Calculate the pH of a 0.42 M Magnesium Hydroxide Solution
Use this interactive calculator to determine hydroxide concentration, pOH, and pH for magnesium hydroxide, Mg(OH)2. The default setup uses the standard classroom assumption of complete dissociation, which gives the expected textbook answer for a 0.42 M solution.
For the standard chemistry exercise “calculate the pH of a 0.42 M magnesium hydroxide solution,” use 0.42 M, 2 hydroxides per formula unit, and 100% dissociation. That produces [OH–] = 0.84 M, pOH = 0.076, and pH = 13.924.
Calculated Results
[OH–] = 2 × 0.42 = 0.84 M
pOH = -log10(0.84) = 0.0757
pH = 14 – 0.0757 = 13.9243
How to calculate the pH of a 0.42 M magnesium hydroxide solution
If you need to calculate the pH of a 0.42 M magnesium hydroxide solution, the most common textbook approach is straightforward. Magnesium hydroxide has the chemical formula Mg(OH)2, which means each formula unit releases two hydroxide ions when it dissociates. Since pH for bases is often found through the hydroxide ion concentration, the key idea is to convert the compound concentration into an OH– concentration, compute pOH, and then convert pOH into pH.
Under the standard classroom assumption that Mg(OH)2 dissociates completely, a 0.42 M magnesium hydroxide solution yields twice that concentration in hydroxide ions because there are two OH– groups in the formula. That gives an OH– concentration of 0.84 M. Using pOH = -log[OH–], we get pOH = -log(0.84) ≈ 0.0757. Finally, pH = 14 – 0.0757 ≈ 13.9243 at 25 degrees Celsius.
Quick answer
- Given: 0.42 M Mg(OH)2
- Dissociation: Mg(OH)2 → Mg2+ + 2OH–
- [OH–]: 2 × 0.42 = 0.84 M
- pOH: -log(0.84) = 0.0757
- pH: 14 – 0.0757 = 13.9243
Step-by-step solution
Let us walk through the chemistry carefully, because many students make one of three mistakes: forgetting the coefficient 2 for hydroxide, taking the log of the original compound concentration instead of the hydroxide concentration, or mixing up pH and pOH at the end.
1. Write the dissociation equation
Magnesium hydroxide dissociates according to the equation:
Mg(OH)2 → Mg2+ + 2OH–
This tells us that one mole of magnesium hydroxide produces two moles of hydroxide ions. That stoichiometric ratio is the reason we multiply the original concentration by 2.
2. Convert compound concentration into hydroxide concentration
Starting concentration:
[Mg(OH)2] = 0.42 M
Because each mole gives 2 moles of OH–:
[OH–] = 2 × 0.42 = 0.84 M
3. Find the pOH
The formula is:
pOH = -log[OH–]
Substitute 0.84:
pOH = -log(0.84) = 0.0757
4. Convert pOH into pH
At 25 degrees Celsius, the standard relationship is:
pH + pOH = 14
So:
pH = 14 – 0.0757 = 13.9243
Why magnesium hydroxide gives two hydroxide ions
The formula Mg(OH)2 contains one magnesium ion and two hydroxide groups. Magnesium typically forms Mg2+, while hydroxide is OH–. To balance the +2 charge on magnesium, two hydroxides are required. That charge balance is reflected directly in the dissociation equation and in the concentration calculation. As a result, if you know the molarity of magnesium hydroxide and assume complete dissociation, you can always get the hydroxide concentration by doubling the molarity.
Important chemistry note about real solutions
This distinction matters. In general chemistry homework, the phrase “calculate the pH of a 0.42 M magnesium hydroxide solution” usually signals a simplified stoichiometric acid-base problem. In laboratory or environmental work, you would also need to think about solubility equilibrium, ionic strength, temperature, and whether the suspension is saturated rather than truly dissolved at that concentration.
Common errors students make
- Using 0.42 M directly as [OH–]
That misses the fact that each formula unit contributes two hydroxide ions. - Calculating pH directly from 0.84 M
For bases, you first calculate pOH from hydroxide concentration, then convert to pH. - Forgetting the logarithm sign
pOH is the negative log base 10 of hydroxide concentration, not the raw concentration itself. - Ignoring assumptions
For advanced chemistry, Mg(OH)2 solubility is limited, so the complete dissociation model is mainly a textbook simplification.
