Calculate the Solubility of Co(OH)2 at pH 11.50
Use this interactive calculator to estimate the molar solubility of cobalt(II) hydroxide in a solution held at pH 11.50 or any other pH you enter. The tool applies the Ksp expression for Co(OH)2, shows the intermediate hydroxide concentration, converts the answer to mg/L, and visualizes how solubility changes with pH.
Solubility Calculator
Default values use a common literature Ksp estimate for cobalt(II) hydroxide near room temperature.
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Click the button to compute the solubility of Co(OH)2 at pH 11.50.
Expert Guide: How to Calculate the Solubility of Co(OH)2 at pH 11.50
Cobalt(II) hydroxide, Co(OH)2, is a sparingly soluble ionic solid. In aqueous chemistry, its dissolution is controlled by the solubility product constant, Ksp. When a problem asks you to calculate the solubility of Co(OH)2 at pH 11.50, the key idea is that the pH already fixes the hydroxide concentration. Once [OH–] is known, the Ksp expression can be rearranged to solve directly for the dissolved cobalt concentration, which is also the molar solubility under buffered, fixed-pH conditions.
1. Start with the dissolution equilibrium
The dissolution reaction for cobalt(II) hydroxide is:
Co(OH)2(s) ⇌ Co2+(aq) + 2OH–(aq)
The corresponding solubility product expression is:
Ksp = [Co2+][OH–]2
For a fixed external pH, [OH–] is determined by the solution conditions rather than primarily by dissolution of the solid. That means the common ion effect is dominant, and the amount of Co(OH)2 that dissolves is reduced as pH rises.
2. Convert pH 11.50 to hydroxide concentration
At 25 degrees C, pH and pOH are related by:
pH + pOH = 14.00
So for pH 11.50:
- pOH = 14.00 – 11.50 = 2.50
- [OH–] = 10-2.50 = 3.16 × 10-3 M
This hydroxide concentration is much larger than the hydroxide contributed by the tiny amount of dissolved Co(OH)2, which justifies the usual fixed-pH approximation.
3. Solve for molar solubility
If we let the molar solubility be s, then under fixed-pH conditions:
[Co2+] = s
Using a common Ksp value of 5.92 × 10-15:
s = Ksp / [OH–]2
s = (5.92 × 10-15) / (3.16 × 10-3)2
s = (5.92 × 10-15) / (1.00 × 10-5) = 5.92 × 10-10 M
So the calculated molar solubility of Co(OH)2 at pH 11.50 is approximately 5.92 × 10-10 M when that Ksp value is used.
4. Convert the answer to mg/L
In laboratory and environmental work, a mass concentration is often more intuitive than molarity. The molar mass of Co(OH)2 is about:
- Co: 58.93 g/mol
- 2O: 32.00 g/mol
- 2H: 2.016 g/mol
- Total: 92.95 g/mol
To convert molar solubility to mg/L:
mg/L = s × 92.95 g/mol × 1000 mg/g
mg/L = 5.92 × 10-10 × 92.95 × 1000
mg/L ≈ 5.50 × 10-5 mg/L
That is an extremely low concentration, which is exactly what you would expect at a high pH where hydroxide is already abundant.
5. Why the solubility drops so sharply at high pH
This result is a textbook example of the common ion effect. Because Co(OH)2 dissolves to release hydroxide ions, adding hydroxide from the surrounding solution pushes the equilibrium back toward the solid. In practical terms, every increase in pH increases [OH–] and suppresses solubility.
For metal hydroxides of the form M(OH)2, the dependence is especially strong because hydroxide appears squared in the Ksp expression. If [OH–] increases by a factor of 10, solubility decreases by a factor of 100, assuming Ksp remains unchanged and no other equilibria dominate.
