Calculate Molar Solubility with Ksp and pH
Use this premium calculator to estimate the molar solubility of a metal hydroxide, M(OH)n, from its Ksp and the solution pH at 25 C. The tool solves the equilibrium expression directly, compares it with the buffered approximation, and plots how solubility changes across the pH scale.
Calculator
pOH = 14 – pH, [OH–]initial = 10-pOH
For M(OH)n(s) ⇌ Mn+ + nOH–
Ksp = s([OH–]initial + ns)n
Results
Enter a Ksp, choose the hydroxide stoichiometry, set the pH, then click Calculate. The output will show the exact molar solubility, the initial hydroxide concentration from pH, and the approximation that is often used for strongly buffered solutions.
Solubility vs pH
The chart uses the same Ksp and stoichiometry you enter above. The vertical axis is logarithmic because molar solubility can change by many orders of magnitude as pH changes.
Expert Guide: How to Calculate Molar Solubility with Ksp and pH
If you want to calculate molar solubility with Ksp and pH, you are working with one of the most important equilibrium ideas in general chemistry, analytical chemistry, environmental chemistry, and geochemistry. Molar solubility tells you how many moles of an ionic solid dissolve per liter at equilibrium. Ksp, or the solubility product constant, tells you how far the dissolution reaction proceeds. pH matters because it controls the concentration of hydrogen ions and, through the water equilibrium, the concentration of hydroxide ions. For salts that contain hydroxide, carbonate, sulfide, phosphate, or other basic anions, pH can dramatically change the amount that dissolves.
This calculator focuses on metal hydroxides, written as M(OH)n. These compounds are ideal for learning the link between Ksp and pH because hydroxide is directly connected to pH through the equation pH + pOH = 14 at 25 C. As pH rises, hydroxide concentration increases. A higher hydroxide concentration usually suppresses dissolution by the common ion effect. As pH falls, hydroxide concentration decreases, which often allows more solid to dissolve. This is why many metal hydroxides are much more soluble in acidic solution than in neutral or basic solution.
Core idea behind the calculation
Consider the dissolution equilibrium:
M(OH)n(s) ⇌ Mn+(aq) + nOH–(aq)
The solubility product expression is:
Ksp = [Mn+][OH–]n
If the molar solubility is s, then at equilibrium:
- [Mn+] = s
- [OH–] = [OH–]initial + ns
Substituting into the Ksp expression gives:
Ksp = s([OH–]initial + ns)n
This is the exact equation used by the calculator. It is especially useful because it does not assume the initial hydroxide concentration is overwhelmingly larger than the amount produced by dissolution. In buffered systems or highly basic solutions, a simpler approximation can often be used:
s ≈ Ksp / [OH–]initialn
That approximation is valid only when [OH–]initial is much larger than ns.
How pH enters the molar solubility problem
The bridge between pH and solubility is the water ion product. At 25 C:
- pOH = 14 – pH
- [H+] = 10-pH
- [OH–] = 10-(14-pH) = 10-pOH
- Kw = [H+][OH–] = 1.0 × 10-14
Once you know pH, you can calculate the initial hydroxide concentration. That concentration then feeds directly into the Ksp expression. This is why pH is not just an acid-base concept. It is also a solubility control variable.
| pH | [H+] (M) | [OH–] (M) | Interpretation for hydroxide salts |
|---|---|---|---|
| 2 | 1.0 × 10-2 | 1.0 × 10-12 | Very low hydroxide concentration, so many hydroxides become much more soluble. |
| 5 | 1.0 × 10-5 | 1.0 × 10-9 | Still acidic enough to increase solubility relative to neutral water. |
| 7 | 1.0 × 10-7 | 1.0 × 10-7 | Neutral benchmark often used in classroom examples. |
| 10 | 1.0 × 10-10 | 1.0 × 10-4 | Common ion suppression becomes significant for many sparingly soluble hydroxides. |
| 12 | 1.0 × 10-12 | 1.0 × 10-2 | Most metal hydroxides show strongly reduced solubility. |
Step by step method to calculate molar solubility with Ksp and pH
- Write the balanced dissolution reaction for the salt.
- Write the Ksp expression from the stoichiometry.
- Convert pH to pOH using pOH = 14 – pH.
- Convert pOH to initial hydroxide concentration with [OH–] = 10-pOH.
- Define molar solubility as s and express all equilibrium concentrations in terms of s.
- Substitute into the Ksp equation and solve for s.
- Check whether any approximation used is valid by comparing [OH–]initial and ns.