Worked comparison table: strong and sparingly soluble bases
| Base | Formula | OH- ions released per formula unit | If formal concentration is 0.42 M, idealized [OH-] | Idealized pOH | Idealized pH at 25 degrees C |
|---|---|---|---|---|---|
| Sodium hydroxide | NaOH | 1 | 0.42 M | 0.3778 | 13.6222 |
| Potassium hydroxide | KOH | 1 | 0.42 M | 0.3778 | 13.6222 |
| Calcium hydroxide | Ca(OH)2 | 2 | 0.84 M | 0.0757 | 13.9243 |
| Magnesium hydroxide | Mg(OH)2 | 2 | 0.84 M | 0.0757 | 13.9243 |
This table highlights the power of stoichiometry. Bases with one hydroxide per formula unit produce half the hydroxide concentration compared with a base that contributes two hydroxides at the same formal molarity. That is why the pH of the idealized 0.42 M Mg(OH)2 problem ends up higher than the pH of a 0.42 M NaOH problem only when viewed through the formula-unit stoichiometry. In real practice, solubility changes the story for magnesium hydroxide and calcium hydroxide.
Reference data table: pH scale benchmarks and water-quality context
| Substance or benchmark | Typical pH | Context | Comparison to 0.42 M Mg(OH)2 idealized result |
|---|---|---|---|
| Pure water at 25 degrees C | 7.0 | Neutral reference point | Far less basic than pH 13.9243 |
| EPA secondary drinking-water recommended range | 6.5 to 8.5 | Common aesthetic guideline for potable water | The calculated value is far above this range |
| Household ammonia cleaner | 11 to 12 | Typical strong household base | Still below the idealized 13.9243 result |
| Concentrated strong base solutions | 13 to 14 | Highly caustic alkaline region | The calculated result falls in this region |
The comparison data above puts the result into perspective. A pH of about 13.92 lies extremely high on the pH scale and corresponds to a very caustic basic medium under idealized assumptions. It is dramatically outside ordinary environmental and drinking-water ranges. In practical safety terms, anything in this region should be treated as corrosive and handled with proper chemical precautions.
What formula should you memorize?
For this exact type of problem, the most useful sequence is:
- Determine the number of OH– ions produced per formula unit.
- Compute hydroxide concentration:
[OH–] = molarity of base × number of OH groups × fraction dissociated - Compute pOH:
pOH = -log[OH–] - Compute pH:
pH = 14 – pOH
For magnesium hydroxide under the complete-dissociation classroom assumption, the fraction dissociated is taken as 1. Therefore:
[OH–] = 0.42 × 2 × 1 = 0.84 M
Why the logarithm matters
The pH and pOH scales are logarithmic, not linear. That means a small change in pOH can represent a significant change in hydroxide concentration. Since 0.84 M is already a large hydroxide concentration, the pOH ends up very close to zero. Once pOH becomes very small, pH approaches 14. This is why the final answer is 13.9243 rather than something like 13.16 or 12.8. The base is extremely concentrated on the pH scale.
When would the answer be different?
The answer changes if any of the following assumptions change:
- Temperature changes: The relationship pH + pOH = 14 strictly applies at 25 degrees Celsius.
- Incomplete dissociation is considered: If only part of the base contributes OH–, the pH falls.
- Solubility is considered: For magnesium hydroxide, realistic dissolved concentration in pure water is far below 0.42 M.
- Activity effects are included: In concentrated ionic solutions, activity can differ from molar concentration.
Practical interpretation of the result
An idealized pH of 13.9243 means the solution is intensely basic. In a lab, a solution in this range would require goggles, gloves, and careful handling to avoid chemical burns. From an educational standpoint, the value shows how metal hydroxides with multiple hydroxide groups can produce high pH values when treated as fully dissociated bases. From a physical chemistry standpoint, the problem is also a reminder that stoichiometric calculations and equilibrium limitations are not always the same thing.
Final answer
Using the standard textbook assumption of complete dissociation:
- [OH–] = 0.84 M
- pOH = 0.0757
- pH = 13.9243
So, the pH of a 0.42 M magnesium hydroxide solution is approximately 13.92.