Unit 7 · Topic 7.8 Beta

Representations of Equilibrium

Equilibrium shows up in a particle diagram as counts that stop changing and on a concentration-time graph as flat lines.

Practice 1: Models and RepresentationsPractice 3: Representing Data and PhenomenaPractice 5: Mathematical Routines

Question set for this topic

Part 1 · Hook

Why this matters

You cannot see molecules, but you can draw them. Exam writers love to show a box of colored circles and ask: is this at equilibrium, which way will it react, and what is K? A student who can count carefully and remembers that K uses concentrations, not raw counts, turns these pictures into easy points.

Part 2 · Before you start

What this builds on

Part 3 · Prerequisite check

Quick check before you start

1. What does a particulate diagram represent?

  1. The particles in a sample, drawn so you can count and identify them
  2. The mass of a sample
  3. The energy changes in a reaction
  4. The rate of a reaction
Show the answer

Particle diagrams show which particles are present and how many.

  • Correct: The particles in a sample, drawn so you can count and identify them:
  • The mass of a sample:
  • The energy changes in a reaction:
  • The rate of a reaction:

2. For X2 + Y2 ⇌ 2 XY, a box has 1 X2, 1 Y2 and 4 XY (equal gas moles on both sides). What is Q?

  1. 16
  2. 4
  3. 8
  4. 0.25
Show the answer

Q = 4² / (1 × 1) = 16.

  • Correct: 16:
  • 4:
  • 8:
  • 0.25:

3. How do you get a concentration from moles?

  1. Divide the moles by the volume in liters
  2. Multiply the moles by the volume
  3. Divide the volume by the moles
  4. Multiply the moles by the molar mass
Show the answer

Molarity = mol / L.

  • Correct: Divide the moles by the volume in liters:
  • Multiply the moles by the volume:
  • Divide the volume by the moles:
  • Multiply the moles by the molar mass:

Part 4 · See it

See it first

A container at equilibrium with 4 W atoms and 4 W2 molecules in 2.0 liters, each particle standing for 0.10 mol. Step 1, count: 4 W and 4 W2. Step 2, convert: 0.40 mol divided by 2.0 L is 0.20 M for each. Step 3, substitute: Kc = [W2] over [W] squared = 0.20 over 0.20 squared = 5.0. A note warns that putting counts straight into K would give 0.25, which is wrong because the volume does not cancel when gas moles differ on the two sides.
Count, convert counts to mol/L, then substitute. Raw counts work only when the gas moles are equal on both sides. LevlPrep original diagram.

Part 5 · Step by step

How it works, step by step

  1. Snapshots of a container show the same counts over timethe system is at equilibrium
  2. Each count is turned into moles and divided by the volumeyou have the molar concentrations Kc needs
  3. The total gas coefficients are equal on both sidesthe volume cancels, so raw counts give the right Q or K
  4. Q from a diagram is compared with Kyou can predict and draw the equilibrium mixture, conserving atoms

Part 6 · Key ideas

Key ideas

  • An equilibrium particle diagram shows a composition that no longer changes; look for identical counts over time.
  • Convert counts → moles → mol/L before using Kc. Counts work directly only when gas moles are equal on both sides.
  • On a concentration-time graph, equilibrium is where curves go flat; changes follow the coefficients.
  • An equilibrium mixture is not a limiting-reactant problem: it stops changing when Q = K.

Part 7 · Misconception

A common mistake

The wrong idea: A reaction shown in a particle diagram keeps going until one reactant runs out, as in a limiting-reactant problem.

What actually happens: A reversible reaction stops changing when Q equals K, with reactants and products both present. Use the equilibrium expression, not limiting-reactant logic.

Part 8 · Check yourself

Check yourself

Exam-style questions. Anything you miss goes into your review queue.

Particle view

A gas forming dimers

t = 0t = 20 st = 40 st = 60 s

Key: WW2

A gas W forms dimers in a sealed 2.0 L container at constant temperature: 2 W(g) ⇌ W2(g). Each particle drawn stands for 0.10 mol.

1. What is the earliest time shown at which the system is at equilibrium?

  1. 40 s
  2. 20 s
  3. 60 s
  4. 0 s
Show the answer

Equilibrium is reached when the particle counts stop changing. The first two identical snapshots are at 40 s and 60 s.

  • Correct: 40 s: Right: the counts at 40 s and 60 s are both 4 W and 4 W₂, so the composition has stopped changing.
  • 20 s: The counts change between 20 s (6 W, 3 W₂) and 40 s (4 W, 4 W₂), so the system was still reacting at 20 s.
  • 60 s: The system is at equilibrium at 60 s, but its composition was already the same at 40 s.
  • 0 s: At 0 s there is no W₂, so the forward reaction is about to change the composition.

