What does a constant disappearance rate look like?
You will be able to: Use a zero-order concentration–time line and respect its depletion limit.
What does a constant disappearance rate look like?
A process removes the same concentration amount each second while its rate-controlling conditions remain unchanged. A graph then falls by equal vertical steps over equal time intervals.
A useful starting point: How can color measurements reveal reaction rate? →
Words and symbols before equations
- Zero order
- Rate independent of the monitored concentration over a stated range.
- Initial concentration, [A]₀
- Concentration at time zero.
- Integrated rate law
- Equation relating concentration to elapsed time.
- Depletion time
- Time at which the idealized model reaches zero reactant.
What this picture assumes
−d[A]/dt=k=0.020 M/s while reactant remains and zero-order conditions hold. The theoretical straight line ends at depletion; negative concentration is never displayed.
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]=0.6 M. Slope=−0.020 M/s while reactant remains; depletion at 40 s.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the chemistry
For a monitored disappearance law −d[A]/dt = k, the integrated relation is [A]t = [A]₀ − kt. The straight [A] versus t line has slope −k.
The initial height is [A]₀. Increasing that height extends the time to depletion without changing slope when k and the zero-order regime stay fixed.
The line cannot continue into negative concentration. The simple law applies only while reactant remains and the assumed zero-order conditions hold.
A flat rate does not mean no reaction. It means a constant positive amount per volume disappears per second; in real systems the limiting conditions can eventually change.
A worked example, step by step
[A]₀=0.60 M and k=0.020 M/s for zero-order disappearance. Find [A] after 10 s and the ideal depletion time.
- Use [A]t = [A]₀ − kt because the disappearance law is zero order.
- At 10 s: 0.60 − 0.020(10) = 0.40 M.
- Set 0 = 0.60 − 0.020t to get t = 30 s.
- Beyond 30 s the formula is outside its valid range; a negative concentration is not a prediction to accept.
Stop the zero-order line at depletion. Mathematical extrapolation is not permission to display negative concentrations.
Does zero order mean the concentration never changes?
Compare with an explanation
No. It decreases linearly while the disappearance rate is independent of concentration in the modeled range.
Predict. Change one thing. Explain.
Move time toward and past depletion. Explain why the display stops at zero and why the original constant disappearance law cannot continue after the reactant is exhausted.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
At 10 s, [A]=0.6 M. Slope=−0.020 M/s while reactant remains; depletion at 40 s.
−d[A]/dt=k=0.020 M/s while reactant remains and zero-order conditions hold. The theoretical straight line ends at depletion; negative concentration is never displayed.
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 zero-order reactant starts at 0.80 M and disappears at 0.020 M/s. Find concentration at 15 s, depletion time, slope and why a 50 s extrapolation is invalid.
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Compare with the answer and four-point rubric
- 1 point: [A]15 = 0.80 − 0.020(15) = 0.50 M.
- 1 point: Ideal depletion time = 0.80/0.020 = 40 s.
- 1 point: Concentration–time slope = −0.020 M/s.
- 1 point: At 50 s the unrestricted formula is negative; the zero-order regime cannot persist past exhaustion.
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 is the zero-order linear plot?
Concentration versus time.
RECALL 2What is its slope?
−k for the stated disappearance law.
RECALL 3What is the domain limit?
The model ends at depletion or when its physical assumptions cease to apply.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
What does a constant disappearance rate look like?
- [A]t = [A]₀ − kt; slope of [A] vs t = −k.
- k units M/s; valid while [A] ≥ 0 and zero-order conditions hold.
Remember: Stop the zero-order line at depletion. Mathematical extrapolation is not permission to display negative concentrations.
Conditions: −d[A]/dt=k=0.020 M/s while reactant remains and zero-order conditions hold. The theoretical straight line ends at depletion; negative concentration is never displayed.
Refresh Kid · AP Chemistry Unit 5 · Objectives 5.3.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 5.3, objective 5.3.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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