How to Calculate pKsp for Ca(OH)2
Use this premium calculator to find the solubility product constant and pKsp of calcium hydroxide from molar solubility, ion concentrations, or a known Ksp value. The tool uses the equilibrium relation Ca(OH)2(s) ⇌ Ca2+ + 2OH–.
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Enter values and click the calculate button to see Ksp, pKsp, equilibrium concentrations, and the formula path used.
How to calculate pKsp for Ca(OH)2: complete expert guide
Calcium hydroxide, written as Ca(OH)2, is a classic slightly soluble ionic compound used in general chemistry, analytical chemistry, environmental chemistry, and water treatment. If you are trying to understand how to calculate pKsp for Ca(OH)2, the key idea is simple: first determine the solubility product constant, Ksp, and then take the negative base-10 logarithm of that value. In compact form, the relationship is pKsp = -log10(Ksp). What makes this problem interesting is that Ca(OH)2 does not dissolve in a 1:1 ratio. Instead, one formula unit releases one calcium ion and two hydroxide ions, so stoichiometry strongly affects the final expression.
The dissolution equilibrium is:
From this equilibrium, the solubility product expression becomes:
That single equation is the foundation of every pKsp calculation for calcium hydroxide. If you know the equilibrium concentrations of the ions, you can plug them directly into the expression. If you know only the molar solubility, usually represented by s, you can use stoichiometry to express each ion concentration in terms of s. Since one mole of Ca(OH)2 produces one mole of Ca2+ and two moles of OH–, we have [Ca2+] = s and [OH–] = 2s. Substituting those into the Ksp expression gives Ksp = s(2s)2 = 4s3.
The shortest method
- Write the balanced dissolution equation.
- Build the Ksp expression from the ion coefficients.
- Insert either the ion concentrations or the solubility-based expressions.
- Compute Ksp.
- Calculate pKsp by taking the negative logarithm: pKsp = -log10(Ksp).
If your teacher, lab manual, or textbook gives you Ksp directly, the work is even faster. For example, if Ksp = 5.50 × 10-6, then pKsp = -log10(5.50 × 10-6) ≈ 5.2596. This tells you that calcium hydroxide is sparingly soluble, but not as insoluble as salts with much larger pKsp values.
Step-by-step derivation for Ca(OH)2
1. Start with the balanced ionic breakup
Calcium hydroxide dissociates according to:
- 1 Ca(OH)2 produces 1 Ca2+
- 1 Ca(OH)2 produces 2 OH–
2. Write the equilibrium constant expression
Solids do not appear in the Ksp expression because their activity is treated as constant. That leaves only dissolved ions:
Ksp = [Ca2+][OH–]2
3. Relate concentrations to molar solubility
If the molar solubility of Ca(OH)2 is s mol/L, then:
- [Ca2+] = s
- [OH–] = 2s
Substitute:
Ksp = s(2s)2 = 4s3
4. Convert Ksp to pKsp
Once Ksp is known:
pKsp = -log10(Ksp)
This is exactly what the calculator above does. It also works in reverse. If you already know Ksp, it can estimate the molar solubility using s = (Ksp/4)1/3.
Worked examples
Example 1: starting from molar solubility
Suppose the molar solubility of Ca(OH)2 in water is 0.0110 M.
- [Ca2+] = 0.0110 M
- [OH–] = 2(0.0110) = 0.0220 M
- Ksp = (0.0110)(0.0220)2
- Ksp = (0.0110)(0.000484) = 5.324 × 10-6
- pKsp = -log10(5.324 × 10-6) ≈ 5.2738
So if s = 0.0110 M, the pKsp is about 5.27.
Example 2: starting from ion concentrations
If equilibrium measurements give [Ca2+] = 0.0105 M and [OH–] = 0.0210 M, then:
- Ksp = (0.0105)(0.0210)2
- 0.02102 = 0.000441
- Ksp = 0.0105 × 0.000441 = 4.6305 × 10-6
- pKsp = -log10(4.6305 × 10-6) ≈ 5.3344
Example 3: starting from a known Ksp
Assume a reference value Ksp = 6.50 × 10-6. Then:
- pKsp = -log10(6.50 × 10-6) ≈ 5.1871
- s = (Ksp/4)1/3 = (1.625 × 10-6)1/3 ≈ 0.01177 M
- [Ca2+] = 0.01177 M
- [OH–] = 0.02354 M
Comparison table: reported Ksp values and calculated pKsp
Published values for calcium hydroxide can vary slightly by source, temperature, ionic strength, and whether activities or concentrations are being emphasized. The table below shows representative reported Ksp numbers often encountered in chemistry references, along with the pKsp value calculated from each.
