5.2.8Additional lessons
Rate Equation (HL) — IB Chemistry HL Revision Notes & Topical Questions
5 min read 5 parts Lesson 103 of 172
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
Section 1 of 5The Rate Equation
A rate equation links the rate of a reaction to the concentrations of the reactants.
Form
- Form For A + B → products the rate equation is rate = k[A]ᵐ[B]ⁿ, where square brackets mean concentration in mol dm⁻³.
Orders
- Orders The powers m and n are the orders of reaction with respect to A and B, and they must be found by experiment.
Overall order
- Overall order The overall order is the sum of the individual orders, m + n.
Not from the equation
- Not from the equation The orders do not come from the coefficients in the balanced equation unless they happen to match.
Section 2 of 5The Rate Constant
The Rate Constant
Meaning
- Meaning k is the rate constant; it is the rate when every concentration in the equation is 1 mol dm⁻³.
Temperature
- Temperature The value of k is constant only at a fixed temperature, and it rises as the temperature increases.
Catalyst
- Catalyst A catalyst also changes the value of k, because it alters the activation energy.
Units
- Units The units depend on the overall order: first order gives s⁻¹, second order gives mol⁻¹ dm³ s⁻¹ and third order mol⁻² dm⁶ s⁻¹.
| Overall order | Units of k |
|---|---|
| 0 | mol dm⁻³ s⁻¹ |
| 1 | s⁻¹ |
| 2 | mol⁻¹ dm³ s⁻¹ |
| 3 | mol⁻² dm⁶ s⁻¹ |
Section 3 of 5Finding Orders from Data
1
Run several experiments in which one concentration is changed at a time while the others and the temperature are kept constant.
2
Measure the initial rate in each experiment, for example from the gradient of a concentration–time graph at time zero.
3
Compare two experiments in which only one concentration changes: if doubling gives the same rate the order is 0, ×2 means 1 and ×4 means 2.
4
Combine the orders to write the full rate equation and state the overall order.
5
Substitute the data from any experiment to calculate k and give it with the correct units.
Section 4 of 5Worked Example
Question
- Initial rates were measured at constant temperature: (1) [A] = 0.10, [B] = 0.10 mol dm⁻³, rate = 2.0 × 10⁻³;
- (2) [A] = 0.20, [B] = 0.10, rate = 8.0 × 10⁻³;
- (3) [A] = 0.10, [B] = 0.20, rate = 4.0 × 10⁻³ mol dm⁻³ s⁻¹.
- Find the rate equation and k.
- Experiments 1 and 2: [A] doubles and the rate is multiplied by 4, so the order in A is 2.
- Experiments 1 and 3: [B] doubles and the rate is multiplied by 2, so the order in B is 1.
- Rate = k[A]²[B], overall order 3. Substitute experiment 1: k = 2.0 × 10⁻³ / (0.10² × 0.10) = 2.0.
- Unitsmol dm⁻³ s⁻¹ / (mol dm⁻³)³ = mol⁻² dm⁶ s⁻¹.
Answer Rate = k[A]²[B]; k = 2.0 mol⁻² dm⁶ s⁻¹
Section 5 of 5Exam Checklist & Tips
5.2.8 – Key Points for the Exam
- Rate equation An expression of the form rate = k[A]ᵐ[B]ⁿ found by experiment.
- Order of reaction The power to which the concentration of a species is raised in the rate equation.
- Rate constant
- The proportionality constant k in the rate equation;
- it depends on temperature.
- The proportionality constant k in the rate equation;
- Initial rate The rate at the start of the reaction, when the concentrations are known precisely.
Common Mistakes
- Taking the orders directly from the stoichiometric coefficients.
- Leaving out the units of k, or using the same units for reactions of different overall order.
- Changing two concentrations at once when comparing experiments.
- Including a zero-order reactant in the rate equation; a species with order zero does not appear in it.
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