Rate equations of the form rate = k[A]^m[B]^n, the order of reaction with respect to each reactant and overall, the rate constant and its units, and the link between the rate equation, the rate-determining step and a reaction mechanism.

What this key area is asking

The SQA wants you to use rate equations of the form $\text{rate} = k[A]^m[B]^n$, to determine the order of reaction from initial-rate data, to calculate the rate constant and its units, and to link the rate equation to the rate-determining step and a reaction mechanism. Finding orders from data, working out the units of $k$, and reasoning about mechanisms are reliable exam earners.

Rate equations and order

Orders cannot be read off the balanced equation; they must be found by experiment. A reaction is zero order in a reactant if its rate is unaffected by that concentration, first order if the rate is proportional to the concentration, and second order if the rate is proportional to the concentration squared.

Finding orders from initial-rate data

The standard method compares experiments in which one concentration is changed while the others are held constant:

• If doubling a concentration leaves the rate unchanged, the order is zero.
• If doubling a concentration doubles the rate, the order is one ($2^1 = 2$).
• If doubling a concentration multiplies the rate by four, the order is two ($2^2 = 4$).

The rate-determining step and mechanisms

For example, if a reaction $A + 2B \rightarrow$ products has the rate equation $\text{rate} = k[A][B]$, the rate-determining step must involve one molecule of A and one of B; the second B reacts in a later, faster step that does not affect the rate. Reasoning between rate equation and mechanism is a key Advanced Higher skill.

Examples in context

Kinetics underpins how chemists control and understand reactions. The hydrolysis of a tertiary haloalkane is first order overall ($\text{rate} = k[\text{haloalkane}]$), which is evidence for an $S_N1$ mechanism with a slow first step forming a carbocation; a primary haloalkane is second order, evidence for a one-step $S_N2$ mechanism. Enzyme-catalysed reactions show how concentration affects rate up to a saturation point. Industrially, knowing the order with respect to each reactant lets a chemist choose concentrations that maximise rate efficiently, and the temperature dependence of $k$ explains why warming a reaction (raising $k$) speeds it up far more than the increase in collision frequency alone would suggest.

Try this

Q1. Define the term overall order of reaction. [1 mark]

• Cue. The sum of the powers of the concentration terms in the rate equation.

Q2. A reaction is first order in A and zero order in B. Write the rate equation. [1 mark]

• Cue. $\text{rate} = k[A]$.

Q3. State what the rate equation tells you about the rate-determining step. [1 mark]

• Cue. Only species in or before the rate-determining step appear in the rate equation.