Solubility from Ksp and pH Calculator
Estimate the molar solubility of a metal hydroxide in a buffered solution using its Ksp and the solution pH. This calculator also compares the result to the ideal pure-water solubility and visualizes how solubility changes across the pH scale.
Interactive Calculator
For display only. The math below assumes a hydroxide salt with formula M(OH)n.
Enter the solubility product at the temperature of interest, usually 25 degrees C.
This model assumes the pH is fixed by a buffer or external acid-base control.
Example: Mg(OH)2 has n = 2 and Fe(OH)3 has n = 3.
Used to convert molar solubility to grams per liter.
Smaller steps create a smoother pH versus solubility curve.
How to Calculate Solubility from Ksp and pH
Calculating solubility from Ksp and pH is one of the most practical applications of equilibrium chemistry. In many real systems, a solid does not dissolve into pure water alone. Instead, it dissolves into an acidic, neutral, or basic environment where the concentration of one of its ions is already influenced by pH. That pH can dramatically increase or decrease the amount of solid that dissolves. For students, researchers, environmental professionals, and water-treatment specialists, understanding this relationship is essential.
This calculator focuses on a common and highly useful case: a metal hydroxide with the general formula M(OH)n. Examples include Mg(OH)2, Zn(OH)2, Fe(OH)3, and Al(OH)3. These compounds obey a Ksp expression that includes hydroxide ion, so pH directly affects their solubility. The key idea is simple: when pH rises, hydroxide concentration rises, and the common-ion effect usually lowers the solubility of the hydroxide solid. When pH drops, hydroxide concentration falls, and the solid can dissolve more readily.
The Core Equilibrium Idea
For a hydroxide solid written as M(OH)n(s), the dissolution equilibrium is:
M(OH)n(s) ⇌ Mn+(aq) + nOH–(aq)
The solubility product expression is:
Ksp = [Mn+][OH–]n
If the pH of the solution is fixed externally, then the hydroxide concentration is not something you solve from scratch. Instead, you compute it from pH and substitute it into the Ksp expression.
- Find pOH from pH: pOH = 14 – pH
- Find hydroxide concentration: [OH–] = 10-pOH
- Use the Ksp expression to solve for molar solubility: s = Ksp / [OH–]n
In this model, s equals the concentration of metal ion formed by dissolution, assuming the pH is maintained by a buffer or large reservoir of acid-base species. That is a very important assumption. Without it, dissolution itself may change the pH and you would need a more complete equilibrium setup.
Why pH Changes Solubility So Strongly
The reason pH matters is the common-ion effect. Hydroxide is already a product in the dissolution of metal hydroxides. If the solution is basic, it already contains a large amount of OH–, so Le Chatelier’s principle predicts that the equilibrium shifts toward the solid phase, reducing solubility. If the solution is acidic, H+ consumes OH– to make water, lowering the hydroxide concentration and pulling the dissolution equilibrium toward more dissolved ions.
This is why hydroxide precipitates are often used in analytical chemistry and wastewater treatment. By adjusting pH upward, operators can force many dissolved metal ions out of solution as solid hydroxides. Conversely, lowering pH can redissolve those precipitates.
Worked Example Using Magnesium Hydroxide
Suppose you want to estimate the solubility of Mg(OH)2 in a buffered solution at pH 10.50. A representative Ksp at 25 degrees C is 5.61 × 10-12.
- pOH = 14.00 – 10.50 = 3.50
- [OH–] = 10-3.50 = 3.16 × 10-4 M
- Because Mg(OH)2 has n = 2, use s = Ksp / [OH–]2
- s = (5.61 × 10-12) / (3.16 × 10-4)2
- s ≈ 5.61 × 10-5 M
That result means the dissolved magnesium concentration under that fixed-pH condition is about 5.61 × 10-5 mol/L. If you know the molar mass, you can also convert to grams per liter. For Mg(OH)2, whose molar mass is about 58.3197 g/mol, the concentration is about 0.00327 g/L.
What This Calculator Assumes
- The solid is a simple hydroxide with stoichiometry M(OH)n.
- The pH is fixed by buffering or external control.
- Activities are approximated by concentrations, which is most reasonable in dilute solutions.
- No complex-ion formation is included.
- No amphoteric dissolution correction is included at very high pH.
- The Ksp value entered matches the temperature and chemical form you care about.
These assumptions make the tool fast and useful for teaching, screening calculations, lab planning, and many engineering estimates. However, they also define its limits. Some hydroxides, especially aluminum, zinc, chromium, and lead hydroxides, can become more soluble again at high pH due to formation of hydroxo-complexes. In those cases, the true solubility curve can be U-shaped rather than simply decreasing with pH.
