Rate equations definitions

Rate equations, orders of reaction and the rate constant

Rate of reaction

The change in the concentration of a reactant or a product per unit time, measured in mol dm⁻³ s⁻¹.

Rate equation

An expression, found by experiment, of the form rate = k[A]ᵐ[B]ⁿ, showing how the rate depends on the concentration of each substance.

Order with respect to a reactant

The power to which the concentration of that reactant is raised in the rate equation.

Overall order

The sum of the powers of all the concentration terms in the rate equation.

Zero order

A reactant is zero order when changing its concentration has no effect on the rate; it does not appear in the rate equation.

Rate constant, k

The constant of proportionality in the rate equation; it is fixed at a given temperature and increases as the temperature rises.

First order

A reactant is first order when the rate is directly proportional to its concentration: doubling the concentration doubles the rate.

Second order

A reactant is second order when the rate is proportional to the square of its concentration: doubling the concentration multiplies the rate by four.

Half-life, t½

The time taken for the concentration of a reactant to fall to half of its starting value.

Finding orders from initial rates, half-lives and graphs

Initial rate

The rate of reaction at the moment the reactants are mixed, found from the gradient of the tangent to a concentration–time graph at t = 0.

Clock reaction

A reaction in which the time taken to form a fixed amount of product is measured, usually by a sudden colour change; 1/t is proportional to the initial rate.

Continuous monitoring

Following one reaction mixture by measuring a property that depends on concentration at regular intervals as the reaction proceeds.

Absorbance

A measure of how much light of a chosen colour a solution absorbs; for a dilute solution it is proportional to the concentration of the coloured species.

Calibration graph

A graph of absorbance against known concentrations of the coloured species, used to convert each absorbance reading into a concentration.

Quenching

Stopping the reaction in a withdrawn sample, by cooling, dilution or removing a reactant or catalyst, so its composition at that moment can be measured.

Isolation method

Finding the order with respect to one reactant by putting every other reactant in large excess, so that only the isolated reactant's concentration changes during the run.

The Arrhenius equation and the rate-determining step

Activation energy, Ea

The minimum energy that colliding particles must have for a reaction to take place.

Arrhenius equation

k = Ae^(−Ea/RT), relating the rate constant to the activation energy and the absolute temperature.

Pre-exponential factor, A

The constant in the Arrhenius equation, with the same units as k, related to the frequency of collisions with the correct orientation.

Reaction mechanism

The sequence of steps by which a reaction takes place, which add up to the overall equation.

Rate-determining step

The slowest step in a reaction mechanism, which limits the overall rate of the reaction.

Intermediate

A species formed in one step of a mechanism and used up in a later step, so it does not appear in the overall equation.

Transition state

The arrangement of highest energy along a single step, in which bonds are partly broken and partly formed; it cannot be isolated.

Catalyst

A substance that increases the rate of a reaction by providing an alternative route of lower activation energy; it is used in one step of a mechanism and regenerated in a later one, so it is chemically unchanged at the end.

SN2

Nucleophilic substitution in one step, in which the nucleophile and the halogenoalkane are both in the rate-determining step, so the reaction is second order.

SN1

Nucleophilic substitution in two steps, in which the carbon–halogen bond breaks heterolytically in the slow first step to give a carbocation, so only the halogenoalkane is in the rate equation.