AHL: Rate laws and reaction order

IB Chemistry HL· 25 min read

1. Definition and structure of a rate law★★☆☆☆⏱ 10 min

📘 Definition

Rate law

\text{rate} = k [A]^m [B]^n

A mathematical expression that relates reaction rate to the concentration of reactants raised to their individual reaction orders, where $k$ is the rate constant.

Example:

For $2 N_{2} O_{5} \to 4 N O_{2} + O_{2}$ , the rate law is $rate = k [N_{2} O_{5}]$

Rate laws can only be determined experimentally; they cannot be deduced from the stoichiometry of the overall balanced reaction. Order with respect to a reactant is independent of its stoichiometric coefficient, unless the reaction is a single elementary step.

📐 Worked Example

Identify the order with respect to each reactant in the rate law: $rate = k [X]^{1} [Y]^{0} [Z]^{2}$

1
The order of a reactant is equal to the power it is raised to in the rate law.
2
Order with respect to X = 1, order with respect to Y = 0, order with respect to Z = 2.

✓ Quick check

Test your basic understanding

True or false: The rate law of a reaction can always be determined from the balanced overall equation
- True
- False
Reveal answer
1 —
Correct: Rate laws are experimental, and depend on the reaction mechanism, not just overall stoichiometry.

2. Determining order from initial rate data★★★☆☆⏱ 15 min

The initial rate method is the most common experimental approach to find reaction order. You change the concentration of one reactant at a time, measure the initial rate, and compare how rate changes with concentration:

If $[A]$ doubles, rate stays the same → order 0
If $[A]$ doubles, rate doubles → order 1
If $[A]$ doubles, rate quadruples → order 2

📐 Worked Example

For the reaction $A + B \to C$ , use the data below to deduce the order with respect to A and B, then write the rate law:

Experiment	[A] / mol dm⁻³	[B] / mol dm⁻³	Initial rate / mol dm⁻³ s⁻¹
1	0.1	0.1	0.002
2	0.2	0.1	0.008
3	0.1	0.2	0.004

1
Compare experiments 1 and 2 ([B] is constant):
2
$\frac{[A]_2}{[A]_1} = 2, \quad \frac{\text{rate}_2}{\text{rate}_1} = 4$
3
For order $m$ : $2^{m} = 4 \to m = 2$ . Order with respect to A = 2.
4
Compare experiments 1 and 3 ([A] is constant):
5
$\frac{[B]_3}{[B]_1} = 2, \quad \frac{\text{rate}_3}{\text{rate}_1} = 2$
6
For order $n$ : $2^{n} = 2 \to n = 1$ . Order with respect to B = 1.
7
Final rate law:
8
$\text{rate} = k[A]^2[B]^1$

Exam tip:

Always compare experiments where only one concentration changes. If both concentrations change, you cannot isolate the effect of each reactant to find order.

3. Properties of zero, first and second order reactions★★★☆☆⏱ 15 min

📘 Definition

Reaction order

The power to which the concentration of a reactant is raised in the rate law, describing how the reactant's concentration affects reaction rate.

Order can be zero, a positive integer, or even negative for inhibition. IB Chemistry HL only assesses positive zero, first and second order behavior.

📐 Worked Example

A reactant has zero order in the rate law. What happens to the reaction rate if the concentration of this reactant is tripled?

1
Zero order means the reactant concentration is raised to the power of 0:
2
$[A]^0 = 1$
3
Substitute into the rate law:
4
$\text{rate} = k [A]^0 = k$
5
Rate is independent of the concentration of a zero order reactant. Tripling the concentration has no effect on rate.

Order	Effect of doubling [A] on rate	Units of k
0	No change	mol dm⁻³ time⁻¹
1	Rate doubles	time⁻¹
2	Rate quadruples	dm³ mol⁻¹ time⁻¹

4. Overall order and rate constant calculation★★★★☆⏱ 10 min

The overall order of a reaction is the sum of all individual reaction orders for reactants in the rate law. Once order is known, you can calculate the value and units of the rate constant $k$ from experimental data.

📐 Worked Example

Using the rate law $rate = k [A]^{2} [B]$ and data from experiment 1 ( $[A] = 0.1$ mol dm⁻³, $[B] = 0.1$ mol dm⁻³, rate = 0.002 mol dm⁻³ s⁻¹), calculate $k$ and its units.

1
Substitute the values into the rate law:
2
$0.002 = k \times (0.1)^2 \times (0.1)$
3
Rearrange to solve for k:
4
$k = \frac{0.002}{(0.1)^2 (0.1)} = 2$
5
Calculate units: Overall order = 2 + 1 = 3. Units of k are $(m o l d m^{- 3})^{1 - overall order} t im e^{- 1}$ :
6
$\text{Units} = dm^6 \ mol^{-2} \ s^{-1}$
7
Final result: $k = 2 d m^{6} m o l^{- 2} s^{- 1}$

5. Common Pitfalls

Wrong move:

Deducing reaction order from stoichiometric coefficients of the overall balanced equation

Why:

Rate laws depend on reaction mechanism, not overall stoichiometry. Only elementary steps follow stoichiometric order

Correct move:

Always use experimental rate data to deduce order; never rely on overall reaction coefficients

Wrong move:

Claims k changes when reactant concentration changes

Why:

The rate constant k is only affected by temperature and catalysts, not concentration

Correct move:

Recognize k is constant at fixed temperature, changing concentration changes rate but not k

Wrong move:

Memorizing units of k incorrectly for different overall orders

Why:

Memorization often leads to errors, especially for higher overall orders

Correct move:

Derive units by rearranging the rate law to isolate k, then substitute concentration and rate units

Wrong move:

Calculating order from two experiments where both reactant concentrations change

Why:

You cannot isolate the effect of each reactant if both change, leading to incorrect order values

Correct move:

Always select pairs of experiments where only one reactant concentration changes to find individual order

6. Quick Reference Cheatsheet

Property	Zero order	First order	Second order
Rate dependence	rate = k, independent of [A]	rate ∝ [A], rate = k[A]	rate ∝ [A]², rate = k[A]²
Units of k	mol dm⁻³ t⁻¹	t⁻¹	dm³ mol⁻¹ t⁻¹
Half-life behavior	Decreases as [A] decreases	Constant, independent of [A]	Increases as [A] decreases
Overall order	Sum of all individual orders	Sum of all individual orders	Sum of all individual orders

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2023 · P2
Deduce rate law from experimental data
2022 · P1
Identify units of rate constant
2021 · P2
Calculate reaction order and k

What's Next

Understanding rate laws and reaction order is the foundation for further study of reaction mechanisms and integrated rate laws in IB Chemistry AHL. This knowledge allows you to connect experimental kinetic data to proposed reaction mechanisms, identify the rate-determining step, and predict how changes to reaction conditions will impact reaction rate. Mastery of this sub-topic is essential for tackling complex kinetics problems that frequently appear in Paper 2 and Paper 3 of IB Chemistry HL exams. Next, you will build on this to study integrated rate equations, half-life properties, and connect reaction order to full reaction mechanisms.