Initial Rates Method
Learn and apply Initial Rates Method in the published Chemistry course sequence.
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The core idea
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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.
- 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
Problem
Study the worked solution
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.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
Problem
Try this before viewing the solution
Hints
Hint 1: deduce A
Hint 2: deduce B and simplify
View solution step by step
Find A's order
Method
Match 2^m to the rate factor 2.Reason
B is constant in that comparison.Working
m = 1.Find B's order
Method
Match 2ⁿ to the unchanged-rate factor 1.Reason
A is constant in that comparison.Working
n = 0.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
Learner conclusion
Assess the comparison
View solution step by step
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.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
Problem
Try this before viewing the solution
View solution step by step
Deduce A order
1 markMethod
Use runs 1 and 2, where only A changes.Reason
Doubling A doubles rate.Working
2^m = 2, so m = 1.Remove A's mixed effect
1 markMethod
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.Deduce B order
1 markMethod
Compare B’s factor 2 with its remaining rate factor 2.Reason
2ⁿ = 2.Working
n = 1.Write the rate equation
1 markMethod
Insert both first-order terms.Reason
The data establish first order in each reactant.Working
rate = k[A][B].
Self-mark with the mark scheme
Compare your response with each mark point. Select a point only when your response contains that evidence.
Credit A order, removal of A's factor, B order and complete rate equation.
Challenge 5
Use the rate equation for a new run
Problem
Try this before viewing the solution
Hints
Hint 1: use both first-order terms
Hint 2: keep the rate unit
View solution step by step
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).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.