SCIENCE · INVESTIGATE AND EXPLAIN

Compare solubilities only after reconstructing ion inventories

The solubility product and formula-unit solubility are not interchangeable quantities.

Learning outcome: Compare all three charge-balanced formula types. Write each dissolution equation, normalize ion activities and distinguish formula-unit amount from each ion concentration.

Starting recap

Refresh normalized free-ion activities, charge-balanced stoichiometry, finite analytical inventories, coupled constants and independent versus shared assay errors.

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Try

For Ksp10⁻⁸, ideal MX has s10⁻⁴ M, while M2X has s=(10⁻⁸/4)^(1/3)≈.00135721 M.

Open the experiment

Predict

Can two solids with the same numerical Ksp have different molar solubilities?

Your prediction and reason

Experiment

Compare all three charge-balanced formula types. Write each dissolution equation, normalize ion activities and distinguish formula-unit amount from each ion concentration.

Convert a dissolution constant into species inventories

Worked teaching model · synthetic values · Fictional ionic solids with charge-balanced identities MX (M+/X−), M2X (M+/X²−), or MX2 (M²+/X−). Ideal activities c/c°, c°=1 M, excess solid, no hydrolysis/complexation. Molar formula-unit solubility s is not the concentration of every ion.

Stoichiometry: 0 MX, 1 M2X, 2 MX2: 1 choice Negative log dimensionless Ksp: 8 pKsp

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Formula solubility versus pKsp: solid

Axes rescale. A solubility comparison, depletion constraint and conditional reservoir scan have different horizontal meanings. Read the axes; these are not measured time traces.

All calculated plot coordinates

Formula solubility versus pKsp
pKsp	formula-unit solubility (mol/L)
6	0.006299605
6.1	0.005834182
6.2	0.005403146
6.3	0.005003954
6.4	0.004634256
6.5	0.004291871
6.6	0.003974782
6.7	0.00368112
6.8	0.003409154
6.9	0.003157282
7	0.002924018
7.1	0.002707988
7.2	0.002507918
7.3	0.00232263
7.4	0.002151031
7.5	0.00199211
7.6	0.00184493
7.7	0.001708625
7.8	0.001582389
7.9	0.00146548
8	0.001357209
8.1	0.001256936
8.2	0.001164072
8.3	0.001078069
8.4	0.0009984201
8.5	0.0009246556
8.6	0.0008563409
8.7	0.0007930733
8.8	0.00073448
8.9	0.0006802157
9	0.0006299605
9.1	0.0005834182
9.2	0.0005403146
9.3	0.0005003954
9.4	0.0004634256
9.5	0.0004291871
9.6	0.0003974782
9.7	0.000368112
9.8	0.0003409154
9.9	0.0003157282
10	0.0002924018
10.1	0.0002707988
10.2	0.0002507918
10.3	0.000232263
10.4	0.0002151031
10.5	0.000199211
10.6	0.000184493
10.7	0.0001708625
10.8	0.0001582389
10.9	0.000146548
11	0.0001357209
11.1	0.0001256936
11.2	0.0001164072
11.3	0.0001078069
11.4	9.984201e-5
11.5	9.246556e-5
11.6	8.563409e-5
11.7	7.930733e-5
11.8	7.344800e-5
11.9	6.802157e-5
12	6.299605e-5

Calculated under the declared model
Quantity	Value	Unit
Formula-unit molar solubility	0.001357209	mol/L
Free metal concentration	0.002714418	mol/L
Free anion concentration	0.001357209	mol/L
Recovered normalized product	1.000000e-8	dimensionless

Stoichiometric coefficients change both the ion inventories and the powers in the dissolution quotient.

For MX, Ksp=s²; for M2X or MX2, Ksp=4s³ when concentration values are normalized by1 M. The two2:1 formulas have equal s at equal Ksp here but different metal/anion concentrations. Comparing Ksp alone across unlike stoichiometries does not rank molar solubility.

These calculated packets are not performed chemical measurements or separation procedures. Keep feasible inventories, activity conventions, fitting observations and independent checks distinct.

Stoichiometric coefficients change both the ion inventories and the powers in the dissolution quotient.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Preserve charge and formula units

Consider three fictional solids: MX with M+ and X−, M2X with M+ and X²−, and MX2 with M²+ and X−. These are different dissolution equations. If s mol of formula units dissolves per liter, each ion concentration follows its coefficient: s/s,2s/s or s/2s respectively.

With ideal activities c/c° and c°=1 M, MX gives Ksp=s² numerically when s is expressed in M. Either2:1 formula gives4s³, but the metal and anion concentrations are interchanged. The thermodynamic product remains dimensionless; the abbreviated concentration numerals must use the declared normalization.

Compare like quantities

At Ksp10⁻⁸, MX has s=.000100 M. M2X has s≈.00135721 M, metal concentration≈.00271442 M and anion concentration≈.00135721 M. Equal numerical constants do not imply equal formula-unit solubility across different stoichiometries.

The comparison assumes excess solid, no ion pairing, no protonation and unit activity coefficients. A real dissolved-total measurement may include other species and cannot automatically be inserted into this ideal free-ion product. Dissolution and precipitation can remain dynamic even when the macroscopic concentration is stable.

Transfer and check

For a fictional MX2 with Ksp3.2×10⁻⁸, solve4s³=3.2×10⁻⁸ to get s=.00200 M, free metal .00200 M and free anion .00400 M. Reinsert the concentrations into [M][X]² after normalization. Explain why simply taking the square root of Ksp would use the wrong reaction.

Source and evidence boundary

Conceptual reference checked 30 October 2026: OpenStax Chemistry 2e. All cases, prose and diagrams are original. Fictional species and explicitly ideal or supplied-activity constraints are not measured solubilities, real assay performance or safe physical separation protocols. No material handling, mixing, filtration or reagent procedure is requested. Retain free versus total species, inventory constraints, boundary conditions and independent evidence limits.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Why does a Ksp ranking across unlike stoichiometries fail to directly rank dissolved formula-unit amounts?

Your explanation and limitations

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Previous: Map an indicator transition onto an asymmetric volume interval Next: Separate common-ion suppression from a prescribed activity correction

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