Lab 09 — Chemical Kinetics

Kinetic vs Thermodynamic Control

Reactant A has two ways out: over a LOW barrier into a SHALLOW well (product B), or over a HIGH barrier into a DEEP well (product C). 240 particles jitter across this energy landscape under Langevin dynamics. At low temperature only the low barrier is passable, so everything piles up in B — speed decides: kinetic control. At high temperature both barriers open up, traffic flows both ways, and the deep well C wins by the Boltzmann factor — stability decides: thermodynamic control.

k = A\,\exp\!\left(-\dfrac{E_{\mathrm{a}}}{k_{\mathrm{B}}T}\right) \qquad \left(\dfrac{[\mathrm{C}]}{[\mathrm{B}]}\right)_{\!\mathrm{eq}} = \exp\!\left(-\dfrac{\Delta E_{\mathrm{C}} - \Delta E_{\mathrm{B}}}{k_{\mathrm{B}}T}\right) \qquad \mathrm{d}x = -V'(x)\,\mathrm{d}t + \sqrt{2k_{\mathrm{B}}T\,\mathrm{d}t}\;\eta

Fill B at low temperature, then heat it up and watch C stage its comeback

TemperatureT = 0.09

B (kinetic product)0%C (thermodynamic product)0%

A concrete case: add one molecule of HBr to 1,3-butadiene (CH₂=CH–CH=CH₂) and two products appear. B is the 1,2-adduct (3-bromo-1-butene): it forms fast over a low barrier — the kinetic product. C is the 1,4-adduct (1-bromo-2-butene): its double bond sits inside the chain, which makes it the more stable one — the thermodynamic product. At −80 °C the mixture is roughly 80 : 20 in favour of B (speed wins); warm it to +40 °C and it flips to about 15 : 85 in favour of C (stability wins). Diamond is the same story: it is less stable than graphite, yet at room temperature it lasts essentially forever, because the barrier to convert is impossibly high — kinetic control. “Which is more stable” and “which forms faster” are different questions — that is this whole page.