What particle-diagram questions test
A particulate diagram粒子示意图 uses small circles for atoms, molecules and ions. It turns up in almost every AP Chemistry unit, most often in five kinds of question:
- Before and after a reaction: conservation of atoms, reacting in the ratio of the coefficients, and which reactant runs out first (U4.5).
- Solutions: strong electrolytes ionizing completely, weak electrolytes ionizing partly, insoluble solids precipitating, dilution, and comparing concentrations (U3.8, U4.2, U8.3).
- Gases: at the same temperature and volume, pressure is proportional to the number of molecules; partial pressures and mole fractions (U3.4).
- Equilibrium: counting particles to calculate K or Q and predict the direction of reaction (U7.8).
- States and forces: how particles are arranged and spaced in solids, liquids and gases, and how water molecules orient around ions (U3.1, U3.3).
Reading a diagram in four steps
- Read the key and the question first. What does each color and size stand for? Are water molecules shown? What does the box size represent (volume, for example)? How many moles does one particle stand for?
- Count. Write down the number of each kind of particle on scratch paper instead of eyeballing it.
- Check conservation and ratios. Atoms are the same before and after; in a solution the total positive charge equals the total negative charge; a reaction goes in the ratio of the coefficients until the limiting reactant is used up.
- Eliminate wrong options. A wrong diagram usually makes one of these mistakes:
- the number of atoms changes;
- both reactants are left over (the reaction hasn’t finished);
- a strong electrolyte is drawn as molecules, or a weak electrolyte as fully ionized;
- an insoluble compound is drawn as free ions, or a soluble one as a precipitate;
- the ion ratio is wrong, e.g. a CaCl₂ solution needs twice as many Cl⁻ as Ca²⁺;
- the number of solute particles changes on dilution;
- water molecules face the wrong way: the O end points toward cations and the H ends toward anions.
Pick a scenario and click the diagram you think is right:
The H₂ and O₂ in a container react by 2H₂ + O₂ → 2H₂O until one reactant is used up. Which diagram shows the container afterward?
A: 5 H₂O contain 5 O atoms, but there were only 4 O atoms (2 O₂) to begin with, so atoms aren’t conserved.
B: O₂ is limiting. 2 O₂ and 4 H₂ make 4 H₂O, leaving 1 H₂. There are 10 H atoms and 4 O atoms both before and after.
C: Atoms are conserved, but both H₂ and O₂ are left over, so the reaction hasn’t finished; it runs until one reactant is used up.
HF is a weak acid. Which diagram best shows the solute particles in an aqueous HF solution?
A: Every HF has ionized into H₃O⁺ and F⁻. That’s what a strong acid such as HCl looks like.
B: No ions at all means HF doesn’t ionize, which contradicts HF solutions being acidic and conducting electricity.
C: Most of it stays as HF molecules, with only a few ionized into H₃O⁺ and F⁻: a weak acid ionizes only partly.
Equal amounts (in moles) of AgNO₃(aq) and NaCl(aq) are mixed. Which diagram shows the result?
A: Ag⁺ and Cl⁻ combine into insoluble AgCl, which settles to the bottom; Na⁺ and NO₃⁻ are spectator ions and stay spread through the solution.
B: AgCl is insoluble, so Ag⁺ and Cl⁻ can’t all stay in solution as free ions.
C: The wrong solid: NaNO₃ is soluble (sodium salts and nitrates always are); AgCl is the insoluble one.
Water is added to some aqueous ammonia until its volume doubles. Which diagram shows the diluted solution? (Box size represents volume.)
A: Half the solute molecules have vanished. Dilution only adds water, so the moles of solute stay the same.
B: The number of solute molecules is unchanged (8) while the volume doubles, so the concentration halves.
C: The solute molecules have doubled. Adding water can’t add solute.
Example 1: K from a particle diagram, then the direction
In a 1.0 L container, A₂(g) ⇌ 2A(g) is at equilibrium; the diagram shows 3 A₂ and 6 A, and each particle represents 0.10 mol. Find K. At the same temperature, another 1.0 L container holds 4 A₂ and 4 A. Which way does that reaction proceed?
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Convert particle counts to concentrations (in M). Each particle is 0.10 mol, in 1.0 L:
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Write K and substitute. The coefficient 2 of A becomes an exponent:
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Q for the second container.
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Compare Q with K. Q = 0.40 < K = 1.2, so there is relatively too little product and the reaction proceeds forward: A₂ breaks apart and A increases.
Example 2: ion ratios and charge balance
A particle diagram shows a small part of a 0.10 M CaCl₂ solution with 4 Ca²⁺ ions. How many Cl⁻ should it show? Another student drew 4 Ca²⁺ and 4 Cl⁻; what’s wrong? If 0.10 M NaCl is drawn in a box of the same size, how does its number of Cl⁻ compare with the CaCl₂ diagram?
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Write the dissociation equation. CaCl₂ is a soluble strong electrolyte and dissociates completely:
Each Ca²⁺ comes with 2 Cl⁻, so the diagram should show 4 × 2 = 8 Cl⁻.
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Check with charge balance.
The charges balance, so the solution is electrically neutral.
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Find the error in the other diagram. 4 Ca²⁺ and 4 Cl⁻ give a total charge of +8 − 4 = +4, so that solution isn’t neutral. In an ionic solution the total charge of the cations and anions balances; their numbers need not.
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Compare with NaCl. In 0.10 M NaCl, [Cl⁻] = 0.10 M; in 0.10 M CaCl₂, [Cl⁻] = 0.20 M. In a box of the same size, the NaCl diagram has half as many Cl⁻ as the CaCl₂ one: 4.
