Problem 13 - Chemistry and Chemical Reactivity

Question

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

Step-by-Step Solution

Answer

The pH of a 0.0015 M solution of \(\mathrm{Ba(OH)}_{2}\) is approximately 11.48.

Step 1: Understanding the Dissociation

Barium hydroxide, \(\mathrm{Ba(OH)}_2\), is a strong base that completely dissociates in water. The dissociation can be represented by the equation: \[\mathrm{Ba(OH)}_2 \rightarrow \mathrm{Ba}^{2+} + 2\mathrm{OH}^-\] Each molecule of \(\mathrm{Ba(OH)}_2\) provides two hydroxide ions, \(\mathrm{OH}^-\).

Step 2: Calculating Hydroxide Ion Concentration

Since each formula unit of \(\mathrm{Ba(OH)}_2\) gives two \(\mathrm{OH}^-\) ions upon dissociation, the concentration of \(\mathrm{OH}^-\) ions is two times the concentration of \(\mathrm{Ba(OH)}_2\). So, \([\mathrm{OH}^-] = 2 \times 0.0015 \ M = 0.0030 \ M\).

Step 3: Finding the pOH from OH- Concentration

pOH is calculated using the formula: \(\text{pOH} = -\log_{10} [\mathrm{OH}^-]\). Substitute the \(\mathrm{OH}^-\) concentration into the formula: \(\text{pOH} = -\log_{10} (0.0030) \approx 2.52\).

Step 4: Calculating the pH from the pOH

The relationship between pH and pOH is given by the equation: \(\text{pH} + \text{pOH} = 14\). Using \(\text{pOH} = 2.52\), we find \(\text{pH} = 14 - 2.52 = 11.48\).

Key Concepts

Strong Bases

Strong bases are substances that completely dissociate into their ions in water. This means they release all their available hydroxide ions into the solution, making the base as strong as it can be.
This complete dissociation is a key characteristic that distinguishes strong bases from weak bases, which only partially dissociate.

• Examples of strong bases include sodium hydroxide (\( ext{NaOH}\)), potassium hydroxide (\( ext{KOH}\)), and as in our exercise, barium hydroxide (\( ext{Ba(OH)}_2\)).
• When dissolved in water, these compounds separate into their respective metal ions and hydroxide ions (\( ext{OH}^-\)).
• In the context of pH calculation, understanding that a substance is a strong base tells us it will fully release hydroxide ions, which is vital for calculations.

Hydroxide Ion Concentration

Knowing the hydroxide ion concentration is essential when calculating the pH in solutions containing bases. For strong bases like \( ext{Ba(OH)}_2\), dissociating them gives the exact amount of hydroxide ions in the solution.
Given that one molecule of barium hydroxide produces two hydroxide ions, the hydroxide ion concentration is always twice its molarity.

• For a \(0.0015 ext{ M}\) solution of \( ext{Ba(OH)}_2\), the hydroxide ion concentration becomes \(0.0030 ext{ M}\).
• Accurate hydroxide ion concentration is crucial for finding the \( ext{pOH}\) and, subsequently, the \( ext{pH}\) of the solution.
• Understanding that each strong base dissociates differently aids in precisely determining the \([ ext{OH}^-]\), depending on how many hydroxide ions each formula unit releases.

pOH and pH Relationship

The relationship between \( ext{pH}\) and \( ext{pOH}\) helps in determining the complete acidity or basicity of a solution. This relationship is given by the equation \( ext{pH} + ext{pOH} = 14\), which is rooted in the ion product of water at 25°C.
Understanding this connection can solve for one when the other is known, an indispensable skill in chemistry.

• The \( ext{pOH}\) is computed by taking the negative logarithm of the hydroxide ion concentration.
• In our example, after finding \( ext{pOH} ext{ (approximately) 2.52}\), we quickly derive \( ext{pH} ext{ as 11.48}\), emphasizing the basic nature of the solution.
• This method directly links the \( ext{OH}^-\) presence in the solution to its pH, underlining the effect of basicity from a strong base.

Dissociation of Barium Hydroxide

Barium hydroxide is a strong base often used in these calculations. Upon dissolution in water, it undergoes complete dissociation. This means that every unit of \( ext{Ba(OH)}_2\) breaks into one \( ext{Ba}^{2+}\) ion and two \( ext{OH}^-\) ions.
This concept is fundamental for calculating hydroxide ion concentration in the solution.

• The dissociation process of barium hydroxide ensures that the hydroxide ion concentration is directly proportional to its molarity.
• It’s crucial to remember the \(2:1\) ratio of \( ext{OH}^-\) ions to \( ext{Ba(OH)}_2\) molecules, emphasizing why \( ext{Ba(OH)}_2\) is used often in examples of strong base calculations.
• Recognizing the \( ext{OH}^-\) contribution is key to accurately using the dissociation data in further calculations, such as determining pH.