Common Formula Patterns You Should Know
Many chemistry problems use one of these formulas:
- For M(OH): Ksp = [M+][OH–], so s = Ksp / [OH–]
- For M(OH)2: Ksp = [M2+][OH–]2, so s = Ksp / [OH–]2
- For M(OH)3: Ksp = [M3+][OH–]3, so s = Ksp / [OH–]3
Notice that each additional hydroxide ion increases pH sensitivity dramatically. A trihydroxide is much more strongly suppressed by increasing pH than a monohydroxide because the hydroxide concentration is raised to the third power.
| Hydroxide | Representative Ksp at 25 degrees C | Stoichiometry n | Implication |
|---|---|---|---|
| Ca(OH)2 | 5.5 × 10-6 | 2 | More soluble than many transition-metal hydroxides; still affected by common OH–. |
| Mg(OH)2 | 5.61 × 10-12 | 2 | Very low solubility in basic water; classic pH-dependent precipitation example. |
| Zn(OH)2 | 3.0 × 10-17 | 2 | Extremely low Ksp, but amphoteric behavior can increase solubility at high pH. |
| Fe(OH)3 | 2.79 × 10-39 | 3 | Tiny Ksp and high hydroxide exponent make dissolved Fe(III) levels very low near neutral pH. |
Comparison: How pH Changes a Buffered Solubility Estimate
To see how powerful the pH effect can be, the table below shows calculated molar solubility values for Mg(OH)2 using Ksp = 5.61 × 10-12 and the fixed-pH formula s = Ksp / [OH–]2.
| pH | [OH–] (M) | Calculated s (M) | Calculated s (g/L) |
|---|---|---|---|
| 9 | 1.0 × 10-5 | 5.61 × 10-2 | 3.27 |
| 10 | 1.0 × 10-4 | 5.61 × 10-4 | 0.0327 |
| 11 | 1.0 × 10-3 | 5.61 × 10-6 | 0.000327 |
| 12 | 1.0 × 10-2 | 5.61 × 10-8 | 0.00000327 |
This table highlights an important pattern: for a dihydroxide, every one-unit increase in pH raises [OH–] by a factor of 10, and because OH– is squared in the denominator, the solubility drops by a factor of 100. For trihydroxides, the drop would be by a factor of 1000 per pH unit. That is why pH control is such a powerful tool for precipitation design.
Pure Water Solubility Versus Fixed-pH Solubility
The calculator also reports an idealized pure-water molar solubility for comparison. In pure water, the hydroxide produced by dissolution comes from the solid itself. For M(OH)n, if the molar solubility is s, then:
[Mn+] = s and [OH–] = ns
Substituting into Ksp gives:
Ksp = s(ns)n = nnsn+1
So the pure-water estimate is:
s = (Ksp / nn)1/(n+1)
This is not the same thing as the fixed-pH result. The pure-water calculation lets the hydroxide concentration develop naturally from dissolution. The fixed-pH result assumes the solution is externally controlled, such as by a buffer, titration environment, or a large surrounding water matrix with stable pH.
Practical Uses in the Real World
- Water treatment: Metal ions such as Fe3+, Al3+, Cu2+, and Zn2+ are often removed by hydroxide precipitation.
- Geochemistry: Soil and groundwater pH influence whether metals remain dissolved or form solids.
- Analytical chemistry: Selective precipitation can separate ions based on Ksp and pH windows.
- Pharmaceutical and materials chemistry: Solubility and precipitation control particle growth, purity, and formulation stability.
- Corrosion science: Protective metal hydroxide layers can form or dissolve depending on pH.
Important Limitations and Advanced Cases
Not every solubility problem can be solved with a single Ksp substitution. Here are the most common situations where you need a more advanced model:
- Amphoteric hydroxides: Al(OH)3 and Zn(OH)2 may dissolve more at very high pH by forming species such as aluminate or zincate.
- Complex ion formation: Ligands like NH3, EDTA, citrate, or carbonate can increase total dissolved metal concentration.
- High ionic strength: Activity corrections may be needed because concentrations no longer equal effective activities.
- Temperature effects: Ksp values change with temperature, sometimes significantly.
- Non-hydroxide salts: Some solids are pH-sensitive because anions are protonated, not because hydroxide is directly involved. Those require a different derivation.
How to Avoid Common Mistakes
- Do not confuse pH with pOH. Convert first using pOH = 14 – pH.
- Always raise [OH–] to the correct stoichiometric power.
- Make sure the Ksp value matches the same solid phase and temperature.
- Check whether the problem states buffered pH or asks for equilibrium in pure water.
- Be cautious with amphoteric metals at high pH because the simple model may underpredict solubility.
Recommended Authoritative Reading
If you want to deepen your understanding of pH, water chemistry, and equilibrium methods, these resources are useful starting points:
- USGS: pH and Water
- U.S. EPA: pH Overview in Aquatic Systems
- MIT OpenCourseWare: Principles of Chemical Science
Bottom Line
To calculate solubility from Ksp and pH for a hydroxide, first convert pH to hydroxide concentration, then substitute that value into the Ksp expression. The method is compact, elegant, and extremely powerful because it connects acid-base chemistry with precipitation equilibria. In a buffered system, the formula s = Ksp / [OH–]n tells you immediately how much metal can remain dissolved. As pH increases, hydroxide concentration rises and solubility usually drops sharply. That is why pH control is central to lab separations, industrial precipitation, geochemical mobility, and environmental cleanup.