Calculate Solubility Given Ksp And Ph

Use this advanced calculator to estimate the molar solubility of a metal hydroxide in a solution with a fixed pH. Enter the Ksp, choose the hydroxide stoichiometry, optionally add molar mass, and instantly visualize how solubility changes across the pH scale.

Solubility Calculator

This calculator uses the fixed-pH approximation for metal hydroxides: if the solution pH is externally maintained, then [OH-] is determined from pH and Ksp = [Mn+][OH-]n, so the molar solubility is s = Ksp / [OH-]n.

How to calculate solubility given Ksp and pH

Calculating solubility from Ksp and pH is one of the most useful equilibrium skills in general chemistry, analytical chemistry, environmental chemistry, and water treatment. The idea is simple: the solubility product constant, Ksp, tells you how much of a sparingly soluble ionic compound can dissolve before equilibrium is reached. When the pH of the solution changes, the concentration of hydrogen ions or hydroxide ions also changes. That shift can either increase or decrease the amount of solid that dissolves, depending on the ions in the dissolution reaction.

This page focuses on a very common and practical case: a metal hydroxide of the form M(OH)n. For these compounds, a higher pH means a higher hydroxide concentration, and because hydroxide is already one of the products of dissolution, extra OH- suppresses solubility through the common ion effect. In other words, many hydroxides dissolve less as pH rises. That is exactly why pH control is so important in precipitation chemistry, wastewater treatment, metallurgy, and qualitative analysis.

If you need authoritative background on pH behavior in water, the U.S. Geological Survey provides a strong overview, and the U.S. Environmental Protection Agency explains why pH matters in chemical and environmental systems. For academic refreshers on equilibrium chemistry, MIT OpenCourseWare is also a reliable resource.

The core chemistry behind the calculator

Suppose you have a metal hydroxide:

M(OH)n(s) ⇌ Mn+(aq) + nOH-(aq)

The solubility product expression is:

Ksp = [Mn+][OH-]n

If the pH is fixed by a buffer or by a much larger solution volume, then [OH-] is effectively known from the pH:

pOH = 14 – pH, then [OH-] = 10-pOH = 10(pH – 14)

If the molar solubility is s, then [Mn+] = s, so:

s = Ksp / [OH-]n

This fixed-pH approach is especially useful when the pH is externally controlled. It gives a direct way to estimate how much solid can remain dissolved at equilibrium. If the pH is not externally maintained, the exact treatment may require solving a more complete equilibrium system because dissolution itself can change the pH.

Step-by-step method

1. Write the balanced dissolution equation for the sparingly soluble hydroxide.
2. Write the Ksp expression, making sure exponents match stoichiometric coefficients.
3. Use the pH to find pOH using pOH = 14 – pH.
4. Convert pOH to hydroxide concentration using [OH-] = 10-pOH.
5. Substitute the hydroxide concentration into the Ksp expression.
6. Solve for the molar solubility, s.
7. If needed, convert molar solubility to g/L using molar mass.

Worked example

Consider Mg(OH)2 with Ksp = 5.6 × 10^-12 at 25 degrees C in a solution with pH 10.50.

1. Dissolution equation: Mg(OH)2(s) ⇌ Mg2+ + 2OH-
2. Ksp expression: Ksp = [Mg2+][OH-]²
3. pOH = 14 – 10.50 = 3.50
4. [OH-] = 10^-3.5 = 3.16 × 10^-4 M
5. s = Ksp / [OH-]² = (5.6 × 10^-12) / (3.16 × 10^-4)²
6. s = 5.6 × 10^-5 M

If you also want solubility in grams per liter, multiply by the molar mass of Mg(OH)2, which is about 58.32 g/mol:

g/L = 5.6 × 10-5 mol/L × 58.32 g/mol ≈ 0.00327 g/L

That result illustrates a major principle: in alkaline solutions, magnesium hydroxide remains only slightly soluble. Raising the pH further would lower solubility even more.

Why pH changes solubility

The reason pH matters is Le Chatelier’s principle. For hydroxides, OH- is a product of dissolution. If you increase pH, you increase [OH-], which pushes the equilibrium left and favors the solid phase. That lowers molar solubility. If you decrease pH, hydrogen ions consume hydroxide to form water, effectively reducing [OH-] and allowing more solid to dissolve.

This pattern is not limited to hydroxides. Salts with basic anions such as CO3^2-, S^2-, PO4^3-, or F- can become much more soluble in acidic conditions because protonation removes the anion from solution. However, the exact treatment for those systems includes acid-base equilibria in addition to Ksp. For a fast and reliable fixed-pH calculation, hydroxides are the cleanest and most common case.

Comparison table: hydroxide concentration at common pH values

The table below shows how strongly hydroxide concentration changes with pH at 25 degrees C. Each one-unit change in pH changes [OH-] by a factor of 10 in the opposite direction of [H+]. That exponential behavior is why solubility can swing dramatically even across a small pH range.

pH	pOH	[OH-] (M)	Effect on hydroxide solubility
4.0	10.0	1.0 × 10^-10	Very low hydroxide concentration, so many hydroxides dissolve much more readily.
7.0	7.0	1.0 × 10^-7	Neutral water still contains enough OH- to affect very insoluble hydroxides.
9.0	5.0	1.0 × 10^-5	Moderately basic conditions begin strongly suppressing metal hydroxide solubility.
11.0	3.0	1.0 × 10^-3	Solubility of many hydroxides drops by orders of magnitude.
13.0	1.0	1.0 × 10^-1	Very high hydroxide concentration heavily favors precipitation for many simple hydroxides.

