Calculate Ksp of a Saturated Solutioon When Given pH
Use this premium calculator to estimate the solubility product constant, Ksp, of a saturated metal hydroxide solution from its measured pH. Enter the pH, choose the number of hydroxide ions released per formula unit, and the calculator will determine pOH, hydroxide concentration, molar solubility, and Ksp instantly.
Ksp Calculator from pH
Example: if a saturated hydroxide solution has pH 10.45, enter 10.45.
Choose the dissolution form of the saturated hydroxide solid.
Optional label used in the result and chart title.
For most classroom problems, the default 25 C value is correct.
Enter the measured pH and select the hydroxide stoichiometry, then click Calculate Ksp.
Expert Guide: How to Calculate Ksp of a Saturated Solutioon When Given pH
If you need to calculate Ksp of a saturated solutioon when given pH, you are working with one of the most common equilibrium problems in general chemistry. The question usually appears in the context of a sparingly soluble metal hydroxide, where the measured pH of the saturated solution tells you the hydroxide concentration, and that hydroxide concentration lets you back-calculate the molar solubility and finally the solubility product constant, Ksp.
This topic matters because Ksp connects measurable laboratory data to equilibrium behavior. Instead of directly measuring every dissolved ion, you can use pH as an indirect path to the same answer. In many chemistry courses, students are asked to determine the Ksp of compounds such as Mg(OH)2, Ca(OH)2, Fe(OH)3, or other basic salts by starting with the pH of the saturated solution. Once you understand the method, these questions become very systematic.
What Ksp Means
Ksp is the solubility product constant for a slightly soluble ionic compound. It describes the equilibrium between the undissolved solid and the dissolved ions. For a generic metal hydroxide:
M(OH)n(s) ⇌ Mn+(aq) + nOH–(aq)
The expression for Ksp is:
Ksp = [Mn+][OH–]n
The solid is omitted from the equilibrium expression because its activity is treated as constant. That means the entire problem depends only on the dissolved ion concentrations.
Why pH Lets You Find Ksp
When a sparingly soluble hydroxide dissolves in pure water, it produces hydroxide ions. Since pH and pOH are related, the pH measurement allows you to find the hydroxide concentration in the saturated solution.
- Measure or receive the pH of the saturated solution.
- Calculate pOH using pOH = 14.00 – pH at about 25 C.
- Convert pOH to hydroxide concentration with [OH–] = 10-pOH.
- Use stoichiometry to find molar solubility, s.
- Substitute into the Ksp expression.
Step by Step Method
Here is the exact workflow you can use every time.
- Write the balanced dissolution equation.
Example for calcium hydroxide:
Ca(OH)2(s) ⇌ Ca2+(aq) + 2OH–(aq) - Calculate pOH.
If pH = 12.35, then pOH = 14.00 – 12.35 = 1.65. - Calculate hydroxide concentration.
[OH–] = 10-1.65 = 2.24 × 10-2 M - Find molar solubility.
Because 2 OH- are produced per formula unit, s = [OH–] / 2 = 1.12 × 10-2 M. - Write and evaluate Ksp.
Ksp = [Ca2+][OH–]2 = s[OH–]2
Ksp = (1.12 × 10-2)(2.24 × 10-2)2 ≈ 5.62 × 10-6
This result is very close to the commonly cited room-temperature Ksp for calcium hydroxide, which is around 5.0 × 10-6. That tells you the method is chemically sound.
General Formula You Can Use
For a generic hydroxide:
M(OH)n(s) ⇌ Mn+ + nOH–
If the molar solubility is s, then:
- [Mn+] = s
- [OH–] = ns
So:
Ksp = s(ns)n
Since s = [OH–] / n, another useful direct form is:
Ksp = ([OH–] / n) × [OH–]n = [OH–]n+1 / n
This shortcut is especially convenient in calculator problems because once you know pH, you can get [OH-], and then Ksp follows quickly.
Worked Example: Magnesium Hydroxide
Suppose a saturated Mg(OH)2 solution has a pH of 10.45.
- pOH = 14.00 – 10.45 = 3.55
- [OH–] = 10-3.55 = 2.82 × 10-4 M
- For Mg(OH)2, s = [OH–] / 2 = 1.41 × 10-4 M
- Ksp = [Mg2+][OH–]2
- Ksp = (1.41 × 10-4)(2.82 × 10-4)2 ≈ 1.12 × 10-11
This is in the expected order of magnitude for magnesium hydroxide and demonstrates how a modestly basic pH can correspond to a very small Ksp.
