Gibbs expression. Mixing kJ and J, or forgetting R = 8.314 J/mol·K. Claiming ΔG = 0 means no reaction. Using Fick's first law for a transient problem. Reading an Ellingham line as a rate rather than a driving-force comparison.