Calculate the Solubility of Mg(OH)2 at pH 8.10
Use this interactive chemistry calculator to estimate the molar solubility, hydroxide concentration, magnesium concentration, and dissolved mass of magnesium hydroxide in water at a specified pH. The default setup is preloaded for pH 8.10.
Expert Guide: How to Calculate the Solubility of Mg(OH)2 at pH 8.10
Magnesium hydroxide, written as Mg(OH)2, is a sparingly soluble ionic compound that dissolves according to the equilibrium:
To calculate the solubility of magnesium hydroxide at pH 8.10, the key idea is to connect the acid-base relationship between pH and pOH with the solubility product expression. This is a common equilibrium problem in general chemistry, analytical chemistry, environmental chemistry, and water treatment calculations. Because Mg(OH)2 produces hydroxide ions when it dissolves, its solubility depends strongly on the hydroxide concentration already present in solution. That means pH matters a lot.
Step 1: Convert pH to pOH
At 25 C, the relationship is:
For a solution at pH 8.10:
Step 2: Convert pOH to hydroxide concentration
The hydroxide ion concentration is found from:
This number is central because the solubility product expression for magnesium hydroxide is:
Step 3: Apply the Ksp expression
A commonly used room-temperature value for the solubility product of Mg(OH)2 is approximately 5.61 × 10-12. If the pH is externally controlled by a buffer and therefore the hydroxide concentration remains fixed, then the molar solubility with respect to magnesium ion concentration is:
Substituting the values for pH 8.10:
That result is mathematically correct under a fixed-pH buffered assumption, but it also reveals an important chemistry insight: at such a modestly basic pH, magnesium hydroxide would appear far more soluble than people often expect if the solution could somehow hold the pH constant while the solid dissolves. In practice, real systems can become limited by ionic strength, non-ideal activity effects, incomplete buffering capacity, and the fact that adding more Mg(OH)2 itself changes the chemistry. So the calculation is best interpreted as an equilibrium estimate under the chosen assumptions.
Why pH 8.10 gives relatively high calculated solubility
Many students expect hydroxides to become less soluble whenever the pH is above 7. That is directionally true, but the amount of hydroxide already present at pH 8.10 is still quite small. A pH of 8.10 corresponds to only about 1.26 micromolar OH-. Since the Ksp expression contains [OH-]2, tiny hydroxide concentrations can still permit a large magnesium concentration before the equilibrium threshold is reached. As pH increases further, the hydroxide concentration rises exponentially and the allowed magnesium concentration falls very quickly.
Comparison table: pH, hydroxide concentration, and calculated Mg(OH)2 solubility
The following table uses Ksp = 5.61 × 10-12 and the buffered-pH assumption. It shows how dramatically solubility changes with pH.
| pH | pOH | [OH-] (M) | Calculated [Mg2+] = Solubility (M) | Dissolved Mg(OH)2 (g/L) |
|---|---|---|---|---|
| 7.00 | 7.00 | 1.00 × 10-7 | 561.0 | 32,717 |
| 8.00 | 6.00 | 1.00 × 10-6 | 5.61 | 327.2 |
| 8.10 | 5.90 | 1.26 × 10-6 | 3.54 | 206.4 |
| 9.00 | 5.00 | 1.00 × 10-5 | 0.0561 | 3.27 |
| 10.00 | 4.00 | 1.00 × 10-4 | 5.61 × 10-4 | 0.0327 |
| 11.00 | 3.00 | 1.00 × 10-3 | 5.61 × 10-6 | 3.27 × 10-4 |
This comparison clearly shows a two-order-of-magnitude change in solubility for each unit increase in pH, because hydroxide concentration changes tenfold per pH unit and the Ksp expression uses hydroxide squared. That is why pH control is such a powerful lever in precipitation and dissolution chemistry.