Comparison Table: Typical Ksp Values for Common Hydroxides at About 25 C
| Compound | Dissolution Equation | Commonly Cited Ksp | Relative Solubility Trend |
|---|---|---|---|
| Ca(OH)2 | Ca(OH)2(s) ⇌ Ca2+ + 2OH– | 5.0 × 10-6 to 5.6 × 10-6 | Moderately sparingly soluble |
| Mg(OH)2 | Mg(OH)2(s) ⇌ Mg2+ + 2OH– | 5.6 × 10-12 to 1.2 × 10-11 | Much less soluble than Ca(OH)2 |
| Fe(OH)3 | Fe(OH)3(s) ⇌ Fe3+ + 3OH– | About 10-38 to 10-39 | Extremely insoluble |
| Al(OH)3 | Al(OH)3(s) ⇌ Al3+ + 3OH– | About 10-33 to 10-34 | Very insoluble in neutral water |
The table shows a broad spread in Ksp values. Calcium hydroxide has a much larger Ksp than magnesium hydroxide, so its saturated solution is much more basic. Iron(III) hydroxide and aluminum hydroxide are so insoluble that tiny dissolved concentrations correspond to extremely small Ksp values.
Comparison Table: How Stoichiometry Changes the Calculation
| Solid Type | Equation | If [OH-] is known | Ksp Expression in Terms of [OH-] |
|---|---|---|---|
| MOH | MOH(s) ⇌ M+ + OH– | s = [OH-] | Ksp = [OH-]2 |
| M(OH)2 | M(OH)2(s) ⇌ M2+ + 2OH– | s = [OH-] / 2 | Ksp = [OH-]3 / 2 |
| M(OH)3 | M(OH)3(s) ⇌ M3+ + 3OH– | s = [OH-] / 3 | Ksp = [OH-]4 / 3 |
| M(OH)4 | M(OH)4(s) ⇌ M4+ + 4OH– | s = [OH-] / 4 | Ksp = [OH-]5 / 4 |
Common Student Mistakes
- Using pH directly as [OH-]. pH is logarithmic, not a concentration.
- Forgetting to convert to pOH. At about 25 C, pOH = 14.00 – pH.
- Ignoring stoichiometry. If the compound produces 2 or 3 hydroxides, you must divide [OH-] by that coefficient to get molar solubility.
- Leaving out exponents in Ksp. The hydroxide concentration must be raised to the correct power.
- Rounding too early. Keep extra digits until the end to avoid significant error.
When This Method Works Best
This pH-to-Ksp method works best when the saturated solution is made in pure water and the dominant source of OH- is the dissolution of the hydroxide solid. If the solution also contains added base, buffers, or other ions that alter equilibrium, then the simple method may not be valid without additional equilibrium corrections.
Likewise, temperature matters. The relation pH + pOH = 14.00 assumes a water ion product near 1.0 × 10-14, which is standard near 25 C. At other temperatures, Kw changes slightly, so highly precise work should use the proper value.
Practical Interpretation of the Result
A larger Ksp means the compound is more soluble. A smaller Ksp means the compound is less soluble. However, Ksp values should only be directly compared for compounds with similar stoichiometry. A hydroxide with a larger exponent on hydroxide can have a tiny Ksp even if its actual dissolved amount does not appear proportionally tiny. That is why it is often useful to calculate molar solubility alongside Ksp.
For example, two solids can have very different Ksp values because their equilibrium expressions include different exponents. That is not a mathematical trick. It reflects the real stoichiometric relationship between dissolved ions and the parent solid.
Fast Exam Strategy
- Write the dissolution equation first.
- From pH, find pOH.
- Convert pOH to [OH-].
- Use stoichiometry to get s.
- Plug into Ksp and only round at the end.
If you follow those five steps consistently, you can solve nearly every standard problem that asks you to calculate Ksp of a saturated solutioon when given pH.
Authoritative Chemistry and Water Science References
Final Takeaway
The core idea is simple: pH gives you access to hydroxide concentration, hydroxide concentration gives you molar solubility, and molar solubility gives you Ksp. For hydroxides, the process is especially direct because the pH measurement is already tied to one of the ions in the equilibrium expression. Use the calculator above to automate the arithmetic, check classwork, and visualize how Ksp changes with pH and hydroxide stoichiometry.