Cobalt(II) hydroxide precipitates once the ion product exceeds its solubility product:
[OH-] = 10^(pH-14)
Q = [Co2+]·[OH-]^2
Ksp(T)= Ksp0·exp(-ΔH/R·(1/T - 1/T0))
S = Q / Ksp(T) (supersaturation ratio)
When S > 1 the solution is supersaturated: nucleation rate follows classical nucleation theory, J ∝ exp(-B/ln²S) — sharply more nuclei at high S, almost none near S≈1 — and every existing particle grows at a rate proportional to (S−1), consuming dissolved Co²⁺ as it does. Push pH high with the "Add NaOH" pulse and you get a burst of many small crystallites (nucleation-dominated); keep S just above 1 and a few particles grow large instead (growth-dominated) — the same trade-off that sets real precipitate morphology. Drop S below 1 (low pH) and precipitate slowly redissolves.
- Ksp0 ≈ 5.92×10⁻¹⁵ mol³/L³ at 298 K (literature value for Co(OH)₂).
- ΔH is an approximate endothermic dissolution enthalpy — raising temperature raises Ksp, making precipitation harder, which is why the temperature slider shifts S.
- This is a simplified teaching model of real nucleation/growth kinetics, not a lab-grade morphology predictor.