INTERACTIVE COMPANION · VOLUME 1, ISSUE 3 · SPRING 2025

The Kinetics Bench

A live model accompanying “The Reaction That Gives You the Wrong Product Because You Were Impatient”

Two reactions share one starting material, \(A \rightleftharpoons B\) and \(A \rightleftharpoons C\), integrated exactly (this page solves the same linear equations as the article's code, in closed form, so nothing here is stepped through time one tick at a time). Drag the barriers and stabilities below and watch the kinetic product \(B\) rise, peak, and fade while the thermodynamic product \(C\) slowly overtakes it. The defaults reproduce the article's headline numbers: a crossover at 111.7 days, a kinetic-limit ratio of 0.01770, and a \(B\) peak of 98.0% at 5,809 s.

Model 1. Watch the crossover happen

Kinetic barrier E_a1 90.0 kJ/mol The barrier to the fast product. Lower it and B forms even faster without changing where it ends up at equilibrium. Thermodynamic barrier E_a2 100.0 kJ/mol The barrier to the slow product. Push this close to E_a1 and the crossover collapses toward zero; pull it far above and the wait stretches toward geological time. Try 130 and watch the crossover marker vanish off the right edge. B stability ΔG_B −15.0 kJ/mol How far below A the kinetic product sits. More negative means a slower reverse reaction and a longer-lived B. C stability ΔG_C −40.0 kJ/mol Drag this toward ΔG_B and C stops being meaningfully more stable: the crossover time explodes, then the map below turns entirely rust-coloured (never). This is the sharpest, least forgiving control on the page. Temperature T 298.15 K Same molecules, hotter or colder. Slide to 400 K and the months-long wait shrinks to about a minute; slide to 250 K and it stretches past a millennium.

k₁ = – s⁻¹ k₂ = – s⁻¹ K₂/K₁ = – crossover: –

–

Model 2. The regime map: temperature against time

Same four barrier and stability sliders (Model 1's settings carry over); this map fixes nothing but temperature and time. The curve is the crossover time itself, recomputed at every temperature from 250 to 400 K. Below the curve, B still leads. Above it, C has taken over. The open circle marks the current temperature slider and the crossover time it implies.

Jump to temperature 298.15 K Linked to Model 1's temperature slider. Move either one and both update, and the marker on the map slides along the boundary curve.

at this T, the thermodynamic product wins in: –

Three numbers to check by hand, on the default settings:
1. \(k_1 = 10^{13}\exp(-90000/(8.314\times298.15)) \approx 1.709\times10^{-3}\,\text{s}^{-1}\) — matches the k₁ readout above.
2. Kinetic limit \(k_2/k_1 = 3.025\times10^{-5} / 1.709\times10^{-3} \approx 0.01770\) — drag both barrier sliders to their minimum step size apart and read the earliest part of the B/C traces.
3. Thermodynamic limit \(K_2/K_1 = \exp((\Delta G_B-\Delta G_C)/RT) = \exp(25000/2478.8) \approx 2.40\times10^4\) — matches the ratio the two curves settle into on the right edge of Model 1's plot.

What to try

Set E_a2 equal to E_a1 and watch the crossover collapse to almost nothing: with no kinetic head start, the more stable product wins almost immediately. Then reset E_a2 and instead push ΔG_C up toward ΔG_B: the crossover time grows without bound and the regime map's boundary curve runs off the top of the chart, then the whole map turns to the "never" colour once C stops being more stable at all. Finally leave the barriers and stabilities alone and just drag temperature: the boundary curve in Model 2 is this article's Figure 4, live.