The acid dissociation constant, K_a, for ethanoic acid is given by the expression $$K_a = \frac{[CH_3COO^-][H^+]}{[CH_3COOH]}$$ The value of K_a for ethanoic acid is 1.74 × 10^-5 mol dm^-3 at 25 °C A buffer solution with a pH of 3.87 was prepared using ethanoic acid and sodium ethanoate. In the buffer solution, the concentration of ethanoate ions was 0.136 mol dm^-3 Calculate the concentration of the ethanoic acid in the buffer solution. Give your answer to three significant figures. In a different buffer solution, the concentration of ethanoic acid was 0.260 mol dm^-3 and the concentration of ethanoate ions was 0.121 mol dm^-3. A 7.00 × 10^-3 mol sample of sodium hydroxide was added to 500 cm³ of this buffer solution. Calculate the pH of the buffer solution after the sodium hydroxide was added. Give your answer to two decimal places.

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The acid dissociation constant, K_a, for ethanoic acid is given by the expression $$K_a = \frac{[CH_3COO^-][H^+]}{[CH_3COOH]}$$ The value of K_a for ethanoic acid is 1.74 × 10^-5 mol dm^-3 at 25 °C A buffer solution with a pH of 3.87 was prepared using ethanoic acid and sodium ethanoate - AQA - A-Level Chemistry - Question 2 - 2017 - Paper 1

Question 2

$The-acid-dissociation-constant,-K_a,-for-ethanoic-acid-is-given-by-the-expression--$$K_a-=-\frac{[CH_3COO^-][H^+]}{[CH_3COOH]}$$--The-value-of-K_a-for-ethanoic-acid-is-1.74-×-10^-5-mol-dm^-3-at-25-°C--A-buffer-solution-with-a-pH-of-3.87-was-prepared-using-ethanoic-acid-and-sodium-ethanoate-AQA-A-Level Chemistry-Question 2-2017-Paper 1.png$

The acid dissociation constant, K_a, for ethanoic acid is given by the expression $$K_a = \frac{[CH_3COO^-][H^+]}{[CH_3COOH]}$$ The value of K_a for ethanoic acid ... show full transcript

Worked Solution & Example Answer:The acid dissociation constant, K_a, for ethanoic acid is given by the expression $$K_a = \frac{[CH_3COO^-][H^+]}{[CH_3COOH]}$$ The value of K_a for ethanoic acid is 1.74 × 10^-5 mol dm^-3 at 25 °C A buffer solution with a pH of 3.87 was prepared using ethanoic acid and sodium ethanoate - AQA - A-Level Chemistry - Question 2 - 2017 - Paper 1

Step 1

Calculate the concentration of the ethanoic acid in the buffer solution.

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Answer

To find the concentration of ethanoic acid, we can rearrange the expression for the acid dissociation constant:

$K_a = \frac{[CH_3COO^-][H^+]}{[CH_3COOH]}$

Given:

$K_a = 1.74 imes 10^{-5} \text{ mol dm}^{-3}$
$[CH_3COO^-] = 0.136 \text{ mol dm}^{-3}$
Using the formula: $[H^+] = 10^{-pH} = 10^{-3.87} \approx 1.3489 \times 10^{-4} \text{ mol dm}^{-3}$ .

Substituting these values into the rearranged formula:

$[CH_3COOH] = \frac{[CH_3COO^-][H^+]}{K_a}$

Calculating:

$[CH_3COOH] = \frac{(0.136)(1.3489 \times 10^{-4})}{1.74 \times 10^{-5}} \approx 1.05 \text{ mol dm}^{-3}$

Thus, the concentration of the ethanoic acid is approximately 1.05 mol dm^-3.

Step 2

Calculate the pH of the buffer solution after the sodium hydroxide was added.

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Answer

First, determine the moles of ethanoic acid and ethanoate before the addition of NaOH:

Moles of ethanoic acid = $0.260 \text{ mol dm}^{-3} \times \frac{500 \text{ cm}^3}{1000} = 0.130 \text{ mol}$
Moles of ethanoate = $0.121 \text{ mol dm}^{-3} \times \frac{500 \text{ cm}^3}{1000} = 0.0605 \text{ mol}$

After adding NaOH, which reacts with ethanoic acid:

Moles of NaOH added = $7.00 \times 10^{-3} \text{ mol}$

Reaction:

Remaining moles of ethanoic acid = $0.130 - 0.007 = 0.123 \text{ mol}$
Moles of ethanoate = $0.0605 + 0.007 = 0.0675 \text{ mol}$

Now, we can calculate the new concentrations:

Concentration of ethanoic acid: $[CH_3COOH] = \frac{0.123}{0.500} = 0.246 \text{ mol dm}^{-3}$
Concentration of ethanoate: $[CH_3COO^-] = \frac{0.0675}{0.500} = 0.135 \text{ mol dm}^{-3}$

Using the Henderson-Hasselbalch equation: $pH = pK_a + \log \frac{[CH_3COO^-]}{[CH_3COOH]}$

Where:

$pK_a = -\log(1.74 \times 10^{-5}) \approx 4.76$

Substituting values: $pH = 4.76 + \log \frac{0.135}{0.246} \approx 4.76 - 0.2081 \approx 4.55$

Thus, the pH of the buffer solution after the sodium hydroxide was added is approximately 4.55.

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Questions answered

Calculate the concentration of the ethanoic acid in the buffer solution.

Calculate the pH of the buffer solution after the sodium hydroxide was added.

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