This is the classic persulfate–iodide clock reaction (a Landolt-type clock), the same chemistry as the 3D version of this simulator — here solved with an explicit numerical integrator instead of a scripted timer. Two reactions run at once in the same well-mixed flask:
(1) S₂O₈²⁻ + 2 I⁻ → 2 SO₄²⁻ + I₂ (slow, rate-determining)
(2) I₂ + 2 S₂O₃²⁻ → 2 I⁻ + S₄O₆²⁻ (fast, "invisible" scavenger)
Reaction (1) is second order overall — first order in each reactant — with an Arrhenius-activated rate constant:
rate r = k[I⁻][S₂O₈²⁻]
k(T) = A·exp(−Eₐ / RT)
d[I⁻]/dt = −2r
d[S₂O₈²⁻]/dt = −r
d[S₂O₃²⁻]/dt = −2r (while [S₂O₃²⁻] > 0)
d[I₂]/dt = r (only once [S₂O₃²⁻] = 0)
This engine integrates that ODE system directly with 4th-order Runge–Kutta at a 5 ms step (RK4 error is O(h⁵) per step — orders of magnitude tighter than the linear "constant-rate" shortcut) rather than assuming the rate stays constant. The clock time tclock shown here is the actual root of the integrated system — the moment the numerically-tracked [S₂O₃²⁻] trajectory crosses zero, found by linear interpolation between the last two integration steps — not a formula plugged in after the fact. The instant the scavenger is gone, I₂ starts accumulating for real (its own ODE turns on) and immediately pairs with starch indicator to form the deep blue-black complex everywhere in the flask at once.
- [I⁻]₀ / [S₂O₈²⁻]₀ sliders — raise the reaction rate, so the numerically-found clock time drops (both are first-order in the rate law).
- Thiosulfate slider — more scavenger to consume means a longer integrated delay before I₂ appears.
- Temperature slider — raises k(T) through the Arrhenius equation (Eₐ ≈ 45 kJ/mol here), shortening tclock the way a real kinetics lab observes.
The bottom panel plots [I⁻], [S₂O₈²⁻], [S₂O₃²⁻] and [I₂] against time as the run integrates, so you can watch the scavenger's straight-line depletion hit zero at exactly the moment the beaker above changes color.