Calculate the pH of a Saturated Mg(OH)2 Solution
Use this premium calculator to estimate molar solubility, hydroxide concentration, pOH, and pH for a saturated magnesium hydroxide solution. The model uses the solubility product relationship for Mg(OH)2: Ksp = [Mg2+][OH–]2.
Interactive pH Calculator
Default example: 5.61 × 10-12 at about 25°C.
Use 14.00 for standard classroom calculations at 25°C.
Changing pKw affects the final pH from the same [OH–].
Controls decimal places for pH, pOH, and concentrations.
This field does not affect the math. It is included for organization and reporting.
Results Dashboard
Enter your values and click Calculate pH to view the saturated Mg(OH)2 solution results.
How to Calculate the pH of a Saturated Mg(OH)2 Solution
Calculating the pH of a saturated magnesium hydroxide solution is a classic equilibrium problem in general chemistry. Magnesium hydroxide, written as Mg(OH)2, is only slightly soluble in water. That limited solubility is exactly why its pH can be calculated from the solubility product constant, Ksp. If you know the dissolution stoichiometry and the Ksp value, you can determine the hydroxide concentration, convert to pOH, and then calculate pH.
This matters in more than just classroom exercises. Mg(OH)2 is relevant in water treatment, neutralization chemistry, environmental systems, antacid formulations, and industrial process control. Because it is sparingly soluble, the pH of its saturated solution does not become arbitrarily large in pure water. Instead, the pH settles at a value controlled by equilibrium. For many standard textbook conditions near 25°C, the pH of a saturated Mg(OH)2 solution is typically around 10.3 to 10.6, depending on the exact Ksp used and whether activities or ideal concentrations are assumed.
Step 1: Write the Dissolution Equation
The first step is to write the equilibrium expression for magnesium hydroxide dissolving in water:
This equation tells you that every 1 mole of dissolved Mg(OH)2 produces 1 mole of Mg2+ and 2 moles of OH–. That 1:2 stoichiometric relationship is the key to the entire calculation.
Step 2: Write the Ksp Expression
For a sparingly soluble ionic compound, the solubility product expression includes only the dissolved ions. The pure solid is omitted because its activity is effectively constant. For Mg(OH)2, the expression is:
If the molar solubility is represented by s, then at equilibrium:
- [Mg2+] = s
- [OH–] = 2s
Substitute these into the Ksp expression:
Now solve for molar solubility:
Once you have s, the hydroxide concentration is simply:
Step 3: Convert [OH–] to pOH and pH
After finding hydroxide concentration, the rest is straightforward:
- Calculate pOH using pOH = -log[OH–]
- Calculate pH using pH = pKw – pOH
At 25°C, pKw is usually taken as 14.00, so the classroom formula becomes:
For example, using a Ksp value of 5.61 × 10-12:
- s = (5.61 × 10-12 / 4)1/3
- s ≈ 1.119 × 10-4 M
- [OH–] = 2s ≈ 2.238 × 10-4 M
- pOH = -log(2.238 × 10-4) ≈ 3.650
- pH = 14.000 – 3.650 ≈ 10.350
That result is why saturated magnesium hydroxide solutions are basic but not nearly as extreme as a strong base like 0.1 M NaOH. The limited solubility caps the hydroxide concentration.
Why Different Sources Give Slightly Different pH Values
Students often notice that different books or websites report slightly different pH values for saturated Mg(OH)2. This usually comes from one or more of the following:
- Different Ksp values reported at the same temperature
- Rounding differences during intermediate steps
- Use of activities instead of simple molar concentrations
- Temperature effects on both Ksp and pKw
- Ignoring or including common ion effects
In introductory chemistry, ideal behavior is usually assumed, and concentration-based Ksp values are used directly. Under those assumptions, this calculator gives exactly the kind of result most instructors expect.
Comparison Table: Ksp Assumptions and Resulting pH at 25°C
| Assumed Ksp for Mg(OH)2 | Molar Solubility, s (M) | [OH–] (M) | pOH | pH at 25°C |
|---|---|---|---|---|
| 1.20 × 10-11 | 1.442 × 10-4 | 2.884 × 10-4 | 3.540 | 10.460 |
| 5.61 × 10-12 | 1.119 × 10-4 | 2.238 × 10-4 | 3.650 | 10.350 |
| 1.80 × 10-11 | 1.651 × 10-4 | 3.302 × 10-4 | 3.481 | 10.519 |
The table makes an important point: even when Ksp varies noticeably between sources, the resulting pH usually remains in a fairly narrow alkaline range. That is why many instructors accept a pH close to 10.4 or 10.5 for a saturated magnesium hydroxide solution.
