Test whether a mechanism fits the rate equation
Compare a proposed multi-step mechanism with the overall equation and experimental rate law.
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
What two checks are needed for a proposed mechanism?
What you will learn
- Add elementary steps to recover the overall equation
- Use a slow step to predict a rate dependence
- Judge whether a mechanism agrees with experimental data
A viable mechanism must conserve species and atoms
When mechanism steps are added, intermediates cancel and the result must match the balanced overall reaction. Any catalyst is used then regenerated and also cancels from the net equation.
A proposed mechanism is consistent with the rate equation when its rate-determining step, together with any preceding fast equilibrium assumptions, predicts the experimentally measured orders.
Do not use an overall equation to invent the rate law
For a single elementary slow step, reactant concentrations in that step determine its rate expression. For a multi-step process, a slow-step expression may contain an intermediate; use a prior fast equilibrium to replace it with measurable reactants when appropriate.
A candidate mechanism that predicts a different order from experiment is not supported, even if its steps add to the correct overall equation.
Pause and explain
For a slow elementary step I + B → P, what immediate rate form is predicted?
Worked example
A proposed mechanism has fast A + B ⇌ I followed by slow I + B → P. What rate equation does it predict if the first step is a fast equilibrium?
Show the worked solution
- The slow step gives rate = k[I][B].
- The fast equilibrium gives [I] proportional to [A][B].
- Substitute for [I].
Answer The predicted rate is proportional to [A][B]². The mechanism is supported only if this agrees with the measured rate law and the steps sum to the overall reaction.
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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.
Fast equilibrium: A + B ⇌ I. Slow step: I → P. Deduce the rate dependence on A and B.
Give me a hint
The slow rate is proportional to [I]; use the fast equilibrium to replace [I].
Compare my reasoning
- Slow step gives rate ∝ [I].
- Fast equilibrium gives [I] ∝ [A][B].
- Substitute the proportionality.
The mechanism predicts rate ∝ [A][B].
Look for these in your work
- Slow-step expression used
- Intermediate related to reactants
- Predicted orders stated
A mechanism sums to the correct overall reaction but predicts rate = k[A]², while experiments show rate = k[A]. Is it consistent?
Give me a hint
Compare its predicted and measured order.
Compare my reasoning
- The overall stoichiometry matches.
- The predicted order is 2 but measured order is 1.
- Both conditions are required.
No. Matching the overall equation is not sufficient; the mechanism predicts second order while experiment shows first order in A.
Look for these in your work
- Stoichiometry checked
- Orders compared
- Conclusion justified
A slow step predicts rate = k[I][B], but I is an intermediate and a preceding fast equilibrium is supplied. What should be done before comparing with an experimental rate law?
Give me a hint
Express the intermediate concentration using the fast equilibrium.
Compare my reasoning
- Write the equilibrium relation for I.
- Substitute it into the slow-step rate expression.
- Compare the resulting measurable-reactant orders with experiment.
Use the fast equilibrium to replace [I] with a relationship involving reactant concentrations, then compare the derived rate law with the measured law.
Look for these in your work
- Intermediate eliminated
- Fast equilibrium used
- Experimental comparison made
Common mistakes
- Using an overall stoichiometric coefficient as an order
- Leaving an intermediate in the summed equation
- Treating the slow step as the whole story when it contains an intermediate
- Accepting a mechanism that conflicts with measured orders
What can you explain now?
What two checks are needed for a proposed mechanism?
Compare with the explanation
It sums to the overall equation and fits the measured rate law
Both stoichiometry and kinetic evidence must agree.
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Make it stick
How must a mechanism satisfy both atom balance and the observed concentration dependence of rate?
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.