Ksp to Molarity: How to Convert Solubility Product

This calculator converts a solubility product constant (Ksp) into molar solubility (molarity) for a sparingly soluble salt. You enter the Ksp value and the salt’s formula (which sets the ion stoichiometry), and you get the molar solubility in mol/L. The calculation uses the standard equilibrium expression relating Ksp to ion concentrations.

Formula

For a salt A_mB_n that dissolves as: A_mB_n(s) ⇌ m Aⁿ⁺(aq) + n B^m−(aq), the Ksp is:

Ksp = [Aⁿ⁺]^m [B^m−]ⁿ

If the molar solubility is s (mol/L), then [Aⁿ⁺] = m·s and [B^m−] = n·s. Substituting gives:

Ksp = (m·s)^m (n·s)ⁿ = m^m nⁿ s^(m+n)

Solving for s:

s = (Ksp / (m^m nⁿ))^1/(m+n)

• Ksp – solubility product constant (unitless, but treated as a concentration product)
• m – number of cations per formula unit
• n – number of anions per formula unit
• s – molar solubility (mol/L)

Worked Example

Using the default values: Ksp = 1.0 × 10⁻¹⁰ and salt type AB (m = 1, n = 1).

1. Write the dissolution: AB(s) ⇌ A⁺(aq) + B⁻(aq)
2. Ksp = [A⁺][B⁻] = s·s = s²
3. s = √(Ksp) = √(1.0 × 10⁻¹⁰) = 1.0 × 10⁻⁵ mol/L

The calculator returns 1.0e−5 mol/L, matching the step-by-step result.

How to Choose the Salt Type

The salt type determines the stoichiometric coefficients in the dissolution equation. The most common patterns are:

• AB – 1:1 salt (e.g., AgCl, BaSO₄). Ksp = s².
• AB₂ – 1:2 salt (e.g., CaF₂, PbCl₂). Ksp = 4s³.
• A₂B – 2:1 salt (e.g., Ag₂CrO₄). Ksp = 4s³.
• AB₃ – 1:3 salt (e.g., Fe(OH)₃, AlCl₃). Ksp = 27s⁴.
• A₃B – 3:1 salt (e.g., Ag₃PO₄). Ksp = 27s⁴.
• A₂B₃ – 2:3 salt (e.g., Fe₂O₃, Al₂(CO₃)₃). Ksp = 108s⁵.

If your salt doesn’t match these, you can still use the general formula by entering m and n manually (the calculator’s dropdown covers the common cases).

Common Mistakes and Misconceptions

• Forgetting the coefficients – The most frequent error is using Ksp = s² for a salt like CaF₂. The correct relation is Ksp = 4s³ because [Ca²⁺] = s and [F⁻] = 2s.
• Ignoring units – Ksp is often quoted without units, but when you compute s, the result is in mol/L. Always include the unit.
• Assuming all salts are 1:1 – Many students default to AB. Check the formula before converting.
• Confusing molar solubility with solubility in g/L – To get g/L, multiply s by the molar mass of the salt. This calculator gives mol/L only.
• Rounding too early – Keep extra digits during intermediate steps, then round at the end.

When to Use This Conversion

You need to convert Ksp to molarity when:

• You are comparing the relative solubilities of different salts – a smaller Ksp usually means lower molar solubility, but only if the salts have the same stoichiometry. For different stoichiometries, you must compute s to compare fairly.
• You are preparing a saturated solution and need to know the maximum concentration of ions.
• You are doing qualitative analysis or precipitation reactions, where knowing the ion concentration helps predict whether a precipitate forms.
• You are studying equilibrium and Le Chatelier’s principle – adding a common ion will shift the equilibrium, but the Ksp remains constant.

Limitations of the Ksp-to-Molarity Calculation

The conversion assumes an ideal, pure water solution with no other ions present. Real solutions may deviate because:

• Ionic strength – High concentrations of other ions reduce the activity coefficients, making the effective concentration lower than the measured one. In such cases, use activities instead of concentrations.
• Common ion effect – If the solution already contains one of the ions, the solubility decreases. The Ksp expression still holds, but the ion concentrations are no longer equal to s.
• Complexation – Some ions form soluble complexes (e.g., Ag⁺ with Cl⁻ forms AgCl₂⁻), increasing solubility beyond the simple Ksp prediction.
• pH effects – If the anion is basic (e.g., OH⁻, CO₃²⁻), acidic solutions will increase solubility by protonating the anion.
• Temperature – Ksp is temperature-dependent. The value you use must correspond to the temperature of your solution.

For most introductory chemistry problems, these factors are ignored, and the simple conversion works well.

Frequently Asked Questions

What is the difference between Ksp and molar solubility?

Ksp is the equilibrium constant for the dissolution reaction, a measure of how far the solid dissolves. Molar solubility (s) is the actual concentration of the dissolved salt in mol/L. They are related but not the same – Ksp is a constant at a given temperature, while s depends on the salt’s stoichiometry and the presence of other ions.

Can I compare Ksp values directly to determine which salt is more soluble?

Only if the salts have the same stoichiometry (e.g., both AB). For salts with different formulas (e.g., AB vs AB₂), you must convert each Ksp to molar solubility using the appropriate formula. A salt with a larger Ksp might actually be less soluble if it produces more ions per formula unit.

How do I convert molar solubility to grams per liter?

Multiply the molar solubility (mol/L) by the molar mass of the salt (g/mol). For example, if s = 1.0 × 10⁻⁵ mol/L and the molar mass is 143.32 g/mol (AgCl), the solubility in g/L is 1.43 × 10⁻³ g/L.

What if my salt has a more complex formula like Ca₃(PO₄)₂?

Use the general formula with m = 3 and n = 2. The dissolution is Ca₃(PO₄)₂ ⇌ 3Ca²⁺ + 2PO₄³⁻, so Ksp = (3s)³(2s)² = 108s⁵. The calculator’s A₂B₃ option covers this case.

Does the calculator work for salts that hydrolyze?

No, it assumes the ions do not react further with water. For salts with basic or acidic anions, the actual solubility will be higher or lower than predicted. In such cases, you need a more advanced calculation that accounts for pH and hydrolysis.

Why is the Ksp value sometimes given without units?

Ksp is technically dimensionless because it is based on activities, not concentrations. In practice, chemists often treat it as a concentration product with implied units (e.g., M² for AB salts). The calculator ignores units and simply uses the numeric value.

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in ksp | Ksp | - | 1.0e-10 | 0
sel stoich | Salt type | AB=1, AB2=2, A2B=3, AB3=4, A3B=5, A2B3=6
out molarity | Molar solubility | mol/L | (ksp / (stoich_factor))^(1/(stoich_sum)) | 3