How does a slow first step predict the rate law?
You will be able to: Derive a rate law for a supplied mechanism with a rate-limiting first elementary step.
How does a slow first step predict the rate law?
A slow entry gate limits the flow into a sequence of faster stations. In a suitable mechanism, a slow first elementary step can similarly control the overall rate.
A useful starting point: If both cancel, how are catalysts and intermediates different? →
Words and symbols before equations
- Rate-limiting step
- Step whose kinetics controls the rate under the stated approximation.
- Slow-step approximation
- Treatment in which later steps remove intermediates rapidly relative to their formation.
- Predicted rate law
- Concentration dependence derived from a proposed mechanism.
What this picture assumes
Supplied slow elementary 2NO₂ step, followed by fast NO₃+CO step. k₁=0.50 M⁻¹ s⁻¹; overall normalized r≈k₁[NO₂]². CO range is assumed sufficient for the fast step; do not extrapolate to absent CO.
Read the picture in three steps
- Read the species and labels first. Identify what each symbol and line represents. Read the units and fixed conditions before comparing quantities.
- r≈0.02 M/s. NO₂ controls this prediction quadratically; changing CO within the assumed fast-step range has no effect. This is a mechanism hypothesis, not universal NO₂/CO kinetics.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the chemistry
Use the supplied model: 2NO₂ → NO₃+NO is slow and elementary; NO₃+CO → NO₂+CO₂ is fast. The first step’s event law is k₁[NO₂]².
Each first-step event leads to one completed net NO₂+CO → NO+CO₂ reaction under this approximation, so r≈k₁[NO₂]².
CO appears in the net equation but not in this predicted rate law because it is used in the fast step. This assumes enough CO for that step to remain fast; the approximation need not hold at arbitrarily low CO.
Compare with measured kinetics. Agreement supports this mechanism under those conditions but does not prove it is unique. A slow later step containing an intermediate requires additional analysis.
A worked example, step by step
For the supplied mechanism A+B → I (slow, elementary), I+B → AB₂ (fast), predict the law and the effect of doubling B.
- The first elementary event requires one A and one B.
- Its event rate is k₁[A][B].
- Under the supplied slow-first-step approximation, the overall reaction rate is approximately that expression.
- Doubling B at fixed A doubles the predicted rate, despite B having coefficient 2 in the net equation.
Use the slow elementary step’s reactants, not the overall reaction coefficients, to form this predicted rate law.
Does zero order in CO mean CO is not consumed?
Compare with an explanation
No. It is consumed in the net reaction, but the modeled rate-limiting step does not depend on its concentration.
Predict. Change one thing. Explain.
Change NO₂ and CO independently in the supplied slow-first-step model. Predict the effect within the model’s valid range and explain the absence of CO from the law.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
r≈0.02 M/s. NO₂ controls this prediction quadratically; changing CO within the assumed fast-step range has no effect. This is a mechanism hypothesis, not universal NO₂/CO kinetics.
Supplied slow elementary 2NO₂ step, followed by fast NO₃+CO step. k₁=0.50 M⁻¹ s⁻¹; overall normalized r≈k₁[NO₂]². CO range is assumed sufficient for the fast step; do not extrapolate to absent CO.
Explain what you noticed: Answer the investigation prompt above. State one observation and explain it using concentration–time slopes, rate-law dependence, encounter geometry or the stated mechanism. Identify what the representation cannot tell you.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionA proposed slow-first-step mechanism predicts r=k[A]² but experiments show doubling A doubles rate. Explain the prediction, the mismatch, what can be concluded and what cannot.
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Compare with the answer and four-point rubric
- 1 point: The proposed law predicts a fourfold increase when A doubles.
- 1 point: The measured increase is only twofold.
- 1 point: The mechanism/approximation is inconsistent with those data and conditions.
- 1 point: The mismatch rejects this proposal but does not by itself identify a unique replacement mechanism.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1Where does the predicted law come from here?
The first rate-limiting elementary step.
RECALL 2Can a net reactant be absent from the law?
Yes, under an appropriate mechanism and concentration range.
RECALL 3What does matching kinetics establish?
Consistency and support, not automatic uniqueness.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
How does a slow first step predict the rate law?
- Slow first elementary A+B step: r≈k₁[A][B].
- Check the summed equation and consistency with measured rates.
Remember: Use the slow elementary step’s reactants, not the overall reaction coefficients, to form this predicted rate law.
Conditions: Supplied slow elementary 2NO₂ step, followed by fast NO₃+CO step. k₁=0.50 M⁻¹ s⁻¹; overall normalized r≈k₁[NO₂]². CO range is assumed sufficient for the fast step; do not extrapolate to absent CO.
Refresh Kid · AP Chemistry Unit 5 · Objectives 5.8.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 5.8, objective 5.8.A. CED effective Fall 2024 and June 2026 clarifications checked September 16, 2026. Unit 5: Kinetics, Topics 5.1–5.11. Focused lesson names, examples, models and assessments are original Refresh Kid teaching materials, not additional official topics or official AP questions. Official corrections.
The model states its assumptions beside the diagram. Arrhenius calculations are not assessed in the current AP framework; temperature and activation energy are taught qualitatively here. Collection of intermediate-detection data is not assigned. Integrated rate laws explicitly use the monitored species’ disappearance constant, while event and normalized reaction rates are labeled separately. Pre-equilibrium models state their timescale assumptions and use free concentrations. Original illustrative data and geometry are not measured kinetics.
Teaching resources: The Organic Chemistry Tutor video titles/descriptions and topic coverage were checked for optional links; no claim is made to have watched every video. No creator scripts, examples, worksheets or artwork were copied. GitHub’s 3D website collection and its Three.js camera-control example informed the idea of controllable spatial inspection. Scientific diagrams, geometry and interactions here are original. The self-hosted Three.js runtime retains its MIT license. Camera rotation changes the view, not the chemistry.
Independent teacher review and observation of students remain pending. Implementation checks do not certify scientific accuracy, accessibility or learning effectiveness. This is a review edition.
Optional official resource: Released AP Chemistry questions and scoring guides. This archive contains questions across units; it is not an assignment of every question to this lesson.
The teaching sequence is informed by the IES learning guide; this exact implementation has not been evaluated with learners.
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