Reaction Kinetics

Rate, Order and Mechanism

Thermodynamics says whether a reaction can happen; kinetics says how fast. For $aA \to$ products the rate law is

$$\text{rate} = k[A]^m$$

where the order $m$ is found by experiment, never read off the balanced equation. The method of initial rates compares runs: if doubling $[A]$ doubles the rate the reaction is first order in A; if it quadruples it, second order; if nothing changes, zero order.

Integrating gives the forms used to test data by straight-line plots:

The first-order half-life is the striking one: it is independent of starting concentration, which is why radioactive decay and many drug clearances have a single quoted half-life.

Most reactions proceed through several elementary steps, and the slowest, the rate-determining step, controls the overall rate. Only for an elementary step may you read the order straight from its stoichiometry.

Temperature dependence follows Arrhenius:

$$k = A e^{-E_a/RT}$$

Raising $T$ increases the fraction of collisions carrying at least the activation energy $E_a$, which is why a modest rise can double a rate. A catalyst provides a different pathway with a lower $E_a$ and is regenerated unchanged. Crucially, it speeds the forward and reverse reactions equally, so it changes how fast equilibrium arrives but never where it lies.

Common pitfall: reading reaction order off the balanced equation. Order is experimental. The overall equation reflects only the net stoichiometry, while the rate law reflects the mechanism, and for $\mathrm{2NO_2 + F_2}$, the reaction is first order in $\mathrm{F_2}$ despite its coefficient of 1 and first order in $\mathrm{NO_2}$ despite its coefficient of 2.