Determine the pH of a 0.461 M C3H5CO,H M solution if the K, of C6H5CO2H is 6.5 x 105. 4.52 11.74 9.48 2.26 5.48

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**Question:**

Determine the pH of a 0.461 M C₆H₅CO₂H solution if the Kₐ of C₆H₅CO₂H is 6.5 × 10⁻⁵.

**Options:**

- ○ 4.52
- ○ 11.74
- ○ 9.48
- ○ 2.26
- ○ 5.48

*Explanation:*

To solve for the pH of the solution, use the formula for calculating pH from the equilibrium constant (Kₐ) and the concentration of the acid (C₆H₅CO₂H).

1. Write the ionization equilibrium expression for the acid:
   \[
   \text{C₆H₅CO₂H} \rightleftharpoons \text{C₆H₅CO₂⁻} + \text{H⁺}
   \]

2. Set up the expression for the acid dissociation constant (\(Kₐ\)):
   \[
   Kₐ = \frac{[\text{C₆H₅CO₂⁻}][\text{H⁺}]}{[\text{C₆H₅CO₂H}]}
   \]

3. Assume \(x\) is the amount dissociated at equilibrium, then:
   \[
   Kₐ = \frac{x \cdot x}{0.461 - x} \approx \frac{x^2}{0.461}
   \]

4. Solve for \(x\) using the given \(Kₐ\):
   \[
   x^2 = 6.5 \times 10^{-5} \cdot 0.461
   \]
   \[
   x = \sqrt{(6.5 \times 10^{-5}) \cdot 0.461}
   \]

5. Calculate the pH:
   \[
   \text{pH} = -\log[\text{H⁺}] = -\log(x)
   \]
Transcribed Image Text:**Question:** Determine the pH of a 0.461 M C₆H₅CO₂H solution if the Kₐ of C₆H₅CO₂H is 6.5 × 10⁻⁵. **Options:** - ○ 4.52 - ○ 11.74 - ○ 9.48 - ○ 2.26 - ○ 5.48 *Explanation:* To solve for the pH of the solution, use the formula for calculating pH from the equilibrium constant (Kₐ) and the concentration of the acid (C₆H₅CO₂H). 1. Write the ionization equilibrium expression for the acid: \[ \text{C₆H₅CO₂H} \rightleftharpoons \text{C₆H₅CO₂⁻} + \text{H⁺} \] 2. Set up the expression for the acid dissociation constant (\(Kₐ\)): \[ Kₐ = \frac{[\text{C₆H₅CO₂⁻}][\text{H⁺}]}{[\text{C₆H₅CO₂H}]} \] 3. Assume \(x\) is the amount dissociated at equilibrium, then: \[ Kₐ = \frac{x \cdot x}{0.461 - x} \approx \frac{x^2}{0.461} \] 4. Solve for \(x\) using the given \(Kₐ\): \[ x^2 = 6.5 \times 10^{-5} \cdot 0.461 \] \[ x = \sqrt{(6.5 \times 10^{-5}) \cdot 0.461} \] 5. Calculate the pH: \[ \text{pH} = -\log[\text{H⁺}] = -\log(x) \]
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