AP® Chemistry review sheet from Aim for Five (aimforfive.com/chem/units/7/7-8)
Unit 7 · Topic 7.8
7.8 Representations of Equilibrium
Particle diagrams show the molecules in a container at different moments. By counting reactant and product particles, you can tell whether the system has reached equilibrium, decide whether K is large or small, and estimate the value of K.
Key terms
- particle diagram
- particulate model
- equilibrium mixture
What a particle diagram represents
In a particle diagram, each shape stands for one molecule, ion or atom, drawn in a box that represents the container. Different colors or sizes show different elements. Because every drawing of the same container has the same volume, the number of particles of a species is proportional to its concentration (or its partial pressure, for a gas).
Has it reached equilibrium?
Look at a series of diagrams taken at different times. While the system is moving toward equilibrium, the counts change from one picture to the next. Once the counts stop changing, the system is at equilibrium.
Two identical diagrams in a row show equilibrium, but don't conclude that particles stopped reacting. Individual molecules are still converting back and forth; the counts stay the same because the rates are equal.
Estimating K from counts
- Count each species in the equilibrium diagram.
- If the problem says what each particle represents (for example, 0.10 mol in a 1.0 L box), convert counts to concentrations.
- If the number of reactant particles in the K expression equals the number of product particles (total exponents top and bottom are equal, as in A₂ + B₂ ⇌ 2AB), the volume cancels and you can use the raw counts directly.
- If the totals differ, you must convert to concentrations first, or you'll get the wrong K.
Judging K without numbers
An equilibrium picture that is mostly product particles means K > 1. One that is mostly reactant particles means K < 1. If two diagrams show the same reaction at two temperatures, the one with more products has the larger K at that temperature.
When you draw your own diagram for an equilibrium mixture, conserve atoms (count each element before and after), show both reactants and products (an equilibrium mixture always has some of each), and keep the ratios consistent with the K or data given.
Before-and-after diagrams for a disturbance
Some questions show an equilibrium mixture, then a disturbance, such as extra reactant particles added or a change in temperature, then a new equilibrium. Count particles in each picture and compare the ratio in the K expression. If the ratio is back to its old value, the temperature didn't change (K is the same). If the new equilibrium picture has a different ratio, K changed, which means the temperature changed. More products at the new equilibrium means K went up.
Worked examples
Try each one yourself first, then open the solution.
- Example 1
K from a diagram when the volume cancels
For A₂(g) + B₂(g) ⇌ 2AB(g), an equilibrium diagram shows 2 A₂ molecules, 2 B₂ molecules and 6 AB molecules. Estimate K. How many A₂ and B₂ were there at the start, if no AB was present?
Show the solutionHide the solution
- Step 1: K = [AB]² / ([A₂][B₂]). The exponents add to 2 on top and 2 on the bottom, so the volume cancels and counts can be used directly.
- Step 2: K = 6² ÷ (2 × 2) = 36 ÷ 4 = 9.
- Step 3: Atom count: 6 AB contain 6 A atoms, which came from 3 A₂. So the start had 2 + 3 = 5 A₂, and likewise 5 B₂.
- Step 4: K > 1 matches the picture: products outnumber reactants.
Answer: K = 9; the system started with 5 A₂ and 5 B₂.
- Example 2
Trap: when the volume doesn't cancel
For X₂(g) ⇌ 2X(g) in a 1.0 L box, each particle represents 0.10 mol. Diagrams at four times show: t₁: 6 X₂, 0 X; t₂: 4 X₂, 4 X; t₃: 3 X₂, 6 X; t₄: 3 X₂, 6 X. When is equilibrium reached, and what is Kc?
Show the solutionHide the solution
- Step 1: Check atoms: t₂ has 8 + 4 = 12 X atoms and t₃ has 6 + 6 = 12, same as the start (12). Good.
- Step 2: The counts stop changing between t₃ and t₄, so equilibrium is reached by t₃.
- Step 3: Convert counts: [X₂] = 3 × 0.10 mol ÷ 1.0 L = 0.30 M; [X] = 6 × 0.10 = 0.60 M.
- Step 4: Kc = [X]² / [X₂] = (0.60)² ÷ 0.30 = 0.36 ÷ 0.30 = 1.2.
- Step 5: Using raw counts would give 6² ÷ 3 = 12, which is wrong, because the exponents (2 on top, 1 on the bottom) don't match, so the conversion factor doesn't cancel.
Answer: Equilibrium by t₃; Kc = 1.2
Common mistakes
- Using raw particle counts in K when the total exponents on top and bottom differ.
- Drawing an equilibrium mixture with zero reactant or zero product particles.
- Not conserving atoms between a 'before' and an 'after' diagram.
- Deciding equilibrium was reached from one diagram alone. You need to see that counts have stopped changing.
On the exam
- Particle-diagram questions ask you to pick or draw the diagram that represents equilibrium, or to estimate K from one. Show the counts you used and the K expression.
- When comparing diagrams at two temperatures, link more products to a larger K, then (if asked) to whether the reaction is endothermic or exothermic.
Connected topics
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Check yourself
5 questions on 7.8 Representations of Equilibrium. Pick an answer to see if you got it, and why.
The reaction A₂(g) + B₂(g) ⇌ 2AB(g) takes place in a sealed container at constant temperature.
Diagram 1 shows the container at equilibrium: it holds 4 A₂ molecules, 2 B₂ molecules and 4 AB molecules.
Diagram 2 shows a different mixture in an identical container at the same temperature: it holds 3 A₂ molecules, 3 B₂ molecules and 2 AB molecules.
Described particle diagrams
Based on diagram 1, what is the value of K for the reaction? (Because the numbers of moles of gas are the same on both sides, particle counts can be used in place of concentrations.)
Which of the following describes what will happen in the mixture shown in diagram 2?
The reaction X₂(g) ⇌ 2X(g) takes place in a sealed 1.0 L container at constant temperature. In each particle diagram, every particle drawn represents 0.10 mol.
Diagram 1 (time 0): 6 X₂ molecules and 0 X atoms
Diagram 2 (1 min): 4 X₂ molecules and 4 X atoms
Diagram 3 (2 min): 3 X₂ molecules and 6 X atoms
Diagram 4 (3 min): 3 X₂ molecules and 6 X atoms
Described particle diagrams
Which is the earliest diagram that shows the system at equilibrium?
What is the value of Kc at this temperature?
Diagram 5 shows a different mixture in an identical container at the same temperature: 2 X₂ molecules and 4 X atoms. Which of the following describes what will happen?
0 of 5 answered