- KNO₃ solution: 4 K⁺ and 4 NO₃⁻, separated from each other
KNO₃ dissociates completely, with K⁺ and NO₃⁻ in a 1 : 1 ratio.
- CH₃COOH solution: 6 CH₃COO⁻ and 6 H₃O⁺, with no CH₃COOH molecules
Acetic acid is weak, so most of it should be CH₃COOH molecules.
- N₂ + 3H₂ → 2NH₃ goes to completion from 2 N₂ and 3 H₂; afterward there are 2 NH₃ and 1 N₂
H₂ is limiting: 3 H₂ and 1 N₂ make 2 NH₃, leaving 1 N₂.
- MgCl₂ solution: 3 Mg²⁺ and 3 Cl⁻
There should be twice as many Cl⁻ as Mg²⁺, i.e. 6.
- BaSO₄ added to water: Ba²⁺ and SO₄²⁻ spread through the whole solution, with no solid at the bottom
BaSO₄ is insoluble, so it should be drawn as solid at the bottom (with very little dissolved).
- A container is compressed to half its volume at constant temperature: same number of gas molecules, packed more closely
Compression changes the spacing, not the number of molecules.
- NaCl solution: the water molecules around each Na⁺ all point their H atoms toward the Na⁺
The partially negative O end of each water molecule faces the cation Na⁺.
- Liquid water becoming vapor: same number of molecules, farther apart, none broken up
Evaporation is a physical change; the H₂O molecules stay intact.
Common mistakes
Mistake 1: “A rough look at a particle diagram is enough; no need to count.” The options often differ by only one or two particles: one extra O₂ or one missing Cl⁻ turns a correct diagram into a wrong one. Count, and write the counts down.
Mistake 2: “A weak acid solution has no ions at all.” A weak acid ionizes partly: the diagram shows mostly molecules plus a few H₃O⁺ and anions. No ions at all would make it a nonelectrolyte.
Mistake 3: “A solution always has equal numbers of cations and anions.” What balances is the total charge, not the number of ions. A CaCl₂ solution has twice as many Cl⁻ as Ca²⁺.
Quick check
A container holds 6 H₂ and 2 N₂, which react completely by N₂ + 3H₂ → 2NH₃. What is in the container afterward?
2 N₂ need exactly 6 H₂ and make 4 NH₃, so both reactants are used up.
In a particle diagram of a Na₂SO₄ solution, how should the numbers of Na⁺ and SO₄²⁻ compare?
Na₂SO₄ → 2Na⁺ + SO₄²⁻, which also balances the charge.
Two identical containers at the same temperature hold gas: X has 8 molecules and Y has 4. What is the ratio of the pressures, X : Y?
At the same temperature and volume, pressure is proportional to the number of molecules.
When drawing water molecules around a Cl⁻ ion, how should they be oriented?
The partially positive H atoms face the anion Cl⁻.
X ⇌ Y is at equilibrium in one container; the diagram shows 2 X and 6 Y (each particle the same amount). What is K?
In one volume the concentration ratio equals the particle ratio: K = [Y]/[X] = 6/2 = 3.
A diagram of a diluted solution shows more solute particles than before dilution. What does this violate?
Adding water adds only solvent; the number of solute particles stays the same and the concentration falls because the volume grows.
AP-style practice
At 25 °C, CO(g) and O₂(g) in a rigid container react by 2CO(g) + O₂(g) → 2CO₂(g). The diagram before the reaction shows 6 CO molecules and 4 O₂ molecules.
(a) Which reactant is limiting? Explain.
(b) Describe the particles in the container after the reaction goes to completion, giving the number of each kind.
(c) Using your answer to (b), show that C atoms and O atoms are both conserved.
(d) The temperature is the same before and after. By what factor has the pressure in the container changed?
(e) A student’s diagram of the container after the reaction shows 6 CO₂ and 4 O₂. Identify the error.
Model answer and scoring
(a) CO is limiting. 6 CO need only 3 O₂, and the container has 4 O₂, so the CO runs out first.
(b) 6 CO₂ and 1 O₂ (6 CO use up 3 O₂ and make 6 CO₂).
(c) C atoms: 6 before (CO) and 6 after (CO₂). O atoms: 6 + 4 × 2 = 14 before and 6 × 2 + 1 × 2 = 14 after. Both are conserved.
(d) At the same temperature and volume, pressure is proportional to the number of molecules: 10 molecules before and 7 after, so the pressure is 7/10 = 0.70 times its starting value.
(e) None of the O₂ has been used: 3 O₂ should have reacted, leaving 1. The student’s diagram has 6 × 2 + 4 × 2 = 20 O atoms, more than the 14 at the start, so atoms aren’t conserved.
Scoring: (a) identifies CO with a reason; (b) 6 CO₂ and 1 O₂; (c) counts for both C and O; (d) 0.70, with pressure proportional to molecules; (e) notes that 1 O₂ should remain, or that atoms aren’t conserved.
Summary
- Four steps: read the key and question, count, check conservation and ratios, eliminate wrong options.
- Common errors: atoms not conserved, both reactants left over, strong and weak electrolytes swapped, the wrong precipitate, wrong ion ratios, particle counts changing on dilution, water molecules facing the wrong way.
- In one volume, the concentration ratio equals the particle ratio; at the same temperature and volume, the pressure ratio equals the ratio of gas molecules.
AP tip: When an FRQ asks you to draw a particle diagram, list the number of each particle on scratch paper and check that atoms and charges balance before you draw. Include a key (what each circle represents), and get the particle ratios exactly right.