Comparison table: example Ksp values and implications

The following values are commonly cited textbook-scale examples near 25 degrees C. Exact tabulated values can vary by source, temperature, and ionic strength, but they are realistic enough to show how Ksp controls solubility range.

Compound	Representative Ksp	Dissolution stoichiometry	Approximate trend at higher pH
Ca(OH)2	5.5 × 10^-6	Ca(OH)2 ⇌ Ca2+ + 2OH-	Still somewhat soluble, but increasingly suppressed as [OH-] rises.
Mg(OH)2	5.6 × 10^-12	Mg(OH)2 ⇌ Mg2+ + 2OH-	Much lower dissolved concentration in alkaline conditions.
Fe(OH)3	2.8 × 10^-39	Fe(OH)3 ⇌ Fe3+ + 3OH-	Extremely insoluble over a wide pH range, especially near neutral and basic pH.
Al(OH)3	About 1 × 10^-33	Al(OH)3 ⇌ Al3+ + 3OH-	Very insoluble in the mid-range, though amphoterism may matter at high pH.

Important assumptions and limitations

Good chemistry requires knowing when a shortcut is valid. This calculator uses a fixed-pH model, and that assumption is excellent in many lab and process situations, but not all. Here are the most important limitations:

• Buffered or controlled pH: The formula works best when pH is maintained by a buffer, titrant, or large reservoir.
• Temperature dependence: Ksp changes with temperature. Values at 25 degrees C should not be reused blindly at very different temperatures.
• Ionic strength effects: In concentrated solutions, activities differ from concentrations, so the simple expression may become less accurate.
• Amphoteric hydroxides: Al(OH)3, Zn(OH)2, Pb(OH)2, and similar compounds may dissolve again at very high pH because they form hydroxo complexes.
• Complex ion formation: Ligands such as NH3, EDTA, citrate, or chloride can increase apparent solubility by stabilizing dissolved metal species.
• Acid-base coupling: For salts containing protonatable anions, you need more than Ksp alone because pH changes the anion speciation.

When this calculation is especially useful

The Ksp-pH relationship is heavily used in real systems. Environmental engineers use it to predict when dissolved metals will precipitate from wastewater. Analytical chemists use it for selective precipitation, where one ion is precipitated while another remains in solution. Geochemists use similar equilibrium ideas to understand groundwater chemistry, mineral stability, and scaling. In pharmaceutical and formulation chemistry, pH-dependent solubility is central to drug delivery, although those systems often involve weak acids or bases instead of inorganic hydroxides.

In water treatment, for example, pH adjustment is a standard way to remove metal contaminants. If a metal forms a poorly soluble hydroxide, increasing the pH can push dissolved metal concentrations downward by many orders of magnitude. However, the optimum pH is not always “the higher the better,” because some metals become amphoteric or form soluble complexes in very basic conditions. That is why a simple Ksp calculation is often a starting point, not the final process design model.

Practical interpretation of your result

After the calculator gives you a molar solubility value, ask what it means in context:

• If the value is very small, the compound is likely to precipitate readily at that pH.
• If the value is larger than expected, acidic conditions may be dissolving more of the solid than you assumed.
• If you convert to g/L, you can compare directly with measured concentrations or process specifications.
• If your compound is amphoteric or complex-forming, treat the result as a baseline estimate rather than a full equilibrium prediction.

Common mistakes students make

1. Using pH directly for hydroxide concentration instead of converting through pOH.
2. Forgetting that [OH-] = 10^{(pH – 14)} at 25 degrees C.
3. Using the wrong exponent for OH- in the Ksp expression.
4. Confusing molar solubility with ion concentration. For M(OH)2, the metal concentration is s but the hydroxide produced from dissolution is 2s.
5. Ignoring the common ion effect when OH- already exists in solution.
6. Applying the same simple approach to amphoteric or strongly complexing systems without correction.

Bottom line

To calculate solubility given Ksp and pH for a metal hydroxide, first convert pH to hydroxide concentration, then substitute that concentration into the Ksp expression. Under fixed-pH conditions, the molar solubility is directly related to Ksp and inversely related to the hydroxide concentration raised to the appropriate stoichiometric power. That means pH is often the single most important operational control variable for precipitation and dissolution behavior.

Use the calculator above for fast estimates, trend analysis, and visualization. It is especially effective for understanding how a one-unit pH shift can change solubility by factors of 10, 100, 1000, or more depending on the hydroxide stoichiometry. If you are working with more complicated systems involving buffers, complex ions, amphoteric species, or variable temperature, treat this result as your first-pass equilibrium estimate and then refine it with a fuller model.

Educational note: pH to pOH conversion assumes water at 25 degrees C, where pKw is approximately 14.00.