Problem 93 - A Complete Resource Book in Chemistry for JEE Main

Question

The \(\mathrm{pH}\) of a \(0.1 \mathrm{M}\) aqueous solution of a weak acid (HA) is \(3 .\) What is its degree of dissociation? (a) \(1 \%\) (b) \(10 \%\) (c) \(50 \%\) (d) \(25 \%\)

Step-by-Step Solution

Answer

The degree of dissociation is 1% (Option a).

Step 1: Understand the Concept

The degree of dissociation refers to the fraction of original solute molecules that dissociate into ions in a solution. It can be represented as \[ \alpha = \frac{\text{amount dissociated}}{\text{initial concentration}} \times 100 \].

Step 2: Use pH to Find Hydronium Ion Concentration

The pH of the solution is given as 3. Use the pH formula to find the concentration of hydrogen ions: \[ \text{pH} = -\log_{10}[\text{H}^+] \]. Thus, \[ [\text{H}^+] = 10^{-3} = 0.001 \, \text{M} \].

Step 3: Establish the Relation with Degree of Dissociation

In a weak acid dissociation \(\text{HA} \rightleftharpoons \text{H}^+ + \text{A}^-\), if the initial concentration of \(\text{HA}\) is \(0.1\,\text{M}\) and degree of dissociation is \(\alpha\), then the concentration of \(\text{H}^+\) is \(\alpha \times 0.1 = [\text{H}^+] = 0.001\).

Step 4: Solve for Alpha

From the relation established, \[ \alpha \times 0.1 = 0.001 \].Thus, \[ \alpha = \frac{0.001}{0.1} = 0.01 = 1\% \times 100 \].

Step 5: Choose the Correct Option

From the calculation, the degree of dissociation \( (\alpha) \) for the acid solution is \(1\%\). Thus, option \((a)\) \(1\%\) is the correct answer.

Key Concepts

Understanding Weak Acids

Weak acids are a type of acid that only partially dissociate into ions when they are dissolved in water. Unlike strong acids, which fully dissociate, weak acids establish an equilibrium between the undissociated acid molecules and the ions formed. This means only a fraction of the acid molecules will release their hydrogen ions, leading to an equilibrium state in the solution.

Key characteristics of weak acids include:

• Partial ionization in solution, meaning not all the acid molecules donate a proton (H⁺).
• Existence of an equilibrium between the reactants (undissociated acids) and products (hydronium ions and conjugate bases).
• Presence of a measurable acid dissociation constant, which quantifies its strength.

This incomplete dissociation is what differentiates weak acids from strong acids and makes them interesting candidates for studying equilibrium concepts in chemistry.

Calculating pH

The pH of a solution is a measure of its acidity or basicity, based on the concentration of hydrogen ions (H⁺) present. It is calculated using the formula:

\[ ext{pH} = -\log_{10}[ ext{H}^+]\]For instance, if we know that the pH of a solution is 3, we can find the concentration of hydrogen ions using the inverse of the pH calculation. In mathematical terms, it becomes:

• [H⁺] = 10^{-3} \, M

The pH scale typically ranges from 0 to 14, where a pH less than 7 represents an acidic solution. Calculating pH is a fundamental aspect of understanding the nature of a solution and its degree of acidity.

Recapping Hydronium Ion Concentration

The hydronium ion concentration, often denoted as [H₃O⁺] or simply [H⁺], is a critical factor in determining the acidity of a solution. In solutions of weak acids, the concentration is related to how much the acid has dissociated.

For a weak acid like HA dissociating in water, we have:

• HA + H₂O \( \rightleftharpoons \) H₃O⁺ + A^-

When given an acid concentration and the pH, the hydronium ion concentration can be found, which further helps in determining the degree of dissociation or other equilibrium properties of the weak acid solution.

Acid Dissociation Constant Explained

The acid dissociation constant (K_a) is a vital concept when discussing weak acids. It provides insight into how easily an acid donates its protons in a solution. This constant is determined by the equilibrium concentrations of the acid and its dissociated ions:

• K_a = \( \frac{[ ext{H}^+][ ext{A}^-]}{[ ext{HA}]} \)

A higher K_a value implies a stronger acid that dissociates more in solution, whereas a lower K_a means a weaker acid. For our weak acid example, the given degree of dissociation and hydronium ion concentration would directly impact the K_a value, illustrating the relationship between equilibrium constants and ion concentrations. Understanding K_a is crucial for predicting the behavior of an acid in various conditions, such as different concentrations or temperatures.