Butyric acid is responsible for the foul smell of rancid butter. The pKa of butyric acid is 4.84. (a) Calculate the pKb for the butyrate ion.

Verified step by step guidance

1. Identify the relationship between pKa and pKb in the context of the acid-base conjugate pair. The formula to use is: pKa + pKb = 14. This equation is derived from the ion product constant of water at 25°C, which is Kw = 10^{-14}.
2. Recognize that butyric acid (CH3CH2CH2COOH) dissociates to form the butyrate ion (CH3CH2CH2COO-) and a hydrogen ion (H+).
3. Use the given pKa value of butyric acid, which is 4.84, to find the pKb of the conjugate base, the butyrate ion.
4. Substitute the pKa value into the formula from step 1: pKb = 14 - pKa.
5. Calculate pKb using the substituted values to find the strength of the butyrate ion as a base.

Key Concepts

pKa and pKb Relationship

The pKa and pKb values are related through the equation pKa + pKb = 14 at 25°C. This relationship allows us to convert between the acidity of a weak acid and the basicity of its conjugate base. In this case, butyric acid has a pKa of 4.84, which can be used to find the pKb of the butyrate ion.

Acid-Base Equilibrium

Acid-base equilibrium describes the balance between an acid and its conjugate base in solution. For butyric acid, the equilibrium can be represented as HA ⇌ H⁺ + A⁻, where HA is the acid and A⁻ is the conjugate base (butyrate ion). Understanding this equilibrium is essential for calculating pKb from pKa.

Conjugate Acid-Base Pairs

Conjugate acid-base pairs consist of an acid and its corresponding base that differ by a proton (H⁺). In this scenario, butyric acid (the acid) and butyrate ion (the base) form a conjugate pair. Recognizing these pairs is crucial for applying the pKa and pKb relationship effectively.