What do concentration and rate graphs show near equilibrium?
You will be able to: Read distinct concentration and rate graphs as a reversible system settles.
What do concentration and rate graphs show near equilibrium?
Imagine measuring a colored product every second. Its signal increases and then levels off. To interpret that plateau, separate how much product is present from how fast each direction is occurring.
A useful starting point: How can a system keep changing without a visible change? →
Words and symbols before equations
- Concentration, [A]
- Amount of A per solution volume, in mol/L or M.
- Plateau
- A nearly horizontal region where the measured quantity changes little.
- Forward/reverse rate
- Concentration converted in each direction per second.
- Time axis
- Horizontal coordinate in seconds, distinct from a reaction-energy coordinate.
What this picture assumes
Same supplied first-order A ⇌ B model: kf=0.30 s⁻¹, kr=0.10 s⁻¹, total 1.00 M, initial all A. Rate laws are model assumptions, not inferred for arbitrary overall reactions.
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.
- At 10 s: [A]=0.26374 M, [B]=0.73626 M; rf=0.079121 and rr=0.073626 M/s. Limiting values: [A]=0.25 M, [B]=0.75 M; both rates 0.075 M/s. The model approaches these limits smoothly.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the chemistry
On a concentration graph, horizontal curves mean nearly constant concentrations. The curves do not need to cross or reach the same height.
On a graph of the opposing rates, equilibrium requires equal heights. Those equal rates can be nonzero.
The supplied elementary first-order A ⇌ B model uses rf=kf[A] and rr=kr[B]. These laws are given assumptions, not rules inferred for every overall reaction from its coefficients.
The mathematical model approaches its limiting composition smoothly. A practical experimental plateau means further change falls below measurement resolution; no arbitrary finite instant makes an exponential exactly constant.
A worked example, step by step
For the supplied model, kf=0.30 s⁻¹, kr=0.10 s⁻¹ and [A]+[B]=1.00 M. Find the limiting concentrations and opposing rates.
- At equilibrium 0.30[A]=0.10[B], so [B]=3[A].
- Use conservation: [A]+3[A]=1.00 M.
- [A]=0.250 M and [B]=0.750 M.
- Both rates equal 0.0750 M/s; the concentration heights differ while the rate heights match.
Do not confuse equal rate-curve heights with equal concentration-curve heights.
Must concentration curves cross when equilibrium is reached?
Compare with an explanation
No. Equilibrium concerns equal opposing rates, not equal concentrations.
Predict. Change one thing. Explain.
Switch between concentration and rate plots. At the same time coordinate, describe what each vertical axis measures. Predict the limiting heights.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
At 10 s: [A]=0.26374 M, [B]=0.73626 M; rf=0.079121 and rr=0.073626 M/s. Limiting values: [A]=0.25 M, [B]=0.75 M; both rates 0.075 M/s. The model approaches these limits smoothly.
Same supplied first-order A ⇌ B model: kf=0.30 s⁻¹, kr=0.10 s⁻¹, total 1.00 M, initial all A. Rate laws are model assumptions, not inferred for arbitrary overall reactions.
Explain what you noticed: Answer the investigation prompt above. State one observation and explain it using relative rates, particle conservation, the Q/K comparison or the stated dissolution equilibrium. 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 model has [A]eq=0.20 M, [B]eq=0.80 M and kf=0.40 s⁻¹. Find kr and describe both concentration and rate graphs near equilibrium.
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Compare with the answer and four-point rubric
- 1 point: Forward rate is 0.40×0.20=0.080 M/s.
- 1 point: Reverse rate must also be 0.080 M/s.
- 1 point: kr=0.080/0.80=0.10 s⁻¹.
- 1 point: Concentrations plateau at 0.20 and 0.80 M; opposing rates meet at 0.080 M/s.
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 1What does a concentration plateau show?
Little net change in concentration.
RECALL 2What does a nonzero rate plateau allow?
Continuing microscopic conversion.
RECALL 3Can overall coefficients establish a general rate law?
No; the displayed first-order laws are model assumptions.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
What do concentration and rate graphs show near equilibrium?
- For the supplied first-order pair: rf=kf[A], rr=kr[B].
- With total C: [B]eq=Ckf/(kf+kr).
Remember: Do not confuse equal rate-curve heights with equal concentration-curve heights.
Conditions: Same supplied first-order A ⇌ B model: kf=0.30 s⁻¹, kr=0.10 s⁻¹, total 1.00 M, initial all A. Rate laws are model assumptions, not inferred for arbitrary overall reactions.
Refresh Kid · AP Chemistry Unit 7 · Objectives 7.1.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 7.1, objective 7.1.A. CED effective Fall 2024 and June 2026 clarifications checked September 17, 2026. Unit 7: Equilibrium, Topics 7.1–7.12. 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. Converting between Kc and Kp and calculations for a dissolved species in equilibrium with its gas phase are excluded from assessed Unit 7 scope. Concentrations use mol/L and gas partial pressures use the stated pressure convention. Supplied constants are teaching data at fixed temperature unless otherwise specified. Ideal dilute-solution and ideal-gas approximations are stated. 3D views show inventories, not molecular trajectories, measured structures or proof of equilibrium from a single snapshot. Approximation checks are explicit; a small K alone does not justify neglecting every change.
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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