A rate equation says exactly how the rate responds when you change each concentration. The orders cannot be read from the balanced equation: they come from experiment, using initial-rates tables, concentration-time graphs and rate-concentration graphs.
A rate equation has the form rate = k[A]m[B]n. The powers m and n are the orders with respect to each reactant (0, 1 or 2 at this level) and their sum is the overall order. Orders are found by experiment, never from the stoichiometric equation. In an initial-rates table, doubling a concentration while the others stay fixed multiplies the rate by 1 (zero order), 2 (first order) or 4 (second order). A first-order reaction has a constant half-life, and k = 0.693 / t½. The rate constant k changes only with temperature (or a catalyst), and its units depend on the overall order.
Measure the rate of a reaction in the simulator at several starting concentrations and see how the initial gradient changes.
| Overall order | Example rate equation | Units of k |
|---|---|---|
| 0 | rate = k | mol dm−3 s−1 |
| 1 | rate = k[A] | s−1 |
| 2 | rate = k[A]2 or k[A][B] | dm3 mol−1 s−1 |
| 3 | rate = k[A]2[B] | dm6 mol−2 s−1 |
Use the simulator to plot concentration against time, then compare the shapes with Fig. 1.
| Order in A | [A] against time | Rate against [A] |
|---|---|---|
| 0 | straight line falling at constant gradient | horizontal line |
| 1 | curve with a constant half-life | straight line through the origin |
| 2 | steeper curve; each half-life is longer than the one before | upward curve (rate ∝ [A]2) |
Orders come from experimental data, not from the coefficients in the balanced equation. Doubling a concentration and seeing the rate quadruple means second order, not fourth. A constant half-life proves first order only; do not use t½ = 0.693/k for other orders. Always give units for k, worked out from the overall order, and remember k does not change with concentration.
Four quick checks. Each correct answer earns XP and records this skill on your profile.
For rate = k[A][B]2, what is the overall order?
Doubling [X] while all other concentrations stay the same quadruples the initial rate. What is the order with respect to X?
What are the units of k for a first-order reaction?
Which graph shape shows that a reactant is zero order?
Unlocks once the four checks above are done. Worth more XP, written to A Level Paper 4 standard.
Rate = k[A]2[B]. [A] = 0.100 mol dm−3, [B] = 0.100 mol dm−3 and the rate is 2.00 × 10−4 mol dm−3 s−1. What is k?
A first-order reaction has a half-life of 40.0 s. What is the rate constant?
For rate = k[A]2[B], both [A] and [B] are tripled. By what factor does the rate increase?
A reaction is first order in P. The temperature is kept constant and [P] is halved. Which statement is correct?
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