Can someone help me solve this problem showing all the correct steps please? Tha

Question

Can someone help me solve this problem showing all the correct steps please? Thank you!

3. The pKa of acetic acid is 4.76. You plan to make a 0.05 M acetate buffer using sodium acetate and acetic acid at pH 5.0. Which of the follow statements about the relative amounts of sodium acetate and acetic acid is true? a. Since the pH is greater than the pKa, the amount of acetic acid required would be less than 0.025 M and the amount of sodium acetate required would be greater than 0.025 M, so the sum of the concentrations would be 0.05 M b. Since the pH is greater that the pKa, the amount of acetic acid required would be greater than 0.02 5 M and the amount of sodium acetate required would be less than 0.025 M, so the sum of the concentrations would be 0.05 M C. Since the pKa is greater that the pH, the amount of acetic acid required would be greater than 0.025 M and the amount of sodium acetate required would be less than 0.025 M, so the sum of the concentrations would be 0.05 M d. you would use the same amounts of acetic acid and sodium acetate to prepare the buffer

Explanation / Answer

pH = pKa + log[acetate/acetic acid]

5 = 4.76 + log([acetate]/[acetic acid])

[acetate] = 1.74[acetic acid]

[acetate] + [acetic acid] = 0.5

[acetate] = 0.5 - [acetic acid] = 1.74[acetic acid]

[acetic acid] = 0.182 M

[acetate] = 0.318 M

Thus, of the given statements the following would be correct,

a. Since the pH is greater then pKa, the amount of acetic acid required would be less then 0.025 M and the amount of acetate required would be greater then 0.025 M, so the sum of the concentrations would be 0.5.

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