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A physician wishes to prepare a buffer s...

A physician wishes to prepare a buffer solution at pH = 3.58 that efficiently resist changes in pH yet contains only small concentration of the buffering agents. Which one of the following weak acid together with its sodium salt would be best to use ?
(a)m-chlorobenzoic acid `(pK_(a)=3.98)`
(b)p-chlorocinnamic acid `(pK_(a)=4.41)`
(c)2,5-dihydroxy benzoic acid `(pK_(a)=2.97)`
(d)Acetoacetic acid `(pK_(a)=3.58)`

A

m-chlorobenzoic acid `(pK_(a)=3.98)`

B

p-chlorocinnamic acid `(pK_(a)=4.41)`

C

2,5-dihydroxy benzoic acid `(pK_(a)=2.97)`

D

Acetoacetic acid `(pK_(a)=3.58)`

Text Solution

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The correct Answer is:
To determine which weak acid and its sodium salt would be best for preparing a buffer solution at pH = 3.58, we can use the Henderson-Hasselbalch equation: \[ \text{pH} = \text{pK}_a + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right) \] where: - \(\text{pH}\) is the desired pH of the buffer solution, - \(\text{pK}_a\) is the dissociation constant of the weak acid, - \([\text{A}^-]\) is the concentration of the salt (the conjugate base), - \([\text{HA}]\) is the concentration of the weak acid. ### Step-by-Step Solution: 1. **Identify the pH and the pK_a values**: - We need a buffer solution with a pH of 3.58. - We have the following weak acids and their pK_a values: - (a) m-chlorobenzoic acid: \(pK_a = 3.98\) - (b) p-chlorocinnamic acid: \(pK_a = 4.41\) - (c) 2,5-dihydroxy benzoic acid: \(pK_a = 2.97\) - (d) Acetoacetic acid: \(pK_a = 3.58\) 2. **Compare pH with pK_a**: - The buffer will work best when the pH is close to the pK_a of the weak acid used. - The closer the pH is to the pK_a, the more effective the buffer will be. 3. **Evaluate the options**: - For m-chlorobenzoic acid: \(pK_a = 3.98\) (not close enough to 3.58) - For p-chlorocinnamic acid: \(pK_a = 4.41\) (too high) - For 2,5-dihydroxy benzoic acid: \(pK_a = 2.97\) (too low) - For acetoacetic acid: \(pK_a = 3.58\) (exact match) 4. **Conclusion**: - Since acetoacetic acid has a pK_a that matches the desired pH of 3.58, it is the best choice. - According to the Henderson-Hasselbalch equation, if we set \(pH = pK_a\), the ratio \(\frac{[\text{A}^-]}{[\text{HA}]}\) becomes 1:1, indicating that equal concentrations of the acid and its salt will provide the best buffering capacity. Thus, the best choice for preparing the buffer solution is **(d) Acetoacetic acid**.
To determine which weak acid and its sodium salt would be best for preparing a buffer solution at pH = 3.58, we can use the Henderson-Hasselbalch equation: \[ \text{pH} = \text{pK}_a + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right) \] where: - \(\text{pH}\) is the desired pH of the buffer solution, ...
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