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Calculate the pH of a buffer solution containing 0.10 mol dm ethanoic acid and 0.20 mol dm 3 sodium ethanoate.

To calculate the pH of a buffer solution containing ethanoic acid (acetic acid) and sodium ethanoate, we can use the **Henderson-Hasselbalch equation**:

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

Where:
- \(\text{p}K_a\) is the negative logarithm of the acid dissociation constant \(K_a\),
- \([\text{A}^-]\) is the concentration of the conjugate base (sodium ethanoate, \(\text{CH}_3\text{COO}^-\)),
- \([\text{HA}]\) is the concentration of the weak acid (ethanoic acid, \(\text{CH}_3\text{COOH}\)).

### Step 1: Identify the values
- The concentration of sodium ethanoate (\(\text{CH}_3\text{COONa}\)) = 0.20 mol/dm³
- The concentration of ethanoic acid (\(\text{CH}_3\text{COOH}\)) = 0.10 mol/dm³
- The \(K_a\) value of ethanoic acid is approximately \(1.8 \times 10^{-5}\), so:

\[
\text{p}K_a = -\log(1.8 \times 10^{-5}) \approx 4.74
\]

### Step 2: Apply the Henderson-Hasselbalch equation
Now, substitute the known values into the equation:

\[
\text{pH} = 4.74 + \log \left( \frac{0.20}{0.10} \right)
\]

\[
\text{pH} = 4.74 + \log(2)
\]

\[
\log(2) \approx 0.30
\]

So,

\[
\text{pH} = 4.74 + 0.30 = 5.04
\]

### Final Answer:
The pH of the buffer solution is approximately **5.04**.

Would you like more details or have any questions? 

Here are five related questions for further exploration:
1. How would the pH change if the concentration of sodium ethanoate was halved?
2. What is the role of the conjugate base in a buffer solution?
3. How is the \(K_a\) value of an acid experimentally determined?
4. What is the difference between a strong acid and a weak acid in terms of dissociation?
5. How do buffer solutions resist changes in pH when small amounts of acid or base are added?

**Tip:** Buffers are most effective when the pH is close to the \(pK_a\) of the weak acid being used.

Calculate the pH of a buffer solution containing 0.10 mol dm ethanoic acid and 0.20 mol dm 3 sodium ethanoate.

Learn how to calculate the pH of a buffer solution containing 0.10 mol dm³ ethanoic acid and 0.20 mol dm³ sodium ethanoate using the Henderson-Hasselbalch equation. This step-by-step guide covers acid-base equilibria and buffer solutions, suitable for Grades 11-12.

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