Calculate the equilibrium concentration for H30* for part a from question 1 based on the fact that K, is 2.5 x 10° and that the initial concentration of HBrO is 0.15 M.

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Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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**Problem Statement:**

Calculate the equilibrium concentration for \( \text{H}_3\text{O}^+ \) for part a from question 1 based on the fact that \( K_a \) is \( 2.5 \times 10^{-9} \) and that the initial concentration of HBrO is 0.15 M.

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**Solution Explanation:**

1. **Understand the Given Data:**
   - \( K_a \) (acid dissociation constant) = \( 2.5 \times 10^{-9} \)
   - Initial concentration of HBrO (weak acid) = 0.15 M

2. **Set Up the Equilibrium Expression:**
   The dissociation of HBrO in water can be represented as:
   \[ \text{HBrO} + \text{H}_2\text{O} \rightleftharpoons \text{H}_3\text{O}^+ + \text{BrO}^- \]

3. **Use the \( K_a \) Expression:**
   The expression for the acid dissociation constant (\( K_a \)) is:
   \[ K_a = \frac{[\text{H}_3\text{O}^+][\text{BrO}^-]}{[\text{HBrO}]} \]

4. **Assume Initial Concentrations and Changes:**
   Let \( x \) be the concentration of \( \text{H}_3\text{O}^+ \) at equilibrium. Therefore:
   - Initial concentration of \( \text{HBrO} \) = 0.15 M
   - Change in \( \text{H}_3\text{O}^+ \) and \( \text{BrO}^- \) = \( +x \)
   - Change in \( \text{HBrO} \) = \( -x \)
   
   At equilibrium:
   \[ [\text{H}_3\text{O}^+] = x \]
   \[ [\text{BrO}^-] = x \]
   \[ [\text{HBrO}] = 0.15 - x \]

5. **Apply the Initial Assumptions to the \( K_a \) Expression:**
   \[ K_a = \frac{x \cdot
Transcribed Image Text:**Problem Statement:** Calculate the equilibrium concentration for \( \text{H}_3\text{O}^+ \) for part a from question 1 based on the fact that \( K_a \) is \( 2.5 \times 10^{-9} \) and that the initial concentration of HBrO is 0.15 M. --- **Solution Explanation:** 1. **Understand the Given Data:** - \( K_a \) (acid dissociation constant) = \( 2.5 \times 10^{-9} \) - Initial concentration of HBrO (weak acid) = 0.15 M 2. **Set Up the Equilibrium Expression:** The dissociation of HBrO in water can be represented as: \[ \text{HBrO} + \text{H}_2\text{O} \rightleftharpoons \text{H}_3\text{O}^+ + \text{BrO}^- \] 3. **Use the \( K_a \) Expression:** The expression for the acid dissociation constant (\( K_a \)) is: \[ K_a = \frac{[\text{H}_3\text{O}^+][\text{BrO}^-]}{[\text{HBrO}]} \] 4. **Assume Initial Concentrations and Changes:** Let \( x \) be the concentration of \( \text{H}_3\text{O}^+ \) at equilibrium. Therefore: - Initial concentration of \( \text{HBrO} \) = 0.15 M - Change in \( \text{H}_3\text{O}^+ \) and \( \text{BrO}^- \) = \( +x \) - Change in \( \text{HBrO} \) = \( -x \) At equilibrium: \[ [\text{H}_3\text{O}^+] = x \] \[ [\text{BrO}^-] = x \] \[ [\text{HBrO}] = 0.15 - x \] 5. **Apply the Initial Assumptions to the \( K_a \) Expression:** \[ K_a = \frac{x \cdot
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