Lesson 1 · 25 min

Reaction rates and rate laws

Mix two colourless solutions and twenty seconds later they snap to blue-black. Time this chemical clock, vary the concentrations and find the reaction orders yourself — they are not the coefficients of the equation.

In this lesson

Define the reaction rate as the rate of change of concentration, normalised by the coefficients
Write a rate law $r = k[\mathrm{A}]^m[\mathrm{B}]^n$ and relate the orders to the units of k
Use the method of initial rates to find each order and the rate constant from a set of runs
Explain why orders must be measured and cannot be read from the coefficients of the equation

Pour two colourless solutions together, stir, and wait. Nothing happens — until, about twenty seconds later, the whole beaker snaps to blue-black as if someone had flicked a switch. This is the iodine clock: persulfate slowly oxidises iodide to iodine, while a little thiosulfate turns the iodine straight back. The moment the thiosulfate runs out, iodine meets starch and the colour appears. By then a fixed amount of persulfate has reacted, so timing the clock measures the rate.

Predict first

Keep everything else the same and double only the concentration of potassium iodide. The time until the colour appears becomes:

Pick an answer and lock it in before you look. A wrong guess teaches more than no guess.

Twice as long Unchanged Half as long A quarter as long

What a reaction rate is

a\mathrm{A} + b\mathrm{B} \rightarrow c\mathrm{C}\qquad r = -\frac{1}{a}\frac{d[\mathrm{A}]}{dt} = -\frac{1}{b}\frac{d[\mathrm{B}]}{dt} = \frac{1}{c}\frac{d[\mathrm{C}]}{dt}

Dividing by the coefficients gives one rate whichever species you follow; units mol L⁻¹ s⁻¹.

$r$: rate of reaction
$d[\mathrm{A}]/dt$: rate of change of [A] (negative)
$a, b, c$: coefficients in the balanced equation

The rate usually falls as the reaction proceeds, because reactants are used up. The initial rate — at the very start, while the concentrations are still their starting values — is the cleanest way to compare runs with different starting concentrations. The iodine clock measures exactly that: only about 1 % of the persulfate has reacted before the colour appears.

Experiment shows that many rates can be written as a rate law:

r = k[\mathrm{A}]^m[\mathrm{B}]^n

The exponents m and n are the orders with respect to A and B, and $m+n$ is the overall order; $k$ is the rate constant, which depends only on temperature (and catalysts). Since a rate is always in mol L⁻¹ s⁻¹, the units of k depend on the overall order: mol L⁻¹ s⁻¹ for zero order, s⁻¹ for first order, L mol⁻¹ s⁻¹ for second order.

The method of initial rates

Three iodine-clock runs at 25 °C (each with [S₂O₃²⁻]₀ = 1.0 mM; computed exactly from this site’s rate model)
Run	$[\ce{S2O8^2-}]_0$ / M	$[\ce{I-}]_0$ / M	Clock time / s	Initial rate / (M s⁻¹)
1	0.040	0.080	19.7	2.54 × 10⁻⁵
2	0.040	0.040	39.3	1.27 × 10⁻⁵
3	0.020	0.080	39.6	1.26 × 10⁻⁵

Source: Rate model: k = 8.0 × 10⁻³ L mol⁻¹ s⁻¹ at 25 °C (see the notes of the bench).

Worked example

The rate law from three runs

Use the table to find m, n and k in $r = k[\ce{S2O8^2-}]^m[\ce{I-}]^n$ .

S₂O₈²⁻ + 2I⁻ → 2SO₄²⁻ + I₂ · timing gives the rate

Iodine clock: the method of initial rates

Volume of 0.200 M KI · 20.0 mL Volume of 0.100 M (NH₄)₂S₂O₈ · 20.0 mL

Water to 50.0 mL: 0.0 mL · Plus 10.0 mL of 0.0050 M Na₂S₂O₃ (with starch)

[I⁻]₀ = 0.080 M · [S₂O₈²⁻]₀ = 0.040 M · [S₂O₃²⁻]₀ = 1.00 mM

Stopwatch 0.0 s

Thiosulfate turns each I₂ straight back into I⁻; the moment it runs out, I₂ meets the starch and the colour appears. So a fixed amount of S₂O₈²⁻ has reacted by time t: rate ≈ [S₂O₃²⁻]₀ / (2t).

Lab notebook

No runs yet. Set the volumes, then press “Mix and start the timer”.

Finding the orders

Order in I⁻ — needs two runs that differ only in this concentration

Order in S₂O₈²⁻ — needs two runs that differ only in this concentration

k from each run (taking both orders as 1) —

r = k\,[\ce{S2O8^2-}]^{m}\,[\ce{I-}]^{n},\qquad n = \dfrac{\lg(r_2/r_1)}{\lg(c_2/c_1)}

Use the quick designs for one series each, or plan your own — change only one concentration per series. The recorded times carry realistic measurement error (stopwatch reaction time, bath temperature drift), so the orders come out close to, but not exactly, 1.

Concept check

For a reaction that is second order overall, the rate constant has units of:

s⁻¹ mol L⁻¹ s⁻¹ L mol⁻¹ s⁻¹ L² mol⁻² s⁻¹

Try the calculation

In one iodine-clock run, $[\ce{S2O3^2-}]_0 = 1.0$ mM and the blue appears after 40 s. What is the initial rate $-d[\ce{S2O8^2-}]/dt$ in μM/s?

Key takeaways

Rate = rate of change of concentration ÷ coefficient, in mol L⁻¹ s⁻¹; initial rates are best for comparing runs.
In rate = k[A]^m[B]^n the orders must be measured, and the units of k depend on the overall order.
Initial rates: change one concentration at a time; n = lg(r₂/r₁)/lg(c₂/c₁).
Iodine clock: rate ≈ [S₂O₃²⁻]₀/(2t); first order in both persulfate and iodide.

Progress is stored only in this browser and never uploaded.

Data and references

IUPAC, Compendium of Chemical Terminology (Gold Book), “rate of reaction” and “order of reaction”.
P. Atkins, J. de Paula, J. Keeler, Atkins’ Physical Chemistry, 11th ed. (2018), Topic 17A–17B (reaction rates and rate laws).
B. Burns, “The kinetics of the reaction between peroxydisulfate and iodide ions in dimethyl sulfoxide”, M.S. thesis, Oregon State University (1966) — the introduction reviews the aqueous kinetics and its salt effect.