The pH of a 0.064-M solution of hypobromous acid (HOBR but usually written HBrO) is 4.97. Calculate K K

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### Calculating the Acidity Constant (Ka) of Hypobromous Acid

#### Problem Statement:
The pH of a 0.064-M solution of hypobromous acid (HOBR but usually written HBrO) is 4.97. Calculate \( K_a \).

#### Solution:
Given data:
- The concentration of hypobromous acid (HBrO): 0.064 M
- The pH of the solution: 4.97

To find:
- The acidity constant \( K_a \)

First, we need to find the concentration of hydrogen ions \([H^+]\) using the pH value.
The pH is related to the hydrogen ion concentration by the formula:
\[ \text{pH} = -\log[H^+] \]

Rearranging the formula to find \([H^+]\):
\[ [H^+] = 10^{-\text{pH}} \]

Substituting the given pH value (4.97):
\[ [H^+] = 10^{-4.97} \]

Now calculate \([H^+]\):
\[ [H^+] \approx 1.07 \times 10^{-5} \, \text{M} \]

Next, we setup the expression for the dissociation of hypobromous acid:
\[ \text{HBrO} \leftrightharpoons \text{H}^+ + \text{BrO}^- \]

At equilibrium:
- The initial concentration of HBrO is 0.064 M.
- The change in concentration is \( x \) for both \([H^+]\) and \([\text{BrO}^-]\).

Thus,
\[ [H^+] = [\text{BrO}^-] = 1.07 \times 10^{-5} \]
\[ [\text{HBrO}] = 0.064 - 1.07 \times 10^{-5} \]

Since \( 1.07 \times 10^{-5} \) is very small compared to 0.064, we approximate:
\[ [\text{HBrO}] \approx 0.064 \, \text{M} \]

The expression for \( K_a \) of HBrO is:
\[ K_a = \frac{[H^+][\text{BrO
Transcribed Image Text:### Calculating the Acidity Constant (Ka) of Hypobromous Acid #### Problem Statement: The pH of a 0.064-M solution of hypobromous acid (HOBR but usually written HBrO) is 4.97. Calculate \( K_a \). #### Solution: Given data: - The concentration of hypobromous acid (HBrO): 0.064 M - The pH of the solution: 4.97 To find: - The acidity constant \( K_a \) First, we need to find the concentration of hydrogen ions \([H^+]\) using the pH value. The pH is related to the hydrogen ion concentration by the formula: \[ \text{pH} = -\log[H^+] \] Rearranging the formula to find \([H^+]\): \[ [H^+] = 10^{-\text{pH}} \] Substituting the given pH value (4.97): \[ [H^+] = 10^{-4.97} \] Now calculate \([H^+]\): \[ [H^+] \approx 1.07 \times 10^{-5} \, \text{M} \] Next, we setup the expression for the dissociation of hypobromous acid: \[ \text{HBrO} \leftrightharpoons \text{H}^+ + \text{BrO}^- \] At equilibrium: - The initial concentration of HBrO is 0.064 M. - The change in concentration is \( x \) for both \([H^+]\) and \([\text{BrO}^-]\). Thus, \[ [H^+] = [\text{BrO}^-] = 1.07 \times 10^{-5} \] \[ [\text{HBrO}] = 0.064 - 1.07 \times 10^{-5} \] Since \( 1.07 \times 10^{-5} \) is very small compared to 0.064, we approximate: \[ [\text{HBrO}] \approx 0.064 \, \text{M} \] The expression for \( K_a \) of HBrO is: \[ K_a = \frac{[H^+][\text{BrO
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