Problem 10 - Chemistry and Chemical Reactivity

Question

A saturated solution of milk of magnesia, \(\mathrm{Mg}(\mathrm{OH})_{2},\) has a pH of \(10.52 .\) What is the hydronium ion concentration of the solution? What is the hydroxide ion concentration? Is the solution acidic or basic?

Step-by-Step Solution

Answer

The solution is basic with a hydroxide concentration of \(3.31 \times 10^{-4} \ M\) and a hydronium concentration of \(3.02 \times 10^{-11} \ M\).

Step 1: Understand the Relationship between pH and pOH

The pH of a solution is a measure of the acidity or basicity of the solution. For room temperature, the sum of pH and pOH is always 14. Thus, knowing the pH, we can determine the pOH using the formula: \( \text{pH} + \text{pOH} = 14 \).

Step 2: Calculate pOH

Given that the pH of the solution is 10.52, we can find the pOH by subtracting the pH from 14.\[pOH = 14 - 10.52 = 3.48\]

Step 3: Calculate Hydroxide Ion Concentration

Once we have the pOH, we can calculate the hydroxide ion concentration using the relationship: \( [\text{OH}^-] = 10^{-\text{pOH}} \). \[[\text{OH}^-] = 10^{-3.48}\]Approximately, \([\text{OH}^-]\) is \(3.31 \times 10^{-4} \ M\).

Step 4: Determine Hydronium Ion Concentration

The hydronium ion concentration \([\text{H}_3\text{O}^+]\) can be found using the inverse relationship with pH:\[[\text{H}_3\text{O}^+] = 10^{-\text{pH}} = 10^{-10.52}\]Calculated, \([\text{H}_3\text{O}^+]\) is approximately \(3.02 \times 10^{-11} \ M\).

Step 5: Identify if Solution is Acidic or Basic

If the pH is greater than 7, the solution is basic and if it is less than 7, the solution is acidic. Here, the pH is 10.52, indicating the solution is basic.

Key Concepts

Hydronium Ion Concentration

The hydronium ion concentration \([\text{H}_3\text{O}^+]\) is an important measure that tells us how many hydronium ions are present in a solution. It is closely related to the pH of the solution. The pH is a logarithmic scale used to specify the acidity or basicity of an aqueous solution.
To find the hydronium ion concentration from pH, we use the formula: \[\text{[H}_3\text{O}^+] = 10^{-\text{pH}}\].This formula shows that even a small pH change can lead to a large change in hydronium ion concentration, due to the logarithmic relationship.
In the given exercise, we start with a pH of 10.52. Using the formula:

• Calculate hydronium ion concentration: \([ \text{H}_3\text{O}^+] = 10^{-10.52} \), resulting in approximately \(3.02 \times 10^{-11} \ M\).

This low concentration indicates that hydronium ions are scarce, aligning with the basicity of the solution.

Hydroxide Ion Concentration

The hydroxide ion concentration \(\text{[OH}^-\text{]}\) characterizes the basicity of a solution. It is computed using the pOH of the solution.Since we know that the pH and pOH add up to 14, we can calculate pOH if pH is known.
Then, the hydroxide concentration can be found using the relation: \[\text{[OH}^-\text{]} = 10^{-\text{pOH}}\].This inverse relationship emphasizes that as pOH decreases, hydroxide ion concentration increases, indicating a more basic solution.
For the example at hand:

• pOH is calculated by \(14 - \text{pH} = 3.48\).
• Hydroxide ion concentration: \(\text{[OH}^-\text{]} = 10^{-3.48}\), resulting in approximately \(3.31 \times 10^{-4} \ M\).

This higher concentration of hydroxide ions is responsible for the basic nature of the milk of magnesia solution.

Acidic or Basic Solutions

Determining whether a solution is acidic or basic is straight-forward when you know the pH. Generally, solutions with a pH less than 7 are acidic, and those with a pH greater than 7 are basic. The pH is a quick indicator because it represents the negative logarithm of the hydronium ion concentration.
More hydronium ions mean a higher acidity, while more hydroxide ions mean a higher basicity.
In the given solution where pH is 10.52:

• The pH is greater than 7, indicating that the solution is basic.
• The low hydronium ion concentration further confirms the basic nature.

Milk of magnesia's slightly higher pH reflects its role as an antacid, neutralizing excess stomach acid.