Why do equilibrium constants multiply when reactions add?
You will be able to: Cancel species and multiply consistently transformed equilibrium expressions.
Why do equilibrium constants multiply when reactions add?
A two-leg journey A to B and B to C connects A to C. In an equilibrium calculation, the shared species B cancels from both the summed equation and the multiplied composition ratios.
A useful starting point: What happens to K when the equation changes? →
Words and symbols before equations
- Constituent reaction
- One reaction used to construct a net equation.
- Cancel
- Remove identical species with the same state appearing on opposite sides.
- Net equation
- Equation remaining after valid cancellation.
- Product of constants
- Multiplication of K values after any required transformations.
What this picture assumes
Supplied K₁=4 for A ⇌ B and K₂ for C ⇌ B, at matching conditions. Target A ⇌ C requires reversing the second equation. Abstract A/B/C represent consistent species; this is not a kinetic mechanism.
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.
- Knet=2. The common species cancels algebraically; the equations do not by themselves establish a kinetic mechanism.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the chemistry
If A ⇌ B has K₁=[B]/[A] and B ⇌ C has K₂=[C]/[B], their product is [C]/[A]. This is the K expression for A ⇌ C.
Before multiplying, reverse or scale each reaction to match the target and transform its K in the same way.
Only identical species in identical states cancel. The algebra describes a thermochemical relation between equilibria; it does not establish that the listed reactions are an actual kinetic mechanism.
All constants must refer to matching temperature and conventions. Q expressions multiply by the same algebra when evaluated at a consistent composition.
A worked example, step by step
A ⇌ B has K₁=4. C ⇌ B has K₂=2. Find K for A ⇌ C.
- Keep A ⇌ B in its given direction.
- Reverse C ⇌ B to B ⇌ C, changing its constant to 1/2.
- Add equations and cancel B, leaving A ⇌ C.
- Multiply transformed constants: K=4×(1/2)=2.
Adding equations multiplies their constants; it does not add them.
Why does the intermediate B disappear from the product of expressions?
Compare with an explanation
Its concentration appears once above and once below the division line, so it cancels.
Predict. Change one thing. Explain.
Change the second supplied constant for C ⇌ B. Predict K for A ⇌ C and identify the reciprocal needed before multiplication.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Knet=2. The common species cancels algebraically; the equations do not by themselves establish a kinetic mechanism.
Supplied K₁=4 for A ⇌ B and K₂ for C ⇌ B, at matching conditions. Target A ⇌ C requires reversing the second equation. Abstract A/B/C represent consistent species; this is not a kinetic mechanism.
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⇌B has K=8; 2C⇌2B has K=16. Construct A⇌C and calculate its K.
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Compare with the answer and four-point rubric
- 1 point: Halve 2C⇌2B to C⇌B; K=√16=4.
- 1 point: Reverse to B⇌C; K=1/4.
- 1 point: Add A⇌B and B⇌C to cancel B.
- 1 point: Knet=8/4=2.
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 happens to K when equations add?
Multiply the transformed constants.
RECALL 2Must equations be kinetic steps?
No; the equilibrium algebra does not establish a mechanism.
RECALL 3What must match between constants?
Temperature and concentration/pressure conventions.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Why do equilibrium constants multiply when reactions add?
- For summed reactions at matching conditions: Knet=∏Ki after reversal/scaling.
- Cancel only identical species and physical states.
Remember: Adding equations multiplies their constants; it does not add them.
Conditions: Supplied K₁=4 for A ⇌ B and K₂ for C ⇌ B, at matching conditions. Target A ⇌ C requires reversing the second equation. Abstract A/B/C represent consistent species; this is not a kinetic mechanism.
Refresh Kid · AP Chemistry Unit 7 · Objectives 7.6.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 7.6, objective 7.6.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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