Finding orders: graphs, initial rates and half-life

Collecting rate data (spec 11.3, 11.4)

Choose a property that changes as the reaction goes:

• gas volume (gas syringe) or mass loss (gas escaping) on a balance
• colorimetry when a reactant or product is coloured, such as iodine or manganate(VII)
• titration of samples removed and quenched (stopped) at timed intervals
• pH or electrical conductivity when the number of ions changes

Continuous monitoring follows one mixture over time and gives a concentration-time graph. The initial rate method runs several mixtures with different starting concentrations and measures the rate at the start; a clock reaction gives the time for a fixed amount to react, so initial rate is proportional to 1/time.

Initial rates table (spec 11.5)

Compare two runs where only one concentration changes:

• rate unchanged: zero order
• rate x2 when concentration x2: first order
• rate x4 when concentration x2: second order

If two concentrations change at once, deal with the one you already know first.

Graph shapes

Half-life (spec 11.2)

The half-life, t½, is the time taken for the concentration of a reactant to fall to half its value. Read successive half-lives from a concentration-time graph. If they are constant, the reaction is first order with respect to that reactant. The rate at any time is the gradient of the tangent to the concentration-time curve.

Worked example

Use the data to find the orders with respect to A and B. Run 1: [A] 0.10, [B] 0.10, rate 2.0 x 10^-4. Run 2: [A] 0.20, [B] 0.10, rate 8.0 x 10^-4. Run 3: [A] 0.10, [B] 0.30, rate 6.0 x 10^-4.

1. Runs 1 and 2: [A] x2, [B] same, rate x4, so second order in A.
2. Runs 1 and 3: [B] x3, [A] same, rate x3, so first order in B.

Answer: rate = k[A]²[B], third order overall

Check yourself

1. When [A] is doubled with all else constant, the initial rate rises from 1.5 x 10^-3 to 6.0 x 10^-3 mol dm^-3 s^-1. What is the order with respect to A?
   Show answer

   2. Rate x4 when [A] x2: 2ⁿ = 4, so n = 2.

2. Successive half-lives on a concentration-time graph are 40 s, 40 s and 40 s. What is the order with respect to that reactant?
   • First order
   • Zero order
   • Second order
   • Third order
   Show answer

   First order. A constant half-life is the test for first order.

3. A concentration-time graph for reactant P is a straight line sloping downwards. What is the order with respect to P?
   • First order
   • Second order
   • Zero order
   • It cannot be found from this graph
   Show answer

   Zero order. A constant gradient means a constant rate, which does not depend on [P].

4. Which method is best for following the rate of a reaction in which purple manganate(VII) ions are used up?
   • Measuring gas volume
   • Colorimetry
   • Measuring mass loss
   • Using a pH meter
   Show answer

   Colorimetry. The colour fades as MnO4- reacts, so absorbance can be measured continuously without disturbing the mixture.

5. A graph of rate against [Q] is a straight line through the origin. What is the order with respect to Q?
   • Zero order
   • Second order
   • Half order
   • First order
   Show answer

   First order. Rate is directly proportional to [Q].

6. A first-order reactant starts at 0.80 mol dm^-3 and has a half-life of 50 s. What is its concentration after 150 s?
   Show answer

   0.10 mol dm^-3. 150 s is three half-lives: 0.80 -> 0.40 -> 0.20 -> 0.10 mol dm^-3.

7. A tangent drawn to a concentration-time curve passes through (0 s, 0.60 mol dm^-3) and (80 s, 0.20 mol dm^-3). What is the rate at the point where the tangent touches the curve?
   Show answer

   0.0050 mol dm^-3 s^-1. Gradient = (0.60 - 0.20) / 80 = 0.0050 mol dm^-3 s^-1 (the rate is the size of the gradient).

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Sources

• Pearson Edexcel IAL Chemistry (2018) specification
• Pearson Edexcel IAL Chemistry (2018) scheme of work

Last updated 7 November 2026. Spotted a mistake? Tell us.