2. Calculate [W] at equilibrium.

Type a number and its unit.

Show the answer

4 particles × 0.10 mol = 0.40 mol W; [W] = 0.40 mol / 2.0 L = 0.20 M.

  • Answer: 0.20 M

3. Calculate Kc for 2 W(g) ⇌ W2(g).

Type a number.

Show the answer

[W] = [W₂] = 0.40 mol / 2.0 L = 0.20 M. Kc = [W₂] / [W]² = 0.20 / (0.20)² = 5.0.

  • Answer: 5.0

Particle view

Which mixture is at equilibrium?

Box 1Box 2Box 3Box 4

Key: X2Y2XY

For X2(g) + Y2(g) ⇌ 2 XY(g), Kc = 4.0 at the temperature of the containers. The four containers have equal volumes.

4. Which boxes show mixtures at equilibrium? Select all that apply.

  1. Box 1
  2. Box 2
  3. Box 3
  4. Box 4
Show the answer

Here the gas moles are equal on both sides (2 and 2), so the volume cancels and counts can go straight into Q. A box is at equilibrium when Q = K = 4.0.

  • Correct: Box 1: Right: Q = 4² / (2 × 2) = 4.0 = K.
  • Box 2: Q = 2² / (3 × 3) = 0.44 < K, so it will react forward.
  • Box 3: Q = 6² / (1 × 1) = 36 > K, so it will react in reverse.
  • Correct: Box 4: Right: Q = 4² / (4 × 1) = 4.0 = K. Unequal amounts of X₂ and Y₂ do not matter; only Q = K does.

5. How will the contents of Box 3 change as it approaches equilibrium?

  1. XY will decrease, because Q > K.
  2. XY will increase, because Q > K.
  3. Nothing will change, because XY is the most abundant species.
  4. X2 will decrease, because there is very little of it.
Show the answer

Compare Q with K. Box 3 has Q = 36 > K, so the net reaction goes in reverse until Q falls to 4.0.

  • Correct: XY will decrease, because Q > K.: Right: Q = 36 > 4.0, so the net reaction runs in reverse and XY breaks down.
  • XY will increase, because Q > K.: Q > K means too much product; the net reaction must lower Q by using up XY.
  • Nothing will change, because XY is the most abundant species.: Abundance alone does not decide; Q = 36 is not K = 4.0.
  • X2 will decrease, because there is very little of it.: The net reverse reaction makes X₂ and Y₂; they increase.

6. Box 2 reaches equilibrium. Which set of counts could it then show?

  1. 2 X2, 2 Y2, 4 XY
  2. 3 X2, 3 Y2, 4 XY
  3. 4 X2, 4 Y2, 0 XY
  4. 1 X2, 1 Y2, 6 XY
Show the answer

Two conditions: atoms are conserved (each X₂ + Y₂ that reacts makes 2 XY), and the final Q equals K.

  • Correct: 2 X2, 2 Y2, 4 XY: Right: one X₂ and one Y₂ react to give 2 XY (atoms conserved), and Q = 16/4 = 4.0 = K.
  • 3 X2, 3 Y2, 4 XY: This adds 2 XY without using any X₂ or Y₂, so atoms are not conserved.
  • 4 X2, 4 Y2, 0 XY: This runs the reaction in reverse, but Box 2 has Q < K, so it must go forward.
  • 1 X2, 1 Y2, 6 XY: Atoms are conserved, but Q = 36 overshoots K = 4.0.

7. In a particle diagram of a system at equilibrium, what is true about two diagrams of the same container drawn at later times?

  1. They show the same numbers of each kind of particle.
  2. They show product particles and no reactants.
  3. They show equal numbers of reactant and product particles.
  4. They show the particles in the same positions.
Show the answer

Equilibrium is constant composition: the counts of each species do not change from snapshot to snapshot.

  • Correct: They show the same numbers of each kind of particle.: Right: at equilibrium the composition is constant, though individual particles keep reacting.
  • They show product particles and no reactants.: An equilibrium mixture contains reactants and products.
  • They show equal numbers of reactant and product particles.: Equilibrium means constant counts, not equal counts.
  • They show the particles in the same positions.: Particles keep moving and reacting; only the counts stay the same.

Part 9 · Summary

Summary

Equilibrium shows up in a particle diagram as counts that stop changing and on a concentration-time graph as flat lines. To get Kc, convert counts to moles and divide by the volume; raw counts work only when the gas coefficients are equal on both sides. Changes follow the coefficients, and a mixture reacts until Q equals K, not until a reactant runs out.

Part 10 · Up next

What comes next

Part 11 · Connections

Connections