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The question in your image asks for the percentage of the acid that is dissociated in an aqueous solution, given the acid's \( \text{p}K_a = 6.54 \) and the solution's pH of 3.84.

To solve this, we can use the Henderson-Hasselbalch equation:

\[
\text{pH} = \text{p}K_a + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right)
\]

Where:
- \( [\text{A}^-] \) is the concentration of the dissociated form (the conjugate base),
- \( [\text{HA}] \) is the concentration of the undissociated form (the acid).

We want to find the fraction of the acid dissociated, which is the ratio:

\[
\frac{[\text{A}^-]}{[\text{HA}] + [\text{A}^-]}
\]

### Steps:

1. Rearrange the Henderson-Hasselbalch equation to solve for \( \frac{[\text{A}^-]}{[\text{HA}]} \):
   \[
   \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) = \text{pH} - \text{p}K_a
   \]
   Substituting the given values:
   \[
   \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) = 3.84 - 6.54 = -2.70
   \]

2. Solve for the ratio \( \frac{[\text{A}^-]}{[\text{HA}]} \):
   \[
   \frac{[\text{A}^-]}{[\text{HA}]} = 10^{-2.70} \approx 0.002
   \]

3. The dissociation fraction is given by:
   \[
   \text{Fraction of dissociation} = \frac{[\text{A}^-]}{[\text{HA}] + [\text{A}^-]} = \frac{0.002}{1 + 0.002} \approx 0.002
   \]

4. Convert this fraction into a percentage:
   \[
   \text{Percent dissociation} \approx 0.002 \times 100 = 0.2\%
   \]

Thus, the percent of the acid dissociated is approximately **0.20%** to two significant digits.

Would you like more details on any step? Here are five questions that might interest you:
1. How is the Henderson-Hasselbalch equation derived?
2. Why is pH important in determining dissociation?
3. What does \( \text{p}K_a \) represent in acid-base chemistry?
4. Can this formula be applied to strong acids?
5. How does the percent dissociation change with pH?

**Tip:** In weak acid calculations, when the pH is much lower than the \( \text{p}K_a \), only a small fraction of the acid dissociates.

In an aqueous solution of a certain acid with pKa = 6.54, the pH is 3.84. Calculate the percent of the acid that is dissociated in this solution. Round your answer to 2 significant digits.

Learn how to calculate the percent dissociation of a weak acid given its pKa and the solution's pH using the Henderson-Hasselbalch equation. Step-by-step calculation for chemistry students at the college or advanced high school level.

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