Understanding the pH of Magnesium Hydroxide: Insights and Calculations

Magnesium hydroxide, a compound often used as a dental cement, is known for its basic properties and is used in various industrial applications. However, determining its pH can be challenging, especially given its solubility in water. In this article, we will delve into the pH value of magnesium hydroxide, the solubility product and how these factors play a significant role in its measurement.

What is the pH of Magnesium Hydroxide?

The pH value of magnesium hydroxide can be determined through its solubility product constant, known as Ksp. The Ksp of magnesium hydroxide is 1.8 × 10?11. To find the pH, we must first understand the solubility equilibrium of magnesium hydroxide:

Mg(OH)2(s) ? Mg2 (aq)   2OH-(aq)

Solubility Equilibrium and pH Calculation

Let's consider the solubility equilibrium of magnesium hydroxide:

Mg(OH)2(s) ? Mg2 (aq)   2OH-(aq)

At equilibrium:

Ksp  [Mg2 ][OH-]2  1.8 × 10-11

Step-by-Step Calculation of pH

Let s represent the molar solubility of magnesium hydroxide. Since the dissociation produces 1 mole of Mg2 and 2 moles of OH-, we have:

Ksp s(2s)2 4s3

Solving for s categorically:

4s3  1.8 × 10-11
s3  (1.8 × 10-11) / 4
s3  4.5 × 10-12
s  ?(4.5 × 10-12)  1.65 × 10-4

Since the concentration of OH- is 2s:

[OH-]  2s  3.30 × 10-4 M

The pOH is given by:

pOH  -log [OH-]  -log (3.30 × 10-4)

pOH 3.5

Using the relationship pH pOH 14, we find the pH:

pH  14 - pOH  14 - 3.5  10.5

Implications and Practical Application

The calculation above provides a detailed understanding of the pH value of magnesium hydroxide. However, it's essential to note that the solubility of magnesium hydroxide is very low, with a Ksp of 1.8 × 10?11. If a larger amount of magnesium hydroxide, such as 3.68 × 108 moles, were to be dissolved, it would result in a different OH- concentration. Assuming complete dissociation, a concentration of 7.36 × 10?8 moles per liter would be more fitting for this context.

Additionally, if the concentration of magnesium hydroxide is as low as 3.68 × 10?8 moles per liter, it is far less than the solubility in water, which is approximately 1.1 × 10?4 moles per liter. This emphasizes the importance of solubility product and the practical significance of pH in chemical applications.

Practical Example: Calculating the pH of Mg(OH)2

Let's further solidify our understanding by solving a practical problem. Suppose we have 4.2 grams of magnesium hydroxide and need to find its pH in a 450 mL solution:

Given:

mass Mg(OH)2 4.2 gmolar mass Mg(OH)2 58.3 g/molevolume of solution 450 mL 0.45 L

To find the pH:

Calculate the molarity of the solution:

moles of solute mass of solute / molar mass solute

moles of solute  4.2 g / 58.3 g/mole  0.072 mole

Molarity M moles of solute / liters of solution 0.072 mole / 0.45 L 0.16 M Mg(OH)2

Since Mg(OH)2 fully dissociates, the concentration of OH- is twice that of Mg2 :

[OH-] 2 × 0.16 M 0.32 M

Calculate the pOH:

pOH -log [OH-] -log (0.32) 0.5

Finally, calculate the pH:

pH 14 - pOH 14 - 0.5 13.5

Conclusion

Understanding the pH value of magnesium hydroxide is crucial in various industries, particularly in water treatment and chemical analysis. The solubility product plays a vital role in determining the concentration of OH- ions, which in turn affects the overall pH of the solution. By delving into the principles of solubility and pH, the above calculations illustrate the practical implications of these concepts in real-world scenarios.