A 0.125 M weak acid (HA) solution has a pH of 2.25. Find the acid ionization constant, Ka-

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**Determining the Acid Ionization Constant (Ka) of a Weak Acid**

**Problem Statement:**

A 0.125 M weak acid (HA) solution has a pH of 2.25. Find the acid ionization constant, Ka.

**Solution:**

Given: 
- Concentration of the weak acid ([HA]) = 0.125 M
- pH of the solution = 2.25

**Step 1: Determine the concentration of H⁺ ions.**

pH is defined as the negative logarithm of the hydrogen ion concentration, so we can express this as:

\[ \text{pH} = -\log [\text{H}^+] \]

Given the pH is 2.25, we can find the hydrogen ion concentration by reversing the formula:

\[ [\text{H}^+] = 10^{-\text{pH}} \]
\[ [\text{H}^+] = 10^{-2.25} \]

Using a calculator:

\[ [\text{H}^+] \approx 5.62 \times 10^{-3} \, \text{M} \]

**Step 2: Set up the expression for the ionization of the weak acid.**

The ionization of a weak acid HA in water can be represented as:

\[ \text{HA} \leftrightarrow \text{H}^+ + \text{A}^- \]

At equilibrium, let \( x \) be the concentration of \([ \text{H}^+ ]\) and \([ \text{A}^- ]\), and the concentration of \([ \text{HA} ]\) will reduce by \( x \).

So, 
\[ [\text{H}^+] = x \approx 5.62 \times 10^{-3} \, \text{M} \]
\[ [\text{A}^-] = x \approx 5.62 \times 10^{-3} \, \text{M} \]
\[ [\text{HA}] = 0.125 - x \approx 0.125 - 5.62 \times 10^{-3} \approx 0.119 \, \text{M} \]

**Step 3: Write the expression for Ka and plug in the values.**

For a weak acid, the
Transcribed Image Text:**Determining the Acid Ionization Constant (Ka) of a Weak Acid** **Problem Statement:** A 0.125 M weak acid (HA) solution has a pH of 2.25. Find the acid ionization constant, Ka. **Solution:** Given: - Concentration of the weak acid ([HA]) = 0.125 M - pH of the solution = 2.25 **Step 1: Determine the concentration of H⁺ ions.** pH is defined as the negative logarithm of the hydrogen ion concentration, so we can express this as: \[ \text{pH} = -\log [\text{H}^+] \] Given the pH is 2.25, we can find the hydrogen ion concentration by reversing the formula: \[ [\text{H}^+] = 10^{-\text{pH}} \] \[ [\text{H}^+] = 10^{-2.25} \] Using a calculator: \[ [\text{H}^+] \approx 5.62 \times 10^{-3} \, \text{M} \] **Step 2: Set up the expression for the ionization of the weak acid.** The ionization of a weak acid HA in water can be represented as: \[ \text{HA} \leftrightarrow \text{H}^+ + \text{A}^- \] At equilibrium, let \( x \) be the concentration of \([ \text{H}^+ ]\) and \([ \text{A}^- ]\), and the concentration of \([ \text{HA} ]\) will reduce by \( x \). So, \[ [\text{H}^+] = x \approx 5.62 \times 10^{-3} \, \text{M} \] \[ [\text{A}^-] = x \approx 5.62 \times 10^{-3} \, \text{M} \] \[ [\text{HA}] = 0.125 - x \approx 0.125 - 5.62 \times 10^{-3} \approx 0.119 \, \text{M} \] **Step 3: Write the expression for Ka and plug in the values.** For a weak acid, the
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