Calculate the Ka of a 0.35M weak acid HA if the pH of the solution is 2.97. Ka *** assume the temperature is 25°C.

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### Calculating the Acid Dissociation Constant (Ka) of a Weak Acid

**Problem Statement:**
Calculate the Ka of a 0.35 M weak acid HA if the pH of the solution is 2.97.

*Assume the temperature is 25°C.*

**Solution:**
To find the acid dissociation constant (Ka), we need to use the information provided:

- The concentration of the weak acid (HA) = 0.35 M
- The pH of the solution = 2.97

**Step-by-Step Calculation:**

1. **Find the concentration of H⁺ ions:**
   The pH of a solution is defined by the equation:
   \[
   \text{pH} = -\log [\text{H}^+]
   \]

   Rearranging this equation to solve for \([\text{H}^+]\):
   \[
   [\text{H}^+] = 10^{-\text{pH}}
   \]

   Substituting the given pH value:
   \[
   [\text{H}^+] = 10^{-2.97} \approx 1.07 \times 10^{-3} \text{ M}
   \]

2. **Set up the expression for the acid dissociation constant (Ka):**
   The dissociation of a weak acid (HA) in water is represented as:
   \[
   \text{HA} \rightleftharpoons \text{H}^+ + \text{A}^-
   \]

   The expression for \(K_a\) is:
   \[
   K_a = \frac{[\text{H}^+][\text{A}^-]}{[\text{HA}]}
   \]

3. **Determine the equilibrium concentrations:**
   - At equilibrium, the concentration of \([\text{H}^+]\) = \([\text{A}^-]\) = \(1.07 \times 10^{-3}\) M (since one mole of \(\text{HA}\) dissociates to give one mole of \(\text{H}^+\) and one mole of \(\text{A}^-)\).
   - The initial concentration of \(\text{HA}\) was 0.35 M, and a small amount, \(1.07 \times
Transcribed Image Text:### Calculating the Acid Dissociation Constant (Ka) of a Weak Acid **Problem Statement:** Calculate the Ka of a 0.35 M weak acid HA if the pH of the solution is 2.97. *Assume the temperature is 25°C.* **Solution:** To find the acid dissociation constant (Ka), we need to use the information provided: - The concentration of the weak acid (HA) = 0.35 M - The pH of the solution = 2.97 **Step-by-Step Calculation:** 1. **Find the concentration of H⁺ ions:** The pH of a solution is defined by the equation: \[ \text{pH} = -\log [\text{H}^+] \] Rearranging this equation to solve for \([\text{H}^+]\): \[ [\text{H}^+] = 10^{-\text{pH}} \] Substituting the given pH value: \[ [\text{H}^+] = 10^{-2.97} \approx 1.07 \times 10^{-3} \text{ M} \] 2. **Set up the expression for the acid dissociation constant (Ka):** The dissociation of a weak acid (HA) in water is represented as: \[ \text{HA} \rightleftharpoons \text{H}^+ + \text{A}^- \] The expression for \(K_a\) is: \[ K_a = \frac{[\text{H}^+][\text{A}^-]}{[\text{HA}]} \] 3. **Determine the equilibrium concentrations:** - At equilibrium, the concentration of \([\text{H}^+]\) = \([\text{A}^-]\) = \(1.07 \times 10^{-3}\) M (since one mole of \(\text{HA}\) dissociates to give one mole of \(\text{H}^+\) and one mole of \(\text{A}^-)\). - The initial concentration of \(\text{HA}\) was 0.35 M, and a small amount, \(1.07 \times
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