e K₂ of a monoprotic weak acid is 0.00485. What is the percent ionization of a 0.101 M solution of this acid? percent ionization: %

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**Problem:**

The \( K_a \) of a monoprotic weak acid is 0.00485. What is the percent ionization of a 0.101 M solution of this acid?

**Solution:**

To find the percent ionization, use the formula:

\[
\text{Percent Ionization} = \left( \frac{[H^+]}{[HA]_0} \right) \times 100\%
\]

Where:
- \([H^+]\) is the concentration of hydrogen ions at equilibrium.
- \([HA]_0\) is the initial concentration of the acid.

Given:
- \( K_a = 0.00485 \)
- \([HA]_0 = 0.101 \, \text{M} \)

Assume \( x \) is the concentration of \( H^+ \) ionized from acid at equilibrium:

\[
K_a = \frac{x^2}{0.101 - x} \approx \frac{x^2}{0.101}
\]

Since \( K_a \) is small, assume \( x \ll 0.101 \):

\[
x^2 \approx K_a \times 0.101
\]

Solve for \( x \):

1. \( x^2 = 0.00485 \times 0.101 \)
2. \( x^2 = 0.000489485 \)
3. \( x = \sqrt{0.000489485} \)
4. \( x \approx 0.0221 \)

Calculate percent ionization:

\[
\text{Percent Ionization} = \left( \frac{0.0221}{0.101} \right) \times 100\% \approx 21.88\%
\]

The percent ionization of the acid in a 0.101 M solution is approximately 21.88%.
Transcribed Image Text:**Problem:** The \( K_a \) of a monoprotic weak acid is 0.00485. What is the percent ionization of a 0.101 M solution of this acid? **Solution:** To find the percent ionization, use the formula: \[ \text{Percent Ionization} = \left( \frac{[H^+]}{[HA]_0} \right) \times 100\% \] Where: - \([H^+]\) is the concentration of hydrogen ions at equilibrium. - \([HA]_0\) is the initial concentration of the acid. Given: - \( K_a = 0.00485 \) - \([HA]_0 = 0.101 \, \text{M} \) Assume \( x \) is the concentration of \( H^+ \) ionized from acid at equilibrium: \[ K_a = \frac{x^2}{0.101 - x} \approx \frac{x^2}{0.101} \] Since \( K_a \) is small, assume \( x \ll 0.101 \): \[ x^2 \approx K_a \times 0.101 \] Solve for \( x \): 1. \( x^2 = 0.00485 \times 0.101 \) 2. \( x^2 = 0.000489485 \) 3. \( x = \sqrt{0.000489485} \) 4. \( x \approx 0.0221 \) Calculate percent ionization: \[ \text{Percent Ionization} = \left( \frac{0.0221}{0.101} \right) \times 100\% \approx 21.88\% \] The percent ionization of the acid in a 0.101 M solution is approximately 21.88%.
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