How Mg(OH)2 Compares with Other Slightly Soluble Hydroxides
It is also helpful to compare magnesium hydroxide with other bases. Some ionic hydroxides such as NaOH and KOH are highly soluble strong bases. Others, like Mg(OH)2 and Ca(OH)2, are less soluble. Solubility strongly affects the final pH of a saturated solution.
| Compound | Dissolution Behavior in Water | Typical Classroom Saturated Solution Character | Approximate pH Range |
|---|---|---|---|
| NaOH | Highly soluble, strong base | Very high [OH–] limited mainly by concentration prepared | 13 to 14+ |
| KOH | Highly soluble, strong base | Similar to NaOH | 13 to 14+ |
| Ca(OH)2 | Sparingly soluble | Saturated limewater is strongly basic but more limited than NaOH | About 12.3 to 12.5 |
| Mg(OH)2 | More sparingly soluble than Ca(OH)2 | Saturated suspension gives a moderate alkaline pH | About 10.3 to 10.6 |
Common Mistakes to Avoid
When you calculate the pH of a saturated Mg(OH)2 solution, a few mistakes appear again and again:
- Forgetting the stoichiometric coefficient on hydroxide. The dissolved hydroxide concentration is 2s, not s.
- Writing Ksp incorrectly. It must be [Mg2+][OH–]2.
- Using pH = -log[OH–]. That gives pOH, not pH.
- Assuming pH always equals 14 – pOH. That shortcut is valid only when pKw is 14.00, typically at 25°C.
- Ignoring units and significant figures. Ksp values are small, and scientific notation matters.
What Happens If a Common Ion Is Present?
If magnesium ions or hydroxide ions are already present before Mg(OH)2 dissolves, the solubility decreases because of the common ion effect. For example, if the solution already contains OH– from another base, less Mg(OH)2 will dissolve. That means the saturated solution under those conditions can behave differently from the pure-water case modeled by this calculator.
In an ideal classroom problem that asks specifically for the pH of a saturated Mg(OH)2 solution, the assumption is almost always pure water, no added salts, no buffer, and equilibrium at a stated or implied temperature. Under those conditions, the Ksp-based approach used here is correct.
Temperature Effects on pH Calculations
Temperature matters in two ways. First, the Ksp itself can change with temperature. Second, the ionic product of water changes, which changes pKw. That is why this calculator includes both a temperature preset and a customizable pKw field. At 25°C, pKw is commonly set to 14.00. At other temperatures, the neutral point shifts, so pH calculations should be adjusted accordingly.
Even if the hydroxide concentration stays the same, the computed pH can shift slightly as pKw changes. That is especially useful in more advanced physical chemistry, analytical chemistry, or environmental chemistry settings where temperature control matters.
Where This Calculation Appears in Real Chemistry
The saturated Mg(OH)2 pH problem appears in multiple scientific contexts:
- General chemistry: Ksp, equilibrium, ICE tables, and pH relationships
- Analytical chemistry: precipitation control and selective ion separation
- Environmental chemistry: alkalinity, mineral equilibria, and water treatment reactions
- Pharmaceutical science: understanding antacid chemistry and suspension behavior
- Industrial chemistry: neutralization and magnesium-based alkaline processes
Authoritative References for pH and Aqueous Chemistry
If you want to verify pH concepts, equilibrium behavior, and water chemistry fundamentals, these sources are excellent starting points:
Fast Summary Method
If you just need the shortest path to the answer, use this sequence:
- Write Mg(OH)2(s) ⇌ Mg2+ + 2OH–
- Set Ksp = [Mg2+][OH–]2
- Let [Mg2+] = s and [OH–] = 2s
- Solve 4s3 = Ksp
- Find [OH–] = 2s
- Compute pOH = -log[OH–]
- Compute pH = pKw – pOH
For a commonly used Ksp near 5.61 × 10-12 at 25°C, the final answer is typically close to pH = 10.35. If your class uses a different Ksp, your answer may shift slightly, but the logic remains the same.
Final Takeaway
To calculate the pH of a saturated Mg(OH)2 solution, you do not treat magnesium hydroxide like a highly soluble strong base. Instead, you respect its limited solubility and use Ksp equilibrium. Because one dissolved unit releases two hydroxide ions, the stoichiometry must be handled carefully. Once [OH–] is known, the conversion to pOH and pH is simple. For standard textbook conditions at 25°C, the pH is usually a little above 10.3 and often around 10.4 to 10.5 depending on the exact Ksp source.