What the result means in practical chemistry
If you are solving a textbook problem that asks, “calculate the solubility of Mg(OH)2 at pH 8.10,” the normal approach is:
- Find pOH from pH.
- Convert pOH to [OH-].
- Substitute into Ksp = [Mg2+][OH-]2.
- Solve for [Mg2+], which is taken as the molar solubility under the fixed-pH condition.
Using that standard method, the calculated solubility is about 3.54 M at pH 8.10 when Ksp = 5.61 × 10-12. If you convert that to a mass concentration using the molar mass of Mg(OH)2, 58.319 g/mol, the corresponding amount is about 206 g/L.
In the laboratory, however, this value may not be physically realized unless a strong external buffer continuously enforces pH 8.10 while large amounts of magnesium dissolve. In unbuffered water, dissolution of Mg(OH)2 raises the hydroxide concentration, increases the pH, and shifts the equilibrium back toward the solid. That feedback lowers the actual observed solubility compared with the idealized fixed-pH estimate.
Common-ion effect and why it matters here
The common-ion effect explains why preexisting hydroxide lowers the solubility of Mg(OH)2. Because hydroxide is already a product of dissolution, adding more OH- pushes the equilibrium left. At pH 8.10, the common-ion effect exists, but it is still relatively weak compared with what happens at pH 10, 11, or 12. This is why magnesium hydroxide is far less soluble in strongly alkaline solutions than in mildly basic or neutral systems.
Comparison table: Key values used in the calculation
| Quantity | Symbol | Value | Role in the calculation |
|---|---|---|---|
| pH | pH | 8.10 | Starting point supplied by the problem |
| pOH | pOH | 5.90 | Computed from 14.00 – 8.10 |
| Hydroxide concentration | [OH-] | 1.26 × 10-6 M | Derived from 10-pOH |
| Solubility product | Ksp | 5.61 × 10-12 | Defines equilibrium for Mg(OH)2 |
| Molar solubility | s or [Mg2+] | 3.54 M | Final buffered-pH estimate |
| Molar mass | M | 58.319 g/mol | Used to convert molarity to g/L |
Worked example in compact form
If you need the shortest exam-style derivation, use the following sequence:
[OH-] = 10^-5.90 = 1.26 × 10^-6 M
Ksp = [Mg2+][OH-]^2
[Mg2+] = (5.61 × 10^-12) / (1.26 × 10^-6)^2
[Mg2+] ≈ 3.54 M
When should you not use this simple formula directly?
- When the solution is not buffered and pH will change as Mg(OH)2 dissolves.
- When activity coefficients are important because ionic strength is high.
- When the problem provides a different Ksp value at another temperature.
- When complexation, carbonate chemistry, or other side equilibria are significant.
- When the system is constrained by total magnesium concentration rather than solid-liquid equilibrium alone.
Environmental and water-treatment relevance
Magnesium hydroxide chemistry matters in environmental engineering because hydroxide precipitation is one route for removing dissolved metals, adjusting alkalinity, and controlling water chemistry. Solubility calculations help engineers predict whether a metal hydroxide will remain dissolved or precipitate under a certain pH regime. At mildly basic pH values such as 8.10, many hydroxide systems still retain substantial dissolved metal concentrations unless buffering or competing equilibria alter the outcome. This is why pH setpoints are chosen carefully in treatment design.
Authoritative sources for further reading
- U.S. Environmental Protection Agency water research resources
- LibreTexts Chemistry analytical chemistry materials
- Khan Academy acid-base and equilibrium tutorials
Final answer for pH 8.10
Under the standard fixed-pH buffered assumption and using Ksp = 5.61 × 10-12 at 25 C, the calculated molar solubility of Mg(OH)2 at pH 8.10 is:
Solubility ≈ 3.54 M
That corresponds to approximately 206 g/L of Mg(OH)2. Use the calculator above if you want to test different pH values, Ksp values, or solution volumes and visualize how the solubility changes across the pH scale.