If an acid with a pK_a of 5.3 is in an aqueous solution of pH 5.7, what percentage of the acid is present in its acidic form?

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Identify the relationship between pH, pKa, and the ratio of the acidic form (HA) to the conjugate base (A⁻) using the Henderson-Hasselbalch equation: \( \text{pH} = \text{pKa} + \log \left( \frac{[A^-]}{[HA]} \right) \).

Rearrange the Henderson-Hasselbalch equation to solve for the ratio \( \frac{[A^-]}{[HA]} \): \( \frac{[A^-]}{[HA]} = 10^{\text{pH} - \text{pKa}} \).

Substitute the given values for pH (5.7) and pKa (5.3) into the equation: \( \frac{[A^-]}{[HA]} = 10^{5.7 - 5.3} \).

Once the ratio \( \frac{[A^-]}{[HA]} \) is determined, calculate the fraction of the acid in its acidic form (HA) using the formula: \( \text{Fraction of HA} = \frac{1}{1 + \frac{[A^-]}{[HA]}} \).

Convert the fraction of HA into a percentage by multiplying by 100: \( \text{Percentage of HA} = \text{Fraction of HA} \times 100 \).

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주요 개념

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pKa and pH Relationship

The pKa of an acid is a measure of its strength, indicating the pH at which half of the acid is dissociated. A lower pKa value means a stronger acid. The pH of a solution reflects the concentration of hydrogen ions; when pH is higher than pKa, the acid is more likely to be in its deprotonated (conjugate base) form.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation relates pH, pKa, and the ratio of the concentrations of the deprotonated and protonated forms of an acid. It is expressed as pH = pKa + log([A-]/[HA]), where [A-] is the concentration of the conjugate base and [HA] is the concentration of the acid. This equation is essential for calculating the proportions of the acid in different forms at a given pH.

Percentage of Acidic Form

To determine the percentage of an acid present in its acidic form, one can use the ratio derived from the Henderson-Hasselbalch equation. By calculating the ratio of [HA] to the total concentration of acid ([HA] + [A-]), the percentage of the acid in its protonated form can be expressed as ( [HA] / ([HA] + [A-]) ) × 100%. This calculation is crucial for understanding the acid's behavior in solution.

If an acid with a pKa of 5.3 is in an aqueous solution of pH 5.7, what percentage of the acid is present in its acidic form?