6. Comparison table: solubility of Co(OH)2 versus pH
The table below uses Ksp = 5.92 × 10-15 and the fixed-pH approximation to show how dramatically solubility changes across alkaline conditions.
| pH | pOH | [OH–] (M) | Calculated Solubility, s (M) | Approx. Solubility (mg/L as Co(OH)2) |
|---|---|---|---|---|
| 9.00 | 5.00 | 1.00 × 10-5 | 5.92 × 10-5 | 5.50 |
| 10.00 | 4.00 | 1.00 × 10-4 | 5.92 × 10-7 | 5.50 × 10-2 |
| 11.00 | 3.00 | 1.00 × 10-3 | 5.92 × 10-9 | 5.50 × 10-4 |
| 11.50 | 2.50 | 3.16 × 10-3 | 5.92 × 10-10 | 5.50 × 10-5 |
| 12.00 | 2.00 | 1.00 × 10-2 | 5.92 × 10-11 | 5.50 × 10-6 |
Notice the pattern: each 1.00 unit increase in pH causes a 100-fold drop in solubility for Co(OH)2 under this model. Moving from pH 10.00 to 11.00 cuts the molar solubility from 5.92 × 10-7 M to 5.92 × 10-9 M.
7. Comparison table: what changes when Ksp data differ
Published Ksp values can vary across data compilations, temperatures, and ionic strengths. That means your final answer may differ slightly from one source or instructor to another. The table below shows the effect of several plausible Ksp values at the same pH 11.50.
| Assumed Ksp | [OH–] at pH 11.50 | Calculated Solubility (M) | Approx. Solubility (mg/L as Co(OH)2) |
|---|---|---|---|
| 1.00 × 10-15 | 3.16 × 10-3 M | 1.00 × 10-10 | 9.30 × 10-6 |
| 5.92 × 10-15 | 3.16 × 10-3 M | 5.92 × 10-10 | 5.50 × 10-5 |
| 1.00 × 10-14 | 3.16 × 10-3 M | 1.00 × 10-9 | 9.30 × 10-5 |
This is why professional calculations often cite the exact source of thermodynamic data. If your chemistry class or reference book provides a specific Ksp, use that value rather than a generic database estimate.
8. Step-by-step method you can use on exams
- Write the dissolution equation: Co(OH)2(s) ⇌ Co2+ + 2OH–
- Write the solubility product: Ksp = [Co2+][OH–]2
- Convert pH to pOH using pOH = 14.00 – pH
- Convert pOH to hydroxide concentration using [OH–] = 10-pOH
- Rearrange the Ksp expression to solve for [Co2+]
- State the molar solubility in M
- Optionally convert to mg/L using the molar mass of Co(OH)2
At pH 11.50, this sequence gives a clean and quick result because the hydroxide concentration is already known from pH.
9. Important assumptions behind this calculation
- Buffered or fixed pH: The method assumes the solution pH remains at 11.50 even as some solid dissolves.
- Ideal behavior: It treats concentration as a practical stand-in for activity. This is common in introductory chemistry.
- No complex ion formation: Advanced cobalt chemistry can involve hydroxo complexes at higher pH, which may modify a more rigorous treatment.
- Temperature near 25 degrees C: pH to pOH conversion and Ksp values are typically referenced around room temperature.
10. Common mistakes students make
- Using pH directly as [H+] without first converting to pOH and [OH–]
- Forgetting that hydroxide is squared in the Ksp expression
- Using s = 4s3 style pure-water setups even though pH is already fixed externally
- Dropping powers of ten during scientific notation calculations
- Converting to mg/L incorrectly by forgetting the factor of 1000 mg per gram
A quick self-check helps: at high pH the solubility should be very small. If you get a large number, revisit the hydroxide term.
11. Final answer for pH 11.50
Using Ksp = 5.92 × 10-15:
- pOH = 2.50
- [OH–] = 3.16 × 10-3 M
- Solubility of Co(OH)2 = 5.92 × 10-10 M
- Approx. mass concentration = 5.50 × 10-5 mg/L as Co(OH)2
That is the core calculation this page automates. If you change the Ksp or pH, the calculator instantly updates both the numeric result and the pH-solubility chart.