Deduce reaction orders from rate data and graphs
Determine orders from initial-rate comparisons, concentration–time plots and rate–concentration graphs.
Section 26 · Reaction kinetics
A Level; Cambridge International Chemistry 9701, 2028–2030 syllabus, Topic 26. Rate laws are empirical unless an elementary step is explicitly stated. Written practice is self-checked
Before you begin
- Use AS collision theory, concentration, graph gradients, and balanced reaction equations.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
How is rate obtained from a concentration–time graph?
What you will learn
- Use an initial-rates comparison to deduce a concentration order
- Interpret concentration–time and rate–concentration graphs
- Use graph shape as evidence without confusing it with a mechanism
Compare experiments where one concentration changes
For experiments at the same temperature, compare pairs where only one reactant concentration changes. If a concentration changes by factor f and rate changes by factor r, solve r=fᵐ for its order m.
If two reactant concentrations change at once, use the already established order for one or compare other trials; do not assign the whole rate factor to one reactant without evidence.
Graphs show how rate relates to concentration or time
A concentration–time graph gives rate from its gradient; the tangent at the start gives an initial rate. A rate–concentration graph can be linear through the origin for first order, horizontal for zero order, or curved for second order over the measured range.
Use the graph together with the stated axes and data. A graph shape supports an order deduction but does not by itself prove a detailed molecular mechanism.
Pause and explain
[A] doubles and rate quadruples. What is the order in A?
Worked example
When [A] doubles at constant temperature, initial rate increases from 0.020 to 0.080 mol dm⁻³ s⁻¹. Deduce the order in A.
Show the worked solution
- The rate factor is 0.080/0.020 = 4.
- The concentration factor is 2.
- Solve 2ᵐ = 4.
Answer m = 2, so the reaction is second order with respect to A.
Try a topic test
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
When [B] triples and [A] is fixed, initial rate triples. Deduce the order in B.
Give me a hint
Set the rate factor equal to the concentration factor raised to the order.
Compare my reasoning
- Concentration factor = 3.
- Rate factor = 3.
- Solve 3ⁿ = 3.
n = 1; the reaction is first order in B.
Look for these in your work
- Trials compared
- Power equation written
- Order deduced
A rate–[A] graph is horizontal while other conditions stay fixed. What order in A is supported?
Give me a hint
A horizontal rate means changing [A] does not change the measured rate.
Compare my reasoning
- Rate is independent of [A] in the range.
- That corresponds to exponent zero.
- State the observed order, not a mechanism.
Zero order in A is supported over the measured concentration range.
Look for these in your work
- Graph trend described
- Order related to rate
- Range limitation noted
Two trials both change [A] and [B], and rate changes by a factor of 8. Explain why the order in A cannot be read as 3 from these trials alone.
Give me a hint
A combined rate factor may reflect both reactant orders.
Compare my reasoning
- Write rate factor = factor(A)^m × factor(B)^n.
- Both concentration factors changed.
- More isolated comparisons are needed to separate m and n.
The factor of 8 reflects both concentration changes and their unknown orders. Without another comparison or prior order information, these trials do not isolate the order in A.
Look for these in your work
- Both changes acknowledged
- Rate factors related to powers
- Need for more evidence stated
Common mistakes
- Comparing trials where several variables change
- Using a single graph point instead of its gradient for rate
- Confusing concentration–time and rate–concentration plots
- Inferring a mechanism directly from an empirical order
What can you explain now?
How is rate obtained from a concentration–time graph?
Compare with the explanation
From the gradient
The gradient is change in concentration per time.
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Make it stick
How do controlled initial-rate comparisons and graph gradients provide evidence for reaction orders?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.