The pKa of acetic acid is 4.76. At what pH would the concentration of acetic acid and acetate ion be the
same?
(1) pH= 7
(2) pH = 6.7
(3) pH = 9.8
(4) pH = 4.76
📘 Problem Statement
The pKa of acetic acid is 4.76. At what pH would the concentration of acetic acid and acetate ion be the same?
Options:
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pH = 7
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pH = 6.7
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pH = 9.8
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pH = 4.76
🔬 Understanding pKa and pH for Acetic Acid
In order to understand when the concentrations of acetic acid (HA) and acetate ion (A⁻) are the same, we need to use the Henderson-Hasselbalch equation, which relates the pH of a solution to the pKa of the acid and the concentrations of the acid and its conjugate base.
The equation is:
pH=pKa+log([A−][HA])\text{pH} = \text{pKa} + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right)
Where:
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pH is the acidity of the solution,
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pKa is the acid dissociation constant of the acid (a measure of its strength),
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[A⁻] is the concentration of the conjugate base (acetate ion),
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[HA] is the concentration of the acid (acetic acid).
🔑 Key Point
At the point where the concentrations of acetic acid and acetate ion are equal, [A⁻] = [HA]. This makes the log term in the Henderson-Hasselbalch equation equal to 0, because:
log(1)=0\log(1) = 0
Thus, the equation simplifies to:
pH=pKa\text{pH} = \text{pKa}
Therefore, at the point where the concentrations of acetic acid and acetate ion are the same, the pH equals the pKa of acetic acid.
✅ Solution
Given that the pKa of acetic acid is 4.76, when the concentrations of acetic acid and acetate ion are equal, the pH will be:
pH=4.76\text{pH} = 4.76
Thus, the correct answer is 4.76.
✅ Correct Answer: (4) pH = 4.76
At pH = 4.76, the concentrations of acetic acid and acetate ion will be equal.
💡 Why This Concept Matters
Understanding the relationship between pH, pKa, and the concentrations of acids and their conjugate bases is essential in various fields, including:
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Biochemistry: Buffers in biological systems, enzyme activity, and metabolic pathways.
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Pharmacology: Drug absorption and behavior in different pH environments.
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Chemistry: Acid-base titrations and buffer systems.
Knowing when an acid and its conjugate base are in equal concentrations helps in preparing buffer solutions with specific pH values.
✅ Key Takeaways
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The Henderson-Hasselbalch equation connects pH, pKa, and the concentration ratio of an acid and its conjugate base.
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When the concentrations of acetic acid and acetate ion are the same, pH = pKa.
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For acetic acid with pKa = 4.76, the pH at which their concentrations are equal is 4.76.