Worked example
Suppose you need the molar solubility of Mg(OH)2 in a solution with pH 10.00, using Ksp = 5.61 × 10-12. First, calculate pOH:
pOH = 14.00 – 10.00 = 4.00
Then calculate the initial hydroxide concentration:
[OH–]initial = 10-4 M
The dissolution reaction is:
Mg(OH)2(s) ⇌ Mg2+ + 2OH–
The exact Ksp equation is:
5.61 × 10-12 = s(10-4 + 2s)2
Since 10-4 is much larger than 2s in this case, the buffered approximation works well:
s ≈ 5.61 × 10-12 / (10-4)2 = 5.61 × 10-4 M
This example shows an important idea: even a very small Ksp can still correspond to a noticeable solubility when the pH environment strongly favors dissolution.
Comparison table for real hydroxide Ksp values
The table below uses widely cited approximate 25 C Ksp values for selected hydroxides and gives illustrative molar solubility estimates at pH 7. These numbers show how strongly stoichiometry and Ksp together influence equilibrium concentration.
| Compound | Approximate Ksp at 25 C | Stoichiometry n | Estimated molar solubility at pH 7 | Key observation |
|---|---|---|---|---|
| Ca(OH)2 | 5.5 × 10-6 | 2 | 1.11 × 10-2 M | Relatively more soluble than many transition metal hydroxides. |
| Mg(OH)2 | 5.61 × 10-12 | 2 | 1.12 × 10-4 M | Much lower Ksp produces a much smaller equilibrium concentration. |
| Al(OH)3 | 3.0 × 10-34 | 3 | 3.0 × 10-13 M | Extremely insoluble near neutral pH. |
| Fe(OH)3 | 2.79 × 10-39 | 3 | 2.79 × 10-18 M | Hydroxide precipitation is heavily favored in neutral water. |
Why pH can change solubility by orders of magnitude
For hydroxide salts, pH changes the common ion concentration directly. If pH rises by 1 unit, [OH–] increases by a factor of 10. Because hydroxide appears in the Ksp expression with an exponent n, the effect on solubility can be enormous. For M(OH)2, a tenfold increase in hydroxide concentration can reduce the approximate solubility by a factor of 102, or 100. For M(OH)3, the same pH shift can reduce it by a factor of 103, or 1000. That is why trivalent metal hydroxides often precipitate so sharply as pH increases.
Most common mistakes students make
- Using pH directly as [H+] instead of converting with 10-pH.
- Forgetting to convert pH to pOH before calculating [OH–].
- Ignoring stoichiometric coefficients in the Ksp expression.
- Setting [OH–] = s for M(OH)2 or M(OH)3, which is incorrect.
- Applying the buffered approximation when ns is not negligible compared with the initial hydroxide concentration.
- Forgetting that Ksp values depend on temperature.
When the simple method is not enough
In advanced systems, molar solubility can be influenced by more than just Ksp and pH. Complex ion formation, ionic strength, competing equilibria, amphoteric behavior, and temperature shifts all matter. Aluminum hydroxide and zinc hydroxide are classic examples because they can dissolve both in acid and in strongly basic solutions due to complex ion formation. In those cases, a simple Ksp-only treatment can underpredict solubility in highly alkaline media. This calculator is intentionally focused on the standard Ksp plus pH framework that appears in most textbook and exam problems.
How to interpret the calculator output
- Exact molar solubility: the numerically solved equilibrium concentration, useful in most practical cases.
- Buffered approximation: a fast estimate when the initial hydroxide concentration dominates over hydroxide generated by dissolution.
- Initial [OH–]: the hydroxide level implied by the pH before dissolution.
- Estimated dissolved metal concentration: the equilibrium metal ion concentration, equal to s in this model.
- Chart trend: a visual demonstration that lower pH usually increases the solubility of metal hydroxides.
Where this matters in the real world
Solubility calculations are not just classroom exercises. They matter in groundwater chemistry, corrosion control, pharmaceutical formulation, metallurgy, environmental treatment, and industrial separations. Engineers adjust pH to precipitate metals from wastewater. Geochemists track mineral stability in soil and natural waters. Analytical chemists use carefully chosen pH ranges to separate ions selectively. In all of these applications, Ksp and pH work together to determine whether a solid dissolves, remains stable, or precipitates.
Authoritative references
- U.S. Geological Survey: pH and Water
- U.S. Environmental Protection Agency: pH Overview
- Purdue University: Solubility Product Constant, Ksp