Question

A saturated solution of milk of magnesia, \(\mathrm{Mg}(\mathrm{OH})_{2},\) has a pH of \(10.5 .\) What is the hydronium ion concentration of the solution? Is the solution acidic or basic?

Short answer

The hydronium ion concentration is approximately \(3.16 \times 10^{-11}\, \text{M}\) and the solution is basic.

Step-by-step solution

Understand pH and Hydronium Ion Concentration

The pH of a solution is a measure that indicates how acidic or basic the solution is. It is calculated using the formula: \( ext{pH} = -\log [\text{H}^+]\), where \([\text{H}^+]\) is the hydronium ion concentration in moles per liter (M).

Solve for Hydronium Ion Concentration

To find the hydronium ion concentration, use the relationship: \([\text{H}^+] = 10^{-\text{pH}}\). Given that \(\text{pH} = 10.5\), plug this value into the formula: \([\text{H}^+] = 10^{-10.5} \approx 3.16 \times 10^{-11}\, \text{M}\).

Determine If the Solution is Acidic or Basic

A solution with a pH less than 7 is acidic, while a pH greater than 7 is basic. Since the given pH is 10.5, which is greater than 7, the solution is basic.

Key concepts

Hydronium Ion Concentration

The concept of hydronium ion concentration is a cornerstone in understanding the nature of a solution's acidity or basicity. In chemistry, the hydronium ion ("""\[\text{H}_3\text{O}^+\]""") is formed when an acid dissolves in water, releasing hydrogen ions ("""\[\text{H}^+\]"""), which then combine with water molecules.

The concentration of these ions in a solution can be directly related to the solution's pH. The relationship is typically expressed mathematically as:

• """\[\text{pH} = -\log [\text{H}^+]\]""": Here, """\[\text{[H}^+]\]""" is the molarity of hydronium ions.
• If you know the pH, you can find the hydronium ion concentration by rearranging the formula: """\[[\text{H}^+] = 10^{-\text{pH}}\]""".

In our exercise, a pH of 10.5 leads to a hydronium ion concentration of approximately """\[3.16 \times 10^{-11}\text{ M}\]""". Understanding this relationship helps you determine the acidity or basicity of the solution.

Acidic and Basic Solutions

Grasping the difference between acidic and basic solutions is essential for any chemistry enthusiast. The pH scale, which ranges from 0 to 14, serves as the standard measure:

• """\[\text{pH} < 7\]""": Considered acidic solutions. More hydronium ions are present.
• """\[\text{pH} \approx 7\]""": Neutral solutions, such as pure water.
• """\[\text{pH} > 7\]""": Indicates basic solutions. Fewer hydronium ions are present compared to hydroxide ions, """\[\text{OH}^-\]""".

In this exercise, the pH of 10.5 indicates a basic solution. Basic solutions are often associated with substances like soaps or items containing magnesium hydroxide ("""\[\text{Mg(OH)}_2\]"""), which are used in antacid products.

Saturated Solutions

A saturated solution can be best described as a solution that is in equilibrium with undissolved solute, where no more solute can be dissolved at a given temperature and pressure. This concept is crucial for understanding reactions and solubility limits:

• At saturation, no additional solute will dissolve.
• It's influenced by temperature and pressure. Higher temperatures often increase solubility for many solutions, while higher pressure can do the same for gases.
• For Mg(OH)"""\[\text{Mg(OH)}_2\]""", the saturation point determines the maximum amount that can dissolve in water, influencing its subsequent pH and ionic concentration.

In this problem, milk of magnesia forms a saturated solution of """\[\text{Mg(OH)}_2\]""", meaning it contains the maximum concentration of dissolved ions at equilibrium.

Mg(OH)2

Magnesium hydroxide, """\[\text{Mg(OH)}_2\]""", is an important compound in both everyday products and chemical reactions. It is commonly known as milk of magnesia and has interesting properties:

• It acts as a base and is used in antacid products to neutralize excess stomach acid.
• In water, """\[\text{Mg(OH)}_2\]""" establishes equilibrium by dissociating into magnesium ions ("""\[\text{Mg}^{2+}\]""") and hydroxide ions ("""\[\text{OH}^-\]""").
• This dissociation influences the solution's pH, making it basic as demonstrated by the pH value of 10.5 in our exercise.

Understanding """\[\text{Mg(OH)}_2\]""" helps explain why the solution behaves as observed, aligning with its pH and basic nature.