AP Chemistry · Unit 7 · Topic 7.8
Representations of Equilibrium
A particle sketch, a graph, and a K expression can describe the same sample. Learning to translate between them is more useful than memorizing what an “equilibrium picture” should look like.
A snapshot is not a time record
A single particle diagram gives composition at one moment. It does not establish equal opposing rates. Several identical-looking snapshots suggest stable bulk composition, but individual particles may have exchanged identities. To infer equilibrium confidently, combine composition data with evidence that the reversible system can relax from either direction.
Count conserved units first
Consider a model \(R\rightleftharpoons S\) in equal-volume boxes, where each symbol represents the same number of particles. R and S have the same atomic inventory. Every conversion preserves the total number of symbols, so the sum is a useful check. For a dissociation reaction, conserved atoms rather than molecule count would be the correct check.
Three representations of one model
| Observation | R symbols | S symbols | [S]/[R] |
|---|---|---|---|
| Start | 18 | 2 | 0.111 |
| Later | 8 | 12 | 1.50 |
| Plateau | 5 | 15 | 3.00 |
A concentration graph would show S rising and R falling toward separate plateaus. A rate graph would instead show forward and reverse rates approaching the same value.
Work from counts to concentrations
Let every symbol represent 0.0020 mol and let the box volume be 0.50 L. At the plateau, \(n_R=0.010\) mol and \(n_S=0.030\) mol, so [R] = 0.020 M and [S] = 0.060 M. Therefore
The count ratio works because both species occupy the same volume and the reaction is one-to-one. Those conditions should be stated, not assumed universally.
Read an instantaneous jump correctly
If extra S is suddenly injected into a fixed-volume vessel, its concentration jumps before reaction redistributes the mixture. R does not jump merely because the equation is reversible; it changes afterward as net reverse reaction occurs. If the injection also changes volume, both concentrations may jump from dilution, so the experimental details matter.
Use graphs to test a story
A student draws both equilibrium concentrations at the same height because the rates are equal. The error is a mismatch between vertical-axis quantities. Ask the student to label axes with units and explain the meaning of the slope. Concentration plateaus mean zero net rate of change; they do not require matching plateau heights.
Respect the resolution of a drawing
Twenty symbols cannot display a very small trace concentration accurately. An absent symbol may represent a value below the drawing's resolution rather than a truly absent species. Particle illustrations also omit solvent molecules and many collisions for readability. A defensible interpretation states what has been simplified.
Practice with answers
- At equilibrium, one equal-volume box has 4 R and 16 S symbols. Find K for \(R\rightleftharpoons S\). 4.
- Which graph must have equal plateau heights: rates or concentrations? The opposing reaction-rate graph.
- Can you infer K for \(R_2\rightleftharpoons2R\) from a simple count ratio alone? No; the squared concentration and the particle-to-concentration scale matter.
Factual references: OpenStax Chemistry 2e, 13.1 and 13.2. The representations, counts, and questions are original.
Official curriculum reference: College Board AP Chemistry course page. The explanation and worked example are independently written for this study site.