Initial Rate Method: Determining Reaction Order Experimentally

What Is the Initial Rate Method?

The initial rate method is an experimental technique for determining the rate equation of a reaction. By measuring how the initial rate changes when you vary the concentration of one reactant (keeping others constant), you can determine the order with respect to each reactant.

Learning Goals: By the end of this guide, you should be able to:

Define rate, rate equation, order, and rate constant.

Use initial rate data tables to determine reaction order.

Calculate the rate constant $k$ and its units.

Link rate equations to rate-determining steps.

Key Definitions

Term	Definition
Rate	Change in concentration per unit time ( $mol\ dm^{-3}\ s^{-1}$ )
Rate equation	$rate = k[A]^m[B]^n$
Order ( $m, n$ )	The power to which concentration is raised in the rate equation
Overall order	Sum of all individual orders ( $m + n$ )
Rate constant ( $k$ )	Proportionality constant; depends on temperature

Determining Order from Data

The Comparison Method

Compare two experiments where one reactant changes and the other stays constant:

If concentration is...	And rate...	Then order =
Doubled	Stays the same	0 (zero order)
Doubled	Doubles	1 (first order)
Doubled	Quadruples ( $×4$ )	2 (second order)
Tripled	Triples	1 (first order)
Tripled	Nine-folds ( $×9$ )	2 (second order)

General formula: If concentration changes by factor $x$ and rate changes by factor $x^n$ , then order = $n$ .

Initial Rate Method Calculator

Enter experimental data and determine reaction orders automatically. Visualise rate vs. concentration plots and calculate the rate constant.

Launch Rate Calculator

Worked Examples

Example 1: Classic Data Table Problem

Experiment	$[A]$ / mol dm⁻³	$[B]$ / mol dm⁻³	Initial Rate / mol dm⁻³ s⁻¹
1	0.10	0.10	$2.0 \times 10^{-3}$
2	0.20	0.10	$8.0 \times 10^{-3}$
3	0.10	0.20	$4.0 \times 10^{-3}$

Order w.r.t. A (compare Exp 1 and 2, B constant): $[A] \times 2$ , rate $\times 4$ → order = 2

Order w.r.t. B (compare Exp 1 and 3, A constant): $[B] \times 2$ , rate $\times 2$ → order = 1

Rate equation: $rate = k[A]^2[B]$

Find k (using Exp 1): $2.0 \times 10^{-3} = k(0.10)^2(0.10)$ → $k = 2.0\ mol^{-2}\ dm^6\ s^{-1}$

Example 2: Calculating Units of k

The units of $k$ depend on the overall order:

Overall Order	Rate Equation	Units of $k$
0	$rate = k$	$mol\ dm^{-3}\ s^{-1}$
1	$rate = k[A]$	$s^{-1}$
2	$rate = k[A]^2$	$mol^{-1}\ dm^3\ s^{-1}$
3	$rate = k[A]^2[B]$	$mol^{-2}\ dm^6\ s^{-1}$

Example 3: Linking to Mechanism

Question: The rate equation for $A + 2B \rightarrow C$ is $rate = k[A][B]$ . What does this tell us about the mechanism?

Solution: The rate equation is first order in both A and B, suggesting the rate-determining step involves one molecule of A and one of B colliding. The stoichiometric equation shows 2B, but only 1B appears in the RDS — the second B must react in a fast subsequent step.

Common Mistakes

Assuming order equals stoichiometric coefficient — The order must be determined experimentally. For $2A + B → C$ , the order w.r.t. A is NOT necessarily 2.
Not keeping other concentrations constant — When comparing experiments, ensure only ONE reactant concentration changes. If both change, you can't determine individual orders.
Wrong units for k — Different overall orders give different units. Always derive units by substituting into the rate equation.
Confusing rate with rate constant — Rate changes with concentration. The rate constant $k$ only changes with temperature.

Exam Tips (A-Level / AP / IB)

Show your comparison clearly: "Comparing Exp 1 and 2: $[A]$ doubles, rate quadruples, so order = 2."
Always calculate $k$ using data from one experiment after finding the rate equation. Check by substituting into another experiment.
When asked about mechanisms: the rate equation tells you what's in the rate-determining step. Species not in the rate equation react in faster steps after the RDS.

Frequently Asked Questions

Can reaction order be a fraction or negative?

Yes, in complex reactions. However, at A-Level and AP, you typically only encounter orders of 0, 1, or 2.

What is a clock reaction?

A clock reaction uses a visual indicator (e.g., colour change) to measure the time for a fixed amount of reaction to occur. The initial rate is approximated as $rate \approx 1/t$ .

Does the rate constant change with concentration?

No. The rate constant $k$ is independent of concentration. It only changes with temperature (described by the Arrhenius equation).

Le Chatelier's Principle — Equilibrium concepts complement kinetics.
Limiting Reagents — Stoichiometry determines how much product forms; kinetics determines how fast.
Gibbs Free Energy — Thermodynamics tells you whether a reaction is feasible; kinetics tells you how fast.