Revise How fast? The rate of chemical change for IB Chemistry (R2.2)

The rate of a reaction is the change in concentration of a reactant or product per unit time. Because a reactant's concentration falls, we write $\text{rate} = -\dfrac{\Delta[\text{reactant}]}{\Delta t}$ (the minus sign keeps the rate positive); for a product it is $\dfrac{\Delta[\text{product}]}{\Delta t}$. The standard units are mol dm⁻³ s⁻¹. To measure a rate we monitor any property that changes as the reaction proceeds and record it against time.

$\text{rate} = \frac{\Delta[\text{substance}]}{\Delta t}$

For particles to react they must first collide, but the overwhelming majority of collisions achieve nothing. A collision only leads to reaction if it satisfies BOTH of two conditions. First, the colliding particles must have a combined kinetic energy at least equal to the activation energy, Ea — enough to break the existing bonds and reach the transition state. Second, the particles must meet in the correct orientation, so that the right atoms are positioned to form the new bonds. A collision meeting both conditions is a successful collision, and the rate of reaction is set by how many successful collisions occur each second.

The power of collision theory is that one framework explains every factor. Group them by which lever they pull: concentration, pressure and surface area change how OFTEN particles collide; temperature changes both the frequency and, decisively, the fraction of collisions energetic enough to react; a catalyst lowers the energy barrier itself.

Not all molecules in a sample move at the same speed. The Maxwell–Boltzmann distribution is a graph of the number (or fraction) of molecules against their kinetic energy. It starts at the origin (no molecule has zero energy in a way that contributes), rises to a peak at the most probable energy, then tails off to the right — a few molecules always have very high energy. Two features carry most of the exam marks. First, the TOTAL AREA under the curve equals the total number of molecules and does not change when you heat the sample or add a catalyst (the amount of substance is fixed). Second, the activation energy Ea can be marked on the energy axis, and the AREA to the right of Ea represents the fraction of molecules with enough energy to react.

On an energy profile, reactants must climb over an energy barrier — the activation energy — to reach the transition state before falling to products. The height of that barrier, not the overall enthalpy change, controls the rate: a large ΔH can accompany a slow reaction if Ea is high. A catalyst does not push molecules over the existing barrier; it opens a different route with a lower barrier. Because Ea is smaller on the catalysed pathway, a larger fraction of molecules possess sufficient energy at any given temperature, so the rate rises. Crucially, the catalyst lowers Ea for the forward and reverse directions equally, leaving ΔH, the products and the equilibrium position untouched — it changes only the speed at which the outcome is reached, and it is regenerated at the end.

At Higher Level we quantify rate. The rate expression is $\text{rate} = k[\text{A}]^m[\text{B}]^n$, where $k$ is the rate constant and the powers $m$ and $n$ are the ORDERS with respect to A and B. A vital point: the orders are found EXPERIMENTALLY and are not read from the stoichiometric coefficients. The reason is mechanism — most reactions proceed through several steps, and the slowest is the rate-determining step (RDS). Only species that appear up to and including the RDS influence the rate, which is why orders can differ from the balanced equation. The overall order is $m + n$, and the units of $k$ change with overall order (for example, a first-order $k$ has units s⁻¹, a second-order $k$ has units mol⁻¹ dm³ s⁻¹).

The Arrhenius equation puts numbers to the temperature effect on the rate constant: $k = A e^{-E_a/RT}$, where $A$ is the pre-exponential (frequency) factor tied to collision frequency and orientation, $E_a$ is the activation energy, $R$ is the gas constant and $T$ is the absolute temperature. Taken in logarithmic form, $\ln k = \ln A - \dfrac{E_a}{R}\cdot\dfrac{1}{T}$, it is the equation of a straight line: plotting $\ln k$ against $1/T$ gives a gradient of $-E_a/R$ (from which Ea is found) and an intercept of $\ln A$. The exponential term $e^{-E_a/RT}$ is precisely the fraction of molecules with E ≥ Ea from the Maxwell–Boltzmann picture — so a higher T or a lower Ea makes that term larger and $k$ (and the rate) rises. It is the same physics, now made quantitative.

$\ln k = \ln A - \frac{E_a}{R}\cdot\frac{1}{T}$

Explain-and-conclude questions in Paper 2 are marked analytically: each distinct valid point is worth one mark, method/reasoning marks (M) build to an answer/conclusion mark (A), and error-carried-forward (ECF) means a reasonable follow-on from an earlier idea is still credited. Study how each mark below is tied to a specific, distinct point — and note the point the engine will NOT accept on its own.

Collision theory and the activation-energy picture underpin everything that follows in reactivity. Equilibrium (R2.3) revisits catalysts and temperature — this time asking not how fast but how far a reaction goes, and why a catalyst speeds both directions equally without shifting the balance. At Higher Level, mechanisms and the rate-determining step explain why rate expressions look the way they do, and the Arrhenius equation turns the Maxwell–Boltzmann tail into a straight-line graph you can extract Ea from. Master the one habit — for any change, ask whether it alters collision frequency, the fraction with E ≥ Ea, or Ea itself — and kinetics becomes a single idea applied over and over.