Initial Rates Method

Learning Objectives (OCR Spec 5.1.1)

By the end of this lesson you should be able to:

• Explain the initial rates method and why it is useful
• Determine orders of reaction from initial rate data
• Calculate the rate constant from initial rate experiments
• Use clock reactions as an experimental technique to measure initial rates

Why Measure Initial Rates?

Measuring rate during a reaction is tricky because the concentrations of reactants and products are changing all the time, and back-reactions and side reactions complicate matters. The initial rates approach avoids these problems: we measure the rate during the very first moments of the reaction, while:

• Product concentration is effectively zero (no back-reaction).
• Reactant concentrations are very close to their initial values (no significant depletion).

By doing this across several experiments — each with different initial concentrations — we can work out how rate depends on each reactant, and hence deduce the orders.

The Method

1. Set up several experiments, varying one initial concentration at a time and keeping the others constant.
2. For each, measure the time t taken for a small fixed change (e.g. a colour change, a precipitate obscuring a cross, a fixed volume of gas produced).
3. Take initial rate ∝ 1/t (the shorter the time, the faster the initial rate).
4. Compare initial rates across experiments to deduce the order with respect to each reactant.
5. Use the rate equation to calculate k.

Clock Reactions

A clock reaction produces a sudden visible change after a set amount of a product accumulates. The classic OCR example is the iodine clock:

H2O2(aq) + 2I-(aq) + 2H+(aq) -> I2(aq) + 2H2O(l)

A small, fixed amount of sodium thiosulfate and starch is added to the mixture. The thiosulfate instantly reacts with any I2 formed, keeping [I2] = 0, until the thiosulfate runs out. At that point free I2 accumulates and turns the starch indicator blue-black.

The time t from mixing to the colour change is inversely proportional to the initial rate: rate ∝ 1/t.

By varying [H2O2], [I-] or [H+] between experiments you can find the order with respect to each.

Worked Example 1 — Full Analysis

The iodine clock is carried out with the following results:

Expt	[H2O2]	[I-]	[H+]	t / s	1/t proportional to rate
1	0.010	0.010	0.010	40	0.0250
2	0.020	0.010	0.010	20	0.0500
3	0.010	0.020	0.010	20	0.0500
4	0.010	0.010	0.020	40	0.0250

Order w.r.t. H2O2: Compare Experiments 1 and 2. [H2O2] doubles; other concentrations constant. 1/t doubles. So order w.r.t. H2O2 = 1.

Order w.r.t. I-: Compare Experiments 1 and 3. [I-] doubles; others constant. 1/t doubles. So order w.r.t. I- = 1.

Order w.r.t. H+: Compare Experiments 1 and 4. [H+] doubles; others constant. 1/t unchanged. So order w.r.t. H+ = 0.

Rate equation: rate = k[H2O2][I-]

Overall order = 2.

Worked Example 2 — Calculating k

Using the rate equation rate = k[H2O2][I-] and data from Experiment 1:

First express initial rate. Suppose the thiosulfate used corresponds to production of n = 5 x 10^-5 mol of I2 in the volume V = 0.10 dm^3 of mixture at time t = 40 s. Then the initial rate in concentration terms is: