How do ion ratios change the solubility calculation?
You will be able to: Connect balanced dissolution coefficients to powers of molar solubility.
How do ion ratios change the solubility calculation?
One formula unit of MX₂ supplies one M²⁺ ion and two X⁻ ions. Counting the ions correctly is essential before inserting numbers into a solubility expression.
A useful starting point: What does a saturated solution mean at particle level? →
Words and symbols before equations
- Formula unit
- The simplest charge-balanced composition of an ionic solid.
- Stoichiometric ion ratio
- Ion numbers released by one formula unit.
- Molar solubility s
- Formula units dissolved in mol per liter.
- Cube root
- Number which, multiplied by itself three times, gives the original value.
What this picture assumes
Ideal dilute concentrations in mol/L (M); fixed temperature, fixed volume except when explicitly changed, and no side reactions. Supplied K values use the stated AP concentration convention. MX₂(s) ⇌ M²⁺+2X⁻ in pure water. Each control setting is a supplied measurement for an independent case; inferred Ksp=4s³.
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.
- Measured s=2×10⁻⁴ mol/L. [M²⁺]=s, [X⁻]=2s; inferred Ksp=s(2s)²=4s³=3.2×10⁻¹¹. These are separate supplied measurement cases.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the chemistry
For MX₂(s)⇌M²⁺+2X⁻, dissolving s mol/L in pure water gives [M²⁺]=s and [X⁻]=2s.
Ksp=[M²⁺][X⁻]²=s(2s)²=4s³. The factor 4 comes from squaring 2s, not from adding ion counts.
Conversely, a measured s gives Ksp by the same relation. To report mass solubility in g/L, multiply s by the solid’s molar mass in g/mol.
Assume no common ions, hydrolysis or complex formation for this first model. If other sources or reactions affect ion concentrations, the simple pure-water substitution must change.
A worked example, step by step
A supplied MX₂ salt has Ksp=3.2×10⁻¹¹. Find s and both ion concentrations in pure water.
- Balance the dissolution: one M²⁺ and two X⁻.
- Use Ksp=4s³, so s³=8.0×10⁻¹².
- s=2.0×10⁻⁴ mol/L.
- [M²⁺]=2.0×10⁻⁴ M and [X⁻]=4.0×10⁻⁴ M; their product with the X power reproduces Ksp.
For MX₂, taking √Ksp is not the correct molar-solubility calculation.
If s doubles for the same ion-ratio calculation, what happens to the inferred Ksp?
Compare with an explanation
The inferred value is multiplied by 2³=8; these would represent different supplied conditions or salts, not a spontaneous change of Ksp at fixed T.
Predict. Change one thing. Explain.
Change the supplied molar solubility. Predict each ion concentration and the factor change in Ksp when s doubles.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Measured s=2×10⁻⁴ mol/L. [M²⁺]=s, [X⁻]=2s; inferred Ksp=s(2s)²=4s³=3.2×10⁻¹¹. These are separate supplied measurement cases.
Ideal dilute concentrations in mol/L (M); fixed temperature, fixed volume except when explicitly changed, and no side reactions. Supplied K values use the stated AP concentration convention. MX₂(s) ⇌ M²⁺+2X⁻ in pure water. Each control setting is a supplied measurement for an independent case; inferred Ksp=4s³.
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 questionAn MX₂ salt has measured molar solubility 3.0×10⁻⁴ mol/L and molar mass 150 g/mol. Find both ion concentrations, Ksp and mass solubility.
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Compare with the answer and four-point rubric
- 1 point: [M²⁺]=3.0×10⁻⁴ M.
- 1 point: [X⁻]=6.0×10⁻⁴ M.
- 1 point: Ksp=(3.0×10⁻⁴)(6.0×10⁻⁴)²=1.08×10⁻¹⁰.
- 1 point: Mass solubility=3.0×10⁻⁴×150=0.045 g/L.
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 1Where does the 4 in 4s³ come from?
Squaring the coefficient factor in (2s)².
RECALL 2Does s equal every ion concentration?
Only when that ion coefficient is one and no other sources or sinks matter.
RECALL 3How do you convert s to g/L?
Multiply by the salt’s molar mass.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
How do ion ratios change the solubility calculation?
- MX₂ in pure water: Ksp=4s³.
- Mass solubility (g/L)=s (mol/L)×molar mass (g/mol).
Remember: For MX₂, taking √Ksp is not the correct molar-solubility calculation.
Conditions: Ideal dilute concentrations in mol/L (M); fixed temperature, fixed volume except when explicitly changed, and no side reactions. Supplied K values use the stated AP concentration convention. MX₂(s) ⇌ M²⁺+2X⁻ in pure water. Each control setting is a supplied measurement for an independent case; inferred Ksp=4s³.
Refresh Kid · AP Chemistry Unit 7 · Objectives 7.11.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 7.11, objective 7.11.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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