How fast is a reactant disappearing?
You will be able to: Calculate an average disappearance rate and distinguish it from an instantaneous rate.
How fast is a reactant disappearing?
A colored reactant fades quickly at first and more slowly later. The amount lost in the first minute need not match the amount lost in the next. A rate tells us how much changes per unit time.
A useful starting point: Review concentration in moles per liter →
Words and symbols before equations
- Concentration, [A]
- Amount of species A per volume; M means mol/L.
- Delta, Δ
- Final value minus initial value.
- Average rate
- Change over a specified time interval.
- Instantaneous rate
- Rate at one instant, represented by a tangent slope.
What this picture assumes
Constant-volume illustrative disappearance: [A]=0.800 exp(−0.030t) M. The secant spans the selected time to 10 s later. Tangent rate is k[A]; curve is not particle motion.
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]=0.59265 M. Instantaneous disappearance 0.01778 M/s; average over 10–20 s is 0.015361 M/s. The concentration curve is flattening.
- 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–time graph, time is horizontal and concentration vertical. A secant connects two measured points; its slope is Δ[A]/Δt.
A consumed reactant has a negative concentration slope. Its positive disappearance rate is −Δ[A]/Δt. A forming product usually has a positive appearance rate.
A tangent touches the curve at a selected instant and represents its local slope. A long-interval average does not necessarily equal that instantaneous value.
The graph is a concentration model at constant volume and temperature, not the path traveled by a molecule. A flatter decreasing curve means slower disappearance, not a smaller remaining volume.
A worked example, step by step
[A] decreases from 0.80 M at 10 s to 0.50 M at 40 s. Find the average disappearance rate.
- Compute Δ[A] = 0.50 − 0.80 = −0.30 M.
- Compute Δt = 40 − 10 = 30 s.
- The concentration slope is −0.30/30 = −0.010 M/s.
- Disappearance rate is the negative of that slope: +0.010 M/s. It describes this interval, not necessarily every instant.
Concentration is the graph’s height; rate is related to its slope. A high concentration does not by itself establish a high rate.
Can a reactant concentration decrease while its disappearance rate is positive?
Compare with an explanation
Yes. The minus sign converts a negative concentration slope into a positive disappearance rate.
Predict. Change one thing. Explain.
Move the observation time while keeping the first-order model fixed. Compare the tangent rate with the average over the following 10 seconds. Explain why the two differ.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
At 10 s, [A]=0.59265 M. Instantaneous disappearance 0.01778 M/s; average over 10–20 s is 0.015361 M/s. The concentration curve is flattening.
Constant-volume illustrative disappearance: [A]=0.800 exp(−0.030t) M. The secant spans the selected time to 10 s later. Tangent rate is k[A]; curve is not particle motion.
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 reactant goes from 0.90 M at 5 s to 0.54 M at 23 s. Calculate average disappearance rate, give units, and explain why a tangent at 5 s might give a different answer.
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Compare with the answer and four-point rubric
- 1 point: Δ[A] = −0.36 M and Δt = 18 s.
- 1 point: Average disappearance rate = 0.020 M/s.
- 1 point: M/s means mol per liter per second.
- 1 point: A tangent gives a local rate; the reaction may slow across the interval.
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 Δ[A]?
Final concentration minus initial concentration.
RECALL 2What does a tangent slope describe?
The instantaneous concentration-change rate.
RECALL 3Why negate a reactant slope?
To report a positive disappearance rate for a consumed reactant.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
How fast is a reactant disappearing?
- Average disappearance rate of A = −Δ[A]/Δt.
- Instantaneous disappearance rate = negative tangent slope; units M/s.
Remember: Concentration is the graph’s height; rate is related to its slope. A high concentration does not by itself establish a high rate.
Conditions: Constant-volume illustrative disappearance: [A]=0.800 exp(−0.030t) M. The secant spans the selected time to 10 s later. Tangent rate is k[A]; curve is not particle motion.
Refresh Kid · AP Chemistry Unit 5 · Objectives 5.1.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 5.1, objective 5.1.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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