Understanding the pH of a 0.04M Solution of Magnesium Hydroxide: A Comprehensive Analysis

When dealing with solutions of strong bases like Mg(OH)2, the calculation of pH is often a common question. This article delves into the intricacies of determining the pH of a 0.04M solution of magnesium hydroxide, utilizing both direct concentration-based approaches and solubility product constants. This analysis will help clarify the principles behind these calculations and provide a deeper understanding of the behavior of such ionic compounds.

The Direct Concentration-Based Approach

The pH of a basic solution can be calculated using the hydroxide ion concentration, [OH-], and the ion-product constant for water, Kw. For a 0.04M solution of magnesium hydroxide (Mg(OH)2):

The hydroxide ion concentration can be determined as:

[OH-] 2 x 0.04 0.08M

The pH can then be calculated from the pOH:

pOH -log [OH-] -log 0.08 ≈ 1.097

Finally, the pH is given by:

pH 14 - pOH 14 - 1.097 ≈ 12.903

However, this straightforward approach assumes Mg(OH)2 is completely soluble and a strong base, which may not be entirely accurate.

Considering Solubility Product

Given the low solubility of Mg(OH)2 and its nature as a strong base, a more accurate method involves the use of the solubility product constant, Ksp. The solubility equilibrium for Mg(OH)2 is:

Mg(OH)2 ? Mg2 2OH-

The solubility product constant expression is:

Ksp [Mg2 ] [OH-]2

For a 0.04M solution, the concentration of OH- is twice the concentration of Mg2 , assuming complete dissociation. Let S represent the solubility of the salt. Then:

Ksp S(2S)2 4S3

Solving for S:

S (Ksp/4)1/3 (5.61 x 1012/4)1/3 ≈ 1.12 x 10-4 M

Since S is the concentration of Mg2 , the concentration of OH- is 2S ≈ 2.24 x 10-4 M.

The pOH is calculated as:

pOH -log [OH-] -log(2.24 x 10-4) ≈ 3.645

Finally, the pH is:

pH 14 - pOH 14 - 3.645 ≈ 10.355

This result shows that the direct concentration-based approach overestimates the solubility and hence the pH, which is a common issue with strong bases like magnesium hydroxide.

Conclusion

Understanding the pH of a 0.04M solution of magnesium hydroxide involves careful consideration of both concentration-based methods and the solubility product constant. The direct approach, while simple, may not accurately reflect the true solubility and behavior of strong bases in solution. This analysis demonstrates the importance of using solubility product constants for more accurate pH calculations, especially for compounds with low solubility.

Related Keywords

Keywords: pH calculation, Magnesium Hydroxide, Solubility Product, Basic Solutions