Initial Rates Method

Learn and apply Initial Rates Method in the published Chemistry course sequence.

  • GCE A-Level H1 Chemistry 8873-2027
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H1 Method of Initial Rates: Orientation

The method of initial rates turns controlled comparisons into reaction orders. The reliable habit is to isolate one changing concentration at a time and show the factor reasoning.

H1 8873 scope
  • Deduce orders and use the resulting equation to calculate an initial rate.
  • Calculation of k from an initial-rates table and design of a rate experiment are outside the prescribed H1 demand.

Definitions (Must Know)

  • The initial rate is the rate measured at the start of a reaction, before concentrations have changed appreciably.
  • A controlled comparison uses two experiments where only one reactant concentration changes.
  • An individual order is the power that matches the concentration factor to the rate factor.

Detailed Explanations

A. Why initial rates are compared

Later in a run, several concentrations may have changed. Initial-rate experiments begin from known conditions, so the effect of a deliberately varied concentration can be isolated.

B. When no direct pair exists

First deduce one known order from a controlled pair. In a mixed comparison, divide out that reactant’s rate factor; the remaining factor belongs to the other reactant.

C. Completing the task

State the rate equation after finding the orders. If k is supplied, substitute a stated set of initial concentrations to calculate an initial rate.

D. Evidence discipline

A data table establishes concentration dependence. It does not by itself justify an H2 multi-step mechanism.

Worked Examples

Modelled example 1

A direct comparison

Core

Problem

At fixed [B], doubling [A] makes the initial rate four times larger. Deduce the order in A.
Study the worked solution
  1. Confirm the control

    Method

    Note that B is held constant.

    Reason

    Only A’s concentration term can produce the observed rate change.

    Working

    A factor: 2; rate factor: 4.
  2. Solve the factor equation

    Method

    Raise 2 to the unknown order m and match the rate factor.

    Reason

    2^m = 4 = 2².

    Working

    m = 2: the reaction is second order in A.

Guided practice 2

A two-reactant table

About 6 min

Problem

Doubling A at fixed B doubles the initial rate. Doubling B at fixed A leaves the rate unchanged. Write the rate equation.

Try this before viewing the solution

Hints

Hint 1: deduce A
A factor 2 produces rate factor 2.
Hint 2: deduce B and simplify
B factor 2 produces rate factor 1; write the zero-power term, then simplify it.
View solution step by step
  1. Find A's order

    Method

    Match 2^m to the rate factor 2.

    Reason

    B is constant in that comparison.

    Working

    m = 1.
  2. Find B's order

    Method

    Match 2ⁿ to the unchanged-rate factor 1.

    Reason

    A is constant in that comparison.

    Working

    n = 0.
  3. Write the rate equation

    Method

    Insert both orders and simplify [B]⁰ to 1.

    Reason

    A complete empirical rate equation includes k.

    Working

    rate = k[A][B]⁰ = k[A].

Common misconception 3

Correct a mixed-comparison conclusion

Find and correct the mistake

Learner conclusion

Between two runs, A doubles, B triples and rate increases twelve-fold. A learner says A must be second order because 2² is part of 12. Explain why the order in A is not established.

Assess the comparison

Because both concentrations change, the data reveal

View solution step by step
  1. Write the combined factor

    Method

    Represent the rate change as 2^m3ⁿ.

    Reason

    Both rate-law terms change between the runs.

    Working

    2^m3ⁿ = 12.
  2. Identify missing evidence

    Method

    Require a controlled pair for one reactant, or a previously known order that can be divided out.

    Reason

    The single equation does not independently determine both m and n.

    Working

    The learner’s choice m = 2 is possible only with an additional assumption about B.

Examiner practice 4

Resolve a mixed comparison

4 marks

Problem

From run 1 to run 2, A doubles at fixed B and rate doubles. From run 1 to run 3, A increases four-fold, B doubles and rate increases eight-fold. Deduce both orders and write the rate equation. [4 marks]

Try this before viewing the solution

View solution step by step
  1. Deduce A order

    1 mark

    Method

    Use runs 1 and 2, where only A changes.

    Reason

    Doubling A doubles rate.

    Working

    2^m = 2, so m = 1.
  2. Remove A's mixed effect

    1 mark

    Method

    Assign factor 4 of the eight-fold increase to first-order A in run 3.

    Reason

    A increases four-fold and is first order.

    Working

    Remaining factor due to B: 8/4 = 2.
  3. Deduce B order

    1 mark

    Method

    Compare B’s factor 2 with its remaining rate factor 2.

    Reason

    2ⁿ = 2.

    Working

    n = 1.
  4. Write the rate equation

    1 mark

    Method

    Insert both first-order terms.

    Reason

    The data establish first order in each reactant.

    Working

    rate = k[A][B].

Challenge 5

Use the rate equation for a new run

Minimal support

Problem

Initial-rate comparisons establish rate = k[A][B]. At the same temperature, k = 0.800 dm³ mol⁻¹s⁻¹. Calculate the initial rate for a new run with [A] = 0.250 and [B] = 0.400 mol dm⁻³.

Try this before viewing the solution

Hints

Hint 1: use both first-order terms
Substitute each concentration once.
Hint 2: keep the rate unit
Calculate 0.800(0.250)(0.400).
View solution step by step
  1. Substitute the new conditions

    Method

    Insert k, [A] and [B] into the established rate equation.

    Reason

    The temperature is unchanged, so the supplied k applies to the new run.

    Working

    rate = 0.800(0.250)(0.400).
  2. Evaluate

    Method

    Complete the product and report the rate unit.

    Reason

    The stated rate equation converts the new initial concentrations into an initial rate.

    Working

    rate = 0.0800 mol dm⁻³s⁻¹.

Mind Stretchers

Attempt each unfamiliar application before opening the hint, then compare your reasoning with the solution.

Mind stretcher 1: Removing a known factorExtension

Question. A is first order. Between two runs A doubles, B triples and rate increases eighteen-fold. Find the order in B.

Show Hint

Divide the total rate factor by the factor due to A.

Show Answer

A contributes 2, leaving 9 from tripling B. Since 3² = 9, B is second order.

Mind stretcher 2: Spotting insufficient evidenceExtension

Question. All runs increase A and B by the same factor. Can their individual orders be found?

Show Hint

Ask whether the data separate the two variables.

Show Answer

No. The data may reveal the overall combined response, but cannot separate the individual orders without an independent comparison.