Problem 15 - Chemistry and Chemical Reactivity

Question

The \(\mathrm{pH}\) of a solution of \(\mathrm{Ba}(\mathrm{OH})_{2}\) is 10.66 at \(25^{\circ} \mathrm{C} .\) What is the hydroxide ion concentration in the solution? If the solution volume is \(125 \mathrm{mL}\) what mass of \(\mathrm{Ba}(\mathrm{OH})_{2}\) must have been dissolved?

Step-by-Step Solution

Answer

The hydroxide ion concentration is \(4.57 \times 10^{-4} \text{ M}\) and the mass of \(\text{Ba(OH)}_2\) is approximately 4.89 mg.

Step 1: Calculate \\( ext{pOH} \\\) from \\( ext{pH} \\\)

We know that \[ ext{pH} + ext{pOH} = 14 \]Given that the \( \text{pH} \) is 10.66, we can find \( \text{pOH} \) as follows:\[ \text{pOH} = 14 - 10.66 = 3.34 \].

Step 2: Determine Hydroxide Ion Concentration

The concentration of hydroxide ions \([\text{OH}^-]\) can be found using \[\text{pOH} = -\log[\text{OH}^-].\]From the previous step, \( \text{pOH} = 3.34 \), so\[[\text{OH}^-] = 10^{-3.34}.\]Calculating this, we find\[[\text{OH}^-] \approx 4.57 \times 10^{-4} \text{ M}.\]

Step 3: Calculate Moles of \\( ext{Ba(OH)}_2 \\\)

Since each molecule of \( \text{Ba(OH)}_2 \) produces two hydroxide ions, the molarity of \( \text{Ba(OH)}_2 \) is half the concentration of \([\text{OH}^-]\):\[ [\text{Ba(OH)}_2] = \frac{4.57 \times 10^{-4}}{2} = 2.285 \times 10^{-4} \text{ M}.\]Thus, the moles of \( \text{Ba(OH)}_2 \) in 125 mL (0.125 L) of solution is:\[ \text{moles} = 2.285 \times 10^{-4} \times 0.125 = 2.85625 \times 10^{-5} \text{ moles}.\]

Step 4: Calculate Mass of \\( ext{Ba(OH)}_2 \\\)

The molar mass of \( \text{Ba(OH)}_2 \) is approximately 171.34 g/mol. Using the moles calculated in the previous step, we find the mass:\[\text{mass} = 2.85625 \times 10^{-5} \times 171.34 = 4.89 \times 10^{-3} \text{ grams}.\]

Key Concepts

Hydroxide Ion Concentration

Determining the hydroxide ion concentration in a solution is key to understanding its basic properties. Starting from the known pH of a solution, we can find the pOH using the formula:

• \( \text{pH} + \text{pOH} = 14 \)

In this exercise, given that the pH is 10.66, we calculate the pOH as 3.34. The pOH is then used to find the hydroxide ion concentration:

• \([\text{OH}^-] = 10^{-\text{pOH}} = 10^{-3.34} \)

After solving, the hydroxide ion concentration is approximately \( 4.57 \times 10^{-4} \text{ M} \). Understanding this allows us to grasp how much hydroxide is present, defining the solution's strength as a base, and setting a foundation for further calculations.

Ba(OH)_2

Barium hydroxide, known as \( \text{Ba(OH)}_2 \), is an important chemical compound commonly used in titrations due to its strong base characteristics. When dissolved in water, each molecule dissociates completely to yield two hydroxide ions:

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

This means the concentration of \( \text{Ba(OH)}_2 \) is only half that of the hydroxide ions in solution, as each barium hydroxide contributes two \( \text{OH}^- \) ions. In our example, knowing the hydroxide ion concentration of \( 4.57 \times 10^{-4} \text{ M} \), the molarity of \( \text{Ba(OH)}_2 \) becomes \( 2.285 \times 10^{-4} \text{ M} \). This basic understanding helps you visualize the proportion of dissolved substances in a solution actively contributing to its basic properties.

pOH

The term pOH is the base-negative logarithmic scale of the hydroxide ion concentration in a solution. It complements the pH scale, which measures the concentration of hydrogen ions. Together, they offer a complete picture of acidic and basic balance in a solution:

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

This formula shows that as hydroxide ion concentration increases, pOH decreases, representing a stronger base. In our exercise, with a pH of 10.66, the calculated pOH is 3.34. This low pOH indicates a relatively strong basic solution. Understanding pOH is essential for anyone studying chemistry as it is vital for characterizing and predicting the behavior of solutions under different conditions.

Molar Mass Calculation

Calculating the molar mass of a compound allows you to convert between mass and moles. It's crucial for determining the exact amount of a substance in chemical reactions. The molar mass of any compound is the sum of the individual atomic masses of its constituent elements:

• Atomic mass of Ba = 137.33 g/mol
• Atomic mass of O = 16.00 g/mol
• Atomic mass of H = 1.01 g/mol

For \( \text{Ba(OH)}_2 \), the calculation is:

• \( 137.33 + (2 \times 16.00) + (2 \times 1.01) = 171.34 \text{ g/mol} \)

In this exercise, knowing the molarity and molar mass allows us to find that the mass of \( \text{Ba(OH)}_2 \) present in 125 mL of solution is approximately 0.00489 grams. This skill is vital for accurately preparing solutions to meet specified conditions in labs and industry.