A. 0.1 solution of acetic acid (CH3COOH) has pH of 2.87. find: the acid dissociation constant (Ka) for acetic acid

To find the acid dissociation constant (\(K_a\)) for acetic acid, we can use the following relationship between pH and \(K_a\):

### Step 1: Write the dissociation equation for acetic acid:
\[
\text{CH}_3\text{COOH} \rightleftharpoons \text{CH}_3\text{COO}^- + \text{H}^+
\]

### Step 2: Calculate the concentration of \( \text{H}^+ \) from the pH:
\[
\text{pH} = -\log[\text{H}^+]
\]
Given pH = 2.87, we can calculate the hydrogen ion concentration \([ \text{H}^+ ]\):
\[
[\text{H}^+] = 10^{-\text{pH}} = 10^{-2.87}
\]
Let's calculate that.

\[
[\text{H}^+] \approx 1.349 \times 10^{-3} \, \text{M}
\]

### Step 3: Set up the expression for the acid dissociation constant \(K_a\):
The dissociation constant expression for acetic acid is:
\[
K_a = \frac{[\text{H}^+][\text{CH}_3\text{COO}^-]}{[\text{CH}_3\text{COOH}]}
\]

Assume the degree of dissociation of acetic acid is small, so the initial concentration of \( \text{CH}_3\text{COOH} \) (0.1 M) remains approximately constant, except for the small amount that dissociates.

Since \( [\text{H}^+] = [\text{CH}_3\text{COO}^-] \) (for each molecule of acetic acid that dissociates, it produces one \( \text{H}^+ \) and one acetate ion), we can rewrite \( K_a \) as:
\[
K_a = \frac{[\text{H}^+]^2}{[\text{CH}_3\text{COOH}]}
\]

Substitute the values:
\[
K_a = \frac{(1.349 \times 10^{-3})^2}{0.1}
\]

Now, let's calculate \(K_a\).

\[
K_a \approx 1.82 \times 10^{-5}
\]

Thus, the acid dissociation constant for acetic acid is approximately \(1.82 \times 10^{-5}\).

---

Would you like more details or have any questions about this solution?

Here are 5 related questions to expand on this:

1. How does temperature affect the value of \(K_a\)?
2. What is the relationship between \(K_a\) and the strength of an acid?
3. Can \(K_a\) be used to find the pH of a weak acid at any concentration?
4. How does adding a salt (like sodium acetate) affect the pH of an acetic acid solution?
5. What is the difference between \(K_a\) and \(pK_a\)?

**Tip:** The smaller the \(K_a\) value, the weaker the acid, as it dissociates less in solution.

A 0.1 M solution of acetic acid (CH3COOH) has a pH of 2.87. Find the acid dissociation constant (Ka) for acetic acid.

Learn how to calculate the acid dissociation constant (Ka) for a 0.1 M solution of acetic acid with a pH of 2.87. This detailed solution involves pH calculation, the equilibrium constant expression, and key concepts in acid-base equilibria. Suitable for students in Grades 10-12.

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