In simple terms
A friendly intro before the formal notes — no formulas yet.
The Recipe for Reaction Speed
A rate equation is like a recipe that tells you how changing the amount of each reactant (concentration) affects the speed of the reaction. The orders of reaction are exponents in this recipe, which we can only find through experiments.
Imagine you're running a pizza delivery service. The rate you deliver pizzas depends on how many chefs you have (reactant A) and how many delivery drivers you have (reactant B). If hiring one more chef lets you make one more pizza per hour, the order with respect to chefs is 1. If hiring one more driver lets you deliver four more pizzas per hour (perhaps because they can coordinate and take more efficient routes), the order with respect to drivers might be 2. The 'rate constant', k, is like your base efficiency - how fast you operate even with a standard team, affected by factors like oven temperature.
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Rate = k[A]^m[B]^n — orders m, n from experiment only. | Sim hint: Initial rates method or half-life method.
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Overall order = m + n; units of k depend on order. | Sim hint: First order: k in s⁻¹; second order: dm³ mol⁻¹ s⁻¹.
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Half-life constant for first order: t_{½} = ln 2 / k. | Sim hint: Independent of initial concentration.
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Arrhenius: k = Ae^{−Ea/RT} — temperature effect on rate. | Sim hint: Plot ln k vs 1/T for Ea.
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Key formulas
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$Rate = k[A]^m[B]^n$
Full topic notes
Formal explanation with the rigour you need for the exam.
The Rate Equation
To express the relationship between the rate of a reaction and the concentration of the reactants, we use a mathematical expression called the rate equation (or rate law). For a general reaction: aA + bB → products, the rate equation is not determined by the stoichiometric coefficients 'a' and 'b'. Instead, it is found experimentally.
Rate = k[A]^m[B]^n
[A] and [B] represent the concentrations of reactants A and B in mol dm⁻³.
k is the rate constant, a value specific to a reaction at a particular temperature.
m is the order of reaction with respect to reactant A.
n is the order of reaction with respect to reactant B.
The overall order of the reaction is the sum of the individual orders, m + n.
Orders of reaction (m and n) are usually integers (0, 1, or 2) but can be fractions. They must be determined from experimental data.
Determining Reaction Orders and the Rate Constant
The most common method to find the orders of reaction is the 'initial rates method'. This involves carrying out a series of experiments where the initial concentration of one reactant is changed while the concentrations of all other reactants are kept constant. By observing the effect on the initial rate of reaction, we can deduce the order with respect to that reactant.
Units of the Rate Constant, k
The units of the rate constant, k, depend on the overall order of the reaction. It is essential that you can derive these units, as it is a frequently tested skill. The method involves rearranging the rate equation to make k the subject and then substituting the standard units for rate (mol dm⁻³ s⁻¹) and concentration (mol dm⁻³).
Overall Order 0: Rate = k. Units of k are mol dm⁻³ s⁻¹.
Overall Order 1: Rate = k[A]. Units of k are s⁻¹.
Overall Order 2: Rate = k[A]². Units of k are dm³ mol⁻¹ s⁻¹.
Overall Order 3: Rate = k[A]³. Units of k are dm⁶ mol⁻² s⁻¹.
First-Order Reactions and Half-Life
The half-life () of a reaction is the time it takes for the concentration of a reactant to fall to half of its initial value. For first-order reactions, the half-life is constant and does not depend on the initial concentration. This is a unique characteristic and can be used to identify a first-order reaction from concentration-time data. The half-life is mathematically related to the rate constant, k.
Since is a constant (approximately 0.693), this equation shows the inverse relationship between half-life and the rate constant for a first-order reaction. A larger k means a faster reaction and therefore a shorter half-life.
Worked examples
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The reaction between propanone and iodine in the presence of an acid catalyst was studied. The following initial rates data were obtained at a constant temperature.
| Experiment | [CH₃COCH₃] / mol dm⁻³ | [I₂] / mol dm⁻³ | [H⁺] / mol dm⁻³ | Initial Rate / mol dm⁻³ s⁻¹ |
|---|---|---|---|---|
| 1 | 0.40 | 0.02 | 0.20 | 2.4 x 10⁻⁵ |
| --- | --- | --- | --- | --- |
| 2 | 0.80 | 0.02 | 0.20 | 4.8 x 10⁻⁵ |
| 3 | 0.40 | 0.04 | 0.20 | 2.4 x 10⁻⁵ |
| 4 | 0.40 | 0.02 | 0.40 | 4.8 x 10⁻⁵ |
a) Deduce the order of reaction with respect to propanone, iodine and H⁺ ions. b) Write the rate equation for the reaction. c) Calculate the value of the rate constant, k, and state its units.
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a) Deducing orders:
The decomposition of hydrogen peroxide, 2H₂O₂(aq) → 2H₂O(l) + O₂(g), is a first-order reaction. In an experiment, the rate constant, k, was found to be 7.30 x 10⁻⁴ s⁻¹ at a certain temperature.
a) Calculate the half-life of this reaction. b) If the initial concentration of H₂O₂ was 1.60 mol dm⁻³, what would be its concentration after three half-lives?
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a) Calculate half-life:
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Glossary
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What is the 'rate of reaction'?
The change in concentration of a reactant or product per unit time. Its units are typically mol dm⁻³ s⁻¹.
Key takeaways
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[A] and [B] represent the concentrations of reactants A and B in mol dm⁻³.
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k is the rate constant, a value specific to a reaction at a particular temperature.
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m is the order of reaction with respect to reactant A.
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n is the order of reaction with respect to reactant B.
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The overall order of the reaction is the sum of the individual orders, m + n.
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Orders of reaction (m and n) are usually integers (0, 1, or 2) but can be fractions. They must be determined from experimental data.
Practice — then mark it
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Practice Questions: Rate Equations
Practice Questions: Rate Equations
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