The K, of propanoic acid (C,H,COOH) is 1.34 × 10-³. Calculate the pH of the solution and the concentrations of C,H,COOH and C,H,COO¯ in a 0.467 M propanoic acid solution at equilibrium. pH = [C,H,COOH] M (C,H,CO0"] = M
The K, of propanoic acid (C,H,COOH) is 1.34 × 10-³. Calculate the pH of the solution and the concentrations of C,H,COOH and C,H,COO¯ in a 0.467 M propanoic acid solution at equilibrium. pH = [C,H,COOH] M (C,H,CO0"] = M
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Question
![### Calculating the pH and Equilibrium Concentrations of Propanoic Acid Solution
**Problem Statement:**
The \( K_a \) of propanoic acid (\( C_2H_5COOH \)) is \( 1.34 \times 10^{-5} \). Calculate the pH of the solution and the concentrations of \( C_2H_5COOH \) and \( C_2H_5COO^- \) in a 0.467 M propanoic acid solution at equilibrium.
**Solution:**
**1. Calculate the pH of the Solution:**
\[ \text{pH} = \large{\boxed{\hspace{400px}}} \]
**2. Calculate the Concentration of \( C_2H_5COOH \):**
\[ [C_2H_5COOH] = \large{\boxed{\hspace{300px}}} \text{ M} \]
**3. Calculate the Concentration of \( C_2H_5COO^- \):**
\[ [C_2H_5COO^-] = \large{\boxed{\hspace{300px}}} \text{ M} \]
### Explanation of Required Calculations:
1. **Determining the pH:**
- Using the \( K_a \) value and the initial concentration of propanoic acid, set up the equilibrium expression.
- Solve for the hydrogen ion concentration \([H^+]\) and subsequently calculate the pH using the formula:
\[ \text{pH} = -\log[H^+] \]
2. **Concentration Calculations:**
- Use the changes in concentrations (dependent on the degree of dissociation) to find the equilibrium concentrations of \( C_2H_5COOH \) and \( C_2H_5COO^- \).
**Note:**
- These calculations involve setting up an ICE (Initial, Change, Equilibrium) table to track the concentration changes and applying the quadratic formula if necessary to find the precise values.
This method allows for understanding how weak acids dissociate in solution and the relationship between \( K_a \), pH, and equilibrium concentrations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbd6e2cac-a13e-4af0-8d42-5fb7a66b94d3%2F89d36c9d-2864-438c-9d36-9c8b271bc39e%2Fiia9jyd_processed.png&w=3840&q=75)
Transcribed Image Text:### Calculating the pH and Equilibrium Concentrations of Propanoic Acid Solution
**Problem Statement:**
The \( K_a \) of propanoic acid (\( C_2H_5COOH \)) is \( 1.34 \times 10^{-5} \). Calculate the pH of the solution and the concentrations of \( C_2H_5COOH \) and \( C_2H_5COO^- \) in a 0.467 M propanoic acid solution at equilibrium.
**Solution:**
**1. Calculate the pH of the Solution:**
\[ \text{pH} = \large{\boxed{\hspace{400px}}} \]
**2. Calculate the Concentration of \( C_2H_5COOH \):**
\[ [C_2H_5COOH] = \large{\boxed{\hspace{300px}}} \text{ M} \]
**3. Calculate the Concentration of \( C_2H_5COO^- \):**
\[ [C_2H_5COO^-] = \large{\boxed{\hspace{300px}}} \text{ M} \]
### Explanation of Required Calculations:
1. **Determining the pH:**
- Using the \( K_a \) value and the initial concentration of propanoic acid, set up the equilibrium expression.
- Solve for the hydrogen ion concentration \([H^+]\) and subsequently calculate the pH using the formula:
\[ \text{pH} = -\log[H^+] \]
2. **Concentration Calculations:**
- Use the changes in concentrations (dependent on the degree of dissociation) to find the equilibrium concentrations of \( C_2H_5COOH \) and \( C_2H_5COO^- \).
**Note:**
- These calculations involve setting up an ICE (Initial, Change, Equilibrium) table to track the concentration changes and applying the quadratic formula if necessary to find the precise values.
This method allows for understanding how weak acids dissociate in solution and the relationship between \( K_a \), pH, and equilibrium concentrations.
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