At which of the following pH's will a buffer made of bypobromite, a weak base, and hypobromous acid (HOBr, K,- 2.3 x 10), its conjugate acid, work best?

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**Buffer Solutions and pH Optimization**

**Question:**

At which of the following pH's will a buffer made of hypobromite, a weak base, and hypobromous acid (HOBr, \( K_a = 2.3 \times 10^{-9} \)), its conjugate acid, work best?

**Explanation:**

As the question points out, the buffer system of interest consists of hypobromite (a weak base) and hypobromous acid (its conjugate acid). To determine the pH at which this buffer system works best, we need to consider the relationship between the acid dissociation constant (\( K_a \)) and the pH.

The optimal buffering capacity of a solution occurs when the concentrations of the weak acid and its conjugate base are equal. This happens around the pKa value of the weak acid.

To find the pKa:
\[ \text{pKa} = -\log(K_a) \]

Given:
\[ K_a = 2.3 \times 10^{-9} \]

Calculate pKa:
\[ \text{pKa} = -\log(2.3 \times 10^{-9}) \]

\[ \text{pKa} \approx 8.64 \]

Therefore, the buffer made of hypobromite and hypobromous acid will work best around a pH of 8.64. 

The graph or diagram accompanying this explanation would likely illustrate the buffering capacity versus pH, showing a peak around pH 8.64.
Transcribed Image Text:**Buffer Solutions and pH Optimization** **Question:** At which of the following pH's will a buffer made of hypobromite, a weak base, and hypobromous acid (HOBr, \( K_a = 2.3 \times 10^{-9} \)), its conjugate acid, work best? **Explanation:** As the question points out, the buffer system of interest consists of hypobromite (a weak base) and hypobromous acid (its conjugate acid). To determine the pH at which this buffer system works best, we need to consider the relationship between the acid dissociation constant (\( K_a \)) and the pH. The optimal buffering capacity of a solution occurs when the concentrations of the weak acid and its conjugate base are equal. This happens around the pKa value of the weak acid. To find the pKa: \[ \text{pKa} = -\log(K_a) \] Given: \[ K_a = 2.3 \times 10^{-9} \] Calculate pKa: \[ \text{pKa} = -\log(2.3 \times 10^{-9}) \] \[ \text{pKa} \approx 8.64 \] Therefore, the buffer made of hypobromite and hypobromous acid will work best around a pH of 8.64. The graph or diagram accompanying this explanation would likely illustrate the buffering capacity versus pH, showing a peak around pH 8.64.
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