Rutile carbochlorination converts solid TiO₂ ore to volatile titanium tetrachloride, the feedstock for the Kroll process:
TiO2(s) + 2Cl2(g) + C(s) -> TiCl4(g) + CO2(g)
Each ore grain reacts outside-in: an unreacted TiO₂ core shrinks inside a porous gangue/ash shell as chlorine diffuses in and TiCl₄ vapor diffuses out. Under chemical-reaction control this shrinking-core model (SCM) gives
1 - (1-x)^(1/3) = k_eff * t
k_eff = k_ref * exp[-(Ea/R)(1/T - 1/Tref)] * f(Cl2) * f(C) / (r0/r_ref)
with Ea ≈ 95 kJ/mol (typical for TiO₂ carbochlorination), so a hotter bed and finer grind both raise the rate — smaller r0 means more surface area per unit volume, so k_eff scales as 1/r0. Reaction time here is compressed roughly 1:2000 for visualization; the temperature, stoichiometry and particle-size dependence are computed exactly, only the clock is sped up.
The limiting reagent sets the maximum reachable conversion X_max = min(Cl2 ratio / 2, C ratio / 1) — starve the bed of chlorine or coke below the 2:1 / 1:1 stoichiometry and conversion plateaus below 100% however long you wait, exactly like a real limiting-reagent problem.
The carbon also drives the Boudouard equilibrium C + CO₂ ⇌ 2CO, which shifts toward CO as temperature rises (favoured above roughly 800–850 °C at 1 atm) — watch the CO:CO₂ readout invert as you raise the temperature slider. Excess free Cl₂ above stoichiometry also chlorinates Fe/V oxide impurities in the ore (FeCl₃, VCl₄), so the impurity-chloride readout climbs with both temperature and Cl₂ excess.