The Ka of hypochlorous acid (HC1O) is 3.0 × 10-8 at 25 °C. What is the percent ionization of hypochlorous acid in a 0.015M aqueous solution of HC1O at 25 °C?
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![### Problem Statement
The \( K_a \) of hypochlorous acid (HClO) is \( 3.0 \times 10^{-8} \) at 25 °C. What is the percent ionization of hypochlorous acid in a 0.015 M aqueous solution of HClO at 25 °C?
### Explanation
This problem involves calculating the percent ionization of hypochlorous acid in a given solution. Percent ionization is a measure of the degree to which a weak acid ionizes in a solution.
### Relevant Formula
To solve this problem, we use the following steps:
1. **Expression for the Equilibrium Constant (\(K_a\))**:
$$ K_a = \frac{[H^+][ClO^-]}{[HClO]} $$
2. **Assumption for Weak Acid Ionization**:
Since \( HClO \) is a weak acid, we assume that \( x \) amount of \( HClO \) ionizes.
$$ [H^+] = [ClO^-] = x $$
$$ [HClO] = 0.015 - x \approx 0.015 \text{ M} \quad (\text{since } x \text{ is very small}) $$
3. **Substitute into the \( K_a \) Expression**:
$$ K_a = \frac{x^2}{0.015} $$
4. **Solve for \( x \)**:
$$ x = \sqrt{K_a \times 0.015} $$
$$ x = \sqrt{(3.0 \times 10^{-8}) \times 0.015} $$
$$ x \approx \sqrt{4.5 \times 10^{-10}} $$
$$ x \approx 6.7 \times 10^{-5} \text{ M} $$
5. **Calculate Percent Ionization**:
Percent Ionization = \( \frac{[\text{Ionized HClO}]}{[\text{Initial HClO}]} \times 100\% \)
$$ \text{Percent Ionization} = \frac{6.7 \times 10^{-5}}{0.015} \times 100\% $$
$$ \text{Percent Ionization} \approx 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa9e8573f-552b-4431-b931-fec80f931989%2F34b36340-7ff6-4d9b-8734-c746e5fb49fd%2F9wv2hz8_processed.png&w=3840&q=75)
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