Problem 13 - Chemistry and Chemical Reactivity

Question

What is the \(\mathrm{pH}\) of a \(0.0015 \mathrm{M}\) solution of \(\mathrm{Ba}(\mathrm{OH})_{2} ?\)

Step-by-Step Solution

Answer

The pH of the solution is 11.48.

Step 1: Identify the key information

First, extract the important data from the problem. We have a solution of barium hydroxide, \( \mathrm{Ba(OH)_2} \), with a concentration of \( 0.0015 \, M \). We need to find the \( \mathrm{pH} \) of this solution.

Step 2: Understand the dissociation of Ba(OH)2

Barium hydroxide dissociates completely in water: \( \mathrm{Ba(OH)_2 \rightarrow Ba^{2+} + 2OH^-} \). This means it produces two hydroxide ions \( ( \mathrm{OH^-} ) \) for every formula unit dissolved.

Step 3: Calculate the hydroxide ion concentration

Since each mole of \( \mathrm{Ba(OH)_2} \) releases two moles of \( \mathrm{OH^-} \), the \( \mathrm{OH^-} \) concentration is twice the concentration of \( \mathrm{Ba(OH)_2} \). \[ [\mathrm{OH^-}] = 2 \times 0.0015 \, M = 0.0030 \, M \]

Step 4: Calculate the pOH

Use the formula \( \mathrm{pOH} = -\log [\mathrm{OH^-}] \) to find the pOH:\[ \text{pOH} = -\log(0.003) \approx 2.52 \]

Step 5: Calculate the pH

Since \( \mathrm{pH} + \mathrm{pOH} = 14 \), we can find the pH by solving:\[ \mathrm{pH} = 14 - \mathrm{pOH} = 14 - 2.52 = 11.48 \]

Key Concepts

Barium Hydroxide Dissociation

Barium hydroxide, represented as \( \mathrm{Ba(OH)_2} \), is known for its strong dissociation properties in water.
When it dissolves, it separates completely into its constituent ions.
This process can be described by the following chemical equation:

• \( \mathrm{Ba(OH)_2 \rightarrow Ba^{2+} + 2OH^-} \)

As you can see, each formula unit of \( \mathrm{Ba(OH)_2} \) produces one barium ion (\( \mathrm{Ba^{2+}} \)) and two hydroxide ions (\( \mathrm{OH^-} \)). This complete dissociation is typical of strong bases.
It’s important to remember this stoichiometry because it dictates the concentration of each ion in solution, which is crucial for calculating the pH of the solution.

Hydroxide Ion Concentration

Understanding how many hydroxide ions are produced is key to determining the pH of the solution.
From the dissociation equation, we've seen that for every mole of \( \mathrm{Ba(OH)_2} \) that dissolves, two moles of \( \mathrm{OH^-} \) ions are released.
So, the concentration of hydroxide ions becomes twice the concentration of \( \mathrm{Ba(OH)_2} \).

Let's work through an example:

• Suppose we have a \( 0.0015 \, \mathrm{M} \) solution of \( \mathrm{Ba(OH)_2} \).
• The concentration of \( \mathrm{OH^-} \) will then be \( 2 \times 0.0015 \, \mathrm{M} = 0.0030 \, \mathrm{M} \).

This doubling of concentration reflects the stoichiometry of the reaction.
It is essential to account for this when proceeding to calculate the pOH and subsequent pH of the solution.

pOH Calculation

The pOH of a solution is a measure of its hydroxide ion concentration.
This is similar to how pH measures the hydrogen ion concentration.
The formula to calculate pOH is:

• \( \mathrm{pOH} = -\log [\mathrm{OH^-}] \)

Consider our previous example:
For a \( 0.0030 \, \mathrm{M} \) hydroxide ion concentration, the pOH is calculated as:

• \( \text{pOH} = -\log(0.003) \approx 2.52 \)

This calculation involves taking the negative logarithm of the hydroxide ion concentration.
It’s important to ensure your calculator is set to the correct mode to get an accurate result.
Understanding the pOH value is crucial as it helps us make the transition to determining the pH.

Relationship between pH and pOH

The pH and pOH scales are interrelated, providing a complete picture of a solution's acidity or basicity.
At 25°C, the sum of pH and pOH always equals 14.
This relationship can be expressed with the equation:

• \( \mathrm{pH} + \mathrm{pOH} = 14 \)

Thus, knowing either pH or pOH allows you to calculate the other.
In our solution, where the pOH was found to be 2.52, you can find the pH easily:

• \( \mathrm{pH} = 14 - 2.52 = 11.48 \)

This result tells us that the solution is basic.
Remember, a pH above 7 indicates a basic solution, whereas a pH below 7 indicates an acidic one.
This fundamental relationship helps us understand and predict the behavior of solutions in various chemical contexts.