Problem 273 - A Complete Resource Book in Chemistry for JEE Main

Question

The pKa of a weak acid, HA is \(4.80\). The \(\mathrm{pK}_{\mathrm{b}}\) of a weak base, \(\mathrm{BOH}\) is \(4.78\). The \(\mathrm{pH}\) of an aqueous solution of the corresponding salt, BA will be \([2008]\) (a) \(9.58\) (b) \(4.79\) (c) \(7.01\) (d) \(9.22\)

Step-by-Step Solution

Answer

The pH of the salt solution BA is 4.79, which is option (b).

Step 1: Understanding the Problem

To find the pH of the salt solution formed from the weak acid HA and the weak base BOH, we need to calculate the hydrolysis of the salt BA formed by the acid-base reaction.

Step 2: Calculate the pKw

The sum of the \( \mathrm{pK}_\mathrm{a} \) of the acid and \( \mathrm{pK}_\mathrm{b} \) of the base is related to the water's ion product constant. So, \( \mathrm{pK}_\mathrm{w} = \mathrm{pK}_\mathrm{a} + \mathrm{pK}_\mathrm{b} = 4.80 + 4.78 = 9.58 \).

Step 3: Use Hydrolysis Equation for Salt

The pH of a solution of the salt from a weak acid and a weak base is given by the equation: \( \text{pH} = \frac{1}{2}(\text{pK}_\text{w}) \. \) Using \( \text{pK}_\text{w} = 9.58 \), we calculate \( \text{pH} = \frac{1}{2}(9.58) = 4.79 \. \)

Step 4: Compare with Options

The calculated pH value of 4.79 matches with option (b).

Key Concepts

Hydrolysis of Salts

When a salt like BA, formed from a weak acid HA and a weak base BOH, is dissolved in water, it undergoes a reaction known as hydrolysis. Hydrolysis occurs when ions in the salt react with water to form the original weak acid and weak base. This can slightly change the pH of the solution.

This process involves the breaking apart of the salt into its constituent ions. The balancing act between these ions and water can lead to either an acidic or basic solution, depending on the relative strength of the acid and base. For the salt BA, formed from a weak acid and base:

• The weak acid's conjugate base (A-) can react with water to produce OH⁻ ions.
• The weak base's conjugate acid (B+) can react with water to produce H⁺ ions.

This delicate balance between OH⁻ and H⁺, established through their respective equilibria, will affect the overall pH of the solution.

Weak Acid and Weak Base

A weak acid, like HA, and a weak base, like BOH, only partially dissociate in water. This partial dissociation results in less free ions available in solution, affecting the overall acidity or basicity of the solution.

Because neither the acid nor the base completely dissociates, the resulting salt solution can have a close to neutral pH. However, due to hydrolysis, the pH will not be exactly neutral.

• The extent of dissociation of the weak acid is defined by its dissociation constant, Ka, which is derived from its pKa value.
• Similarly, the dissociation of the weak base is defined by its Kb, derived from its pKb value.

Understanding how these values interplay is crucial to predicting the outcome of their reaction and the properties of the resultant salt solution.

Ion Product Constant of Water (pKw)

The ion product constant of water, denoted as Kw, is a fundamental parameter in understanding acidity, basicity, and the neutral point of water solutions.

In any aqueous solution, water can self-ionize to form H⁺ and OH⁻ ions. The equilibrium constant for this process is represented by Kw, which is always equal to the product of the concentrations of these ions: \[ K_w = [H^+][OH^-] \]

The logarithmic form of this equilibrium constant, pKw, is often used in pH calculations:\[ \text{pK}_w = \text{pK}_a + \text{pK}_b \]
For the given problem, when HA and BOH form the salt BA, we use the pKa of HA and pKb of BOH to determine the pKw. With their sum, we find pKw = 9.58, which facilitates calculating the pH of the resultant solution. This value is indicative of the medium in which the salt is placed and determines how close to neutral the solution is.