| Reported Ksp for Ca(OH)2 at about 25 C | Calculated pKsp | Estimated molar solubility, s (mol/L) | Estimated [OH–] from pure dissolution (mol/L) |
|---|---|---|---|
| 4.68 × 10-6 | 5.3298 | 0.01054 | 0.02108 |
| 5.50 × 10-6 | 5.2596 | 0.01112 | 0.02224 |
| 6.50 × 10-6 | 5.1871 | 0.01177 | 0.02354 |
Second comparison table: how stoichiometry changes the result
One of the biggest mistakes students make is forgetting the coefficient of hydroxide. This second table shows why the factor of 2 matters so much.
| Molar solubility, s (mol/L) | Correct [Ca2+] (mol/L) | Correct [OH–] (mol/L) | Correct Ksp = 4s3 | Incorrect Ksp if someone uses s3 |
|---|---|---|---|---|
| 0.0080 | 0.0080 | 0.0160 | 2.048 × 10-6 | 5.120 × 10-7 |
| 0.0100 | 0.0100 | 0.0200 | 4.000 × 10-6 | 1.000 × 10-6 |
| 0.0120 | 0.0120 | 0.0240 | 6.912 × 10-6 | 1.728 × 10-6 |
Why pKsp matters
pKsp is useful because it compresses very small equilibrium constants into a more readable number. Instead of writing 5.50 × 10-6, you can write pKsp = 5.26. Chemists like logarithmic scales because they make trends easier to compare. Just as pH is a logarithmic measure of hydrogen ion concentration, pKsp is a logarithmic measure of sparing solubility. A lower pKsp corresponds to a larger Ksp, which generally means greater solubility under the same conditions.
Common mistakes when calculating pKsp for Ca(OH)2
- Forgetting stoichiometric coefficients. Hydroxide gets squared because there are two OH– ions in the dissolution equation.
- Using 2s incorrectly. Only hydroxide is 2s. Calcium stays at s.
- Mixing pKsp and Ksp. pKsp is not the same as Ksp. You must take the negative log.
- Ignoring temperature dependence. Reported Ksp values can change with temperature, so always match your source conditions.
- Confusing concentration with activity. Introductory chemistry usually uses concentrations, but rigorous thermodynamics may use activities, especially in concentrated solutions.
- Rounding too early. Keep extra digits during intermediate steps, then round at the end.
How pKsp connects to pH and hydroxide concentration
Since dissolution of Ca(OH)2 releases hydroxide ions, a saturated solution is basic. If you calculate [OH–] from the solubility, you can also estimate pOH and pH using:
- pOH = -log10[OH–]
- pH = 14.00 – pOH at 25 C
For instance, if [OH–] = 0.0222 M, then pOH ≈ 1.65 and pH ≈ 12.35. This is why calcium hydroxide, often called slaked lime, is used in systems where basicity matters, including certain water-treatment and neutralization contexts.
When the simple formula Ksp = 4s3 is valid
The compact formula works best when calcium hydroxide dissolves in pure water and the only significant source of calcium and hydroxide comes from the solid itself. In more advanced problems, you may need to account for:
- Common ion effects, such as extra OH– from NaOH
- Added calcium salts, which reduce solubility
- Changes in ionic strength
- Activity corrections in nonideal solutions
- Temperature-specific equilibrium constants
In those cases, the general expression Ksp = [Ca2+][OH–]2 still applies, but the concentrations may not be as simple as s and 2s.
Authoritative chemistry and reference sources
If you want to verify constants, atomic masses, or background on the compound, the following sources are useful starting points:
- NIST: Atomic Weights and Isotopic Compositions
- Purdue University: Solubility Product Constants and Ksp Concepts
- CDC/NIOSH: Calcium Hydroxide Reference Information
Quick summary
To calculate pKsp for Ca(OH)2, begin with the dissolution equilibrium Ca(OH)2(s) ⇌ Ca2+ + 2OH–. Then write the equilibrium expression Ksp = [Ca2+][OH–]2. If the molar solubility is s, substitute [Ca2+] = s and [OH–] = 2s to obtain Ksp = 4s3. Finally, calculate pKsp using pKsp = -log10(Ksp). That is the entire logic chain, and it works consistently across homework, lab calculations, and exam problems.
The calculator on this page automates all three common pathways. You can enter molar solubility, direct ion concentrations, or a known Ksp value. It then computes the missing quantities, displays the formula route used, and plots the chemistry values in a chart so you can visualize the relationship between calcium concentration, hydroxide concentration, Ksp, and pKsp.