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The problem asks for the percentage of benzoic acid that is dissociated in a 4.5 M solution.

To solve this, you'll need the dissociation constant \( K_a \) for benzoic acid, which is typically around \( 6.3 \times 10^{-5} \). With the molarity and \( K_a \), you can use the following steps:

1. **Set up the ICE table for the dissociation of benzoic acid \( C_6H_5COOH \):**

\[
\text{C}_6\text{H}_5\text{COOH} \rightleftharpoons \text{H}^+ + \text{C}_6\text{H}_5\text{COO}^-
\]

Let the initial concentration of \( C_6H_5COOH \) be 4.5 M.

2. **Write the expression for \( K_a \):**

\[
K_a = \frac{[\text{H}^+][\text{C}_6\text{H}_5\text{COO}^-]}{[\text{C}_6\text{H}_5\text{COOH}]}
\]

3. **Assume that \( x \) is the concentration of dissociated \( \text{H}^+ \) and \( \text{C}_6\text{H}_5\text{COO}^- \), and the change in benzoic acid concentration is \( -x \):**

\[
K_a = \frac{x^2}{4.5 - x}
\]

Since \( x \) is typically small compared to the initial concentration (because \( K_a \) is small), we can approximate:

\[
K_a \approx \frac{x^2}{4.5}
\]

4. **Solve for \( x \):**

\[
x^2 = K_a \times 4.5
\]
\[
x = \sqrt{K_a \times 4.5} = \sqrt{(6.3 \times 10^{-5}) \times 4.5} = \sqrt{2.835 \times 10^{-4}} \approx 0.0168
\]

This value \( x \) is the concentration of \( \text{H}^+ \) ions, which is also the amount of benzoic acid that dissociates.

5. **Calculate the percent dissociation:**

\[
\text{Percent dissociation} = \frac{x}{4.5} \times 100 = \frac{0.0168}{4.5} \times 100 \approx 0.373\%
\]

Thus, the percentage of benzoic acid dissociated is approximately **0.37%**.

Let me know if you'd like further details on this process!

### Relative questions:
1. What is the general significance of \( K_a \) values in weak acids?
2. How can the approximation \( 4.5 - x \approx 4.5 \) be justified mathematically?
3. What other acids have dissociation constants similar to benzoic acid?
4. Why is it important to round the final answer to two significant digits?
5. How would increasing the initial concentration affect the percent dissociation?

### Tip: 
When dealing with weak acid dissociation, always check if the \( x \)-approximation is valid by comparing \( x \) to the initial concentration!

A student prepares a 4.5 M aqueous solution of benzoic acid (C6H5COOH). Calculate the fraction of benzoic acid that is in the dissociated form in this solution. Express your answer as a percentage. Round your answer to 2 significant digits.

Learn how to calculate the percent dissociation of benzoic acid in a 4.5 M aqueous solution using its Ka value. This step-by-step guide walks through weak acid equilibrium and approximations.

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