Summary — What This Chapter Covers
- A rate equation, rate = k[A]m[B]n, is found by experiment, never from the stoichiometric equation.
- Orders of 0, 1 and 2 each have a recognisable concentration–time graph and rate–concentration graph.
- Orders come from the initial-rates method or the half-life method; a first-order reaction has a constant half-life.
- k can be calculated from initial rates, or from k = 0.693/t½ for a first-order reaction.
- Species in the rate equation are the ones in (or before) the rate-determining step; intermediates and catalysts can be picked out of a mechanism.
- Raising the temperature increases k, and so increases the rate.
- Heterogeneous catalysts work by adsorption, bond weakening and desorption; homogeneous catalysts are used in one step and reformed in a later one.
1. Rate Equations, Orders of Reaction and Rate Constants
26.1
The key terms
| Term | Meaning |
|---|
| Rate equation | An experimentally determined equation that links the rate of reaction to the concentrations of reactants, e.g. rate = k[A]m[B]n. |
| Order of reaction (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 in the rate equation, m + n. |
| Rate constant, k | The constant of proportionality in the rate equation. It is constant at a fixed temperature. |
| Half-life, t½ | The time taken for the concentration of a reactant to fall to half of its initial value. |
| Rate-determining step | The slowest step in a reaction mechanism; it controls the overall rate. |
| Intermediate | A species formed in one step of a mechanism and used up in a later step. It does not appear in the overall equation. |
Only species whose concentration affects the rate appear in the rate equation. A reactant that is zero order is left out, because [X]0 = 1.
Rate equation
rate = k[A]m[B]n (m, n = 0, 1 or 2) overall order = m + n
Units of k
Rearrange the rate equation: k = rate / ([A]m[B]n), with rate in mol dm−3 s−1.
| Overall order | Units of k |
|---|
| 0 | mol dm−3 s−1 |
| 1 | s−1 |
| 2 | dm3 mol−1 s−1 |
| 3 | dm6 mol−2 s−1 |
Reading orders from graphs
| Order | Concentration–time graph | Rate–concentration graph |
|---|
| 0 | Straight line with a negative gradient; the rate stays constant until the reactant runs out. | Horizontal line: rate does not change with concentration. |
| 1 | Curve (exponential decay) with a constant half-life. | Straight line through the origin: rate ∝ [A]. |
| 2 | Steeper curve at the start that levels off more; successive half-lives get longer (each one doubles). | Upward curve; a plot of rate against [A]2 is a straight line through the origin. |
The rate at any moment is the gradient of the tangent to the concentration–time curve at that time (ignore the minus sign). The initial rate is the gradient of the tangent at t = 0.
Initial-rates method