Problem 59 - A Complete Resource Book in Chemistry for JEE Main

Question

pKa values of three acids \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) are \(4.3,3.3\) and 5.5 respectively. Which of the following represents the correct order of acid strength? (a) \(\mathrm{A}>\mathrm{B}>\mathrm{C}\) (b) \(\mathrm{C}>\mathrm{A}>\mathrm{B}\) (c) \(\mathrm{B}>\mathrm{A}>\mathrm{C}\) (d) \(C>B>A\)

Step-by-Step Solution

Answer

(c) B > A > C

Step 1: Understanding pKa and Acid Strength

The acid dissociation constant (Ka) is a measure of the strength of an acid in solution. The pKa is the negative logarithm (base 10) of the Ka value. Therefore, lower pKa values indicate stronger acids because a stronger acid will dissociate more in solution, resulting in a higher Ka.

Step 2: Analyzing Given pKa Values

The pKa values provided are: - Acid A: 4.3 - Acid B: 3.3 - Acid C: 5.5. Lower pKa values indicate stronger acids, so we need to compare these values to determine the order of acid strength.

Step 3: Arranging Acids by Strength

Since we know that the lower the pKa value, the stronger the acid, we arrange acids by increasing pKa values: - Acid B (pKa 3.3) is the strongest. - Acid A (pKa 4.3) is next. - Acid C (pKa 5.5) is the weakest. So the correct order from strongest to weakest is B > A > C.

Step 4: Selecting the Correct Option

Given the order of acid strength we determined (B > A > C), we look at the options provided: - (a) A > B > C - (b) C > A > B - (c) B > A > C - (d) C > B > A The correct option is (c) B > A > C since it matches our determined order.

Key Concepts

Understanding Acid Strength and pKa Values

When we talk about acid strength, we are referring to how easily an acid donates protons (H⁺ ions) in a solution. The ease with which this happens depends on the acid's dissociation. More dissociation means a stronger acid.

The measure we use to understand this concept is the pKa value, which is derived from the acid dissociation constant (K_a). The pKa is calculated as the negative logarithm of the K_a (\(\text{pKa} = -\log(\text{K}_a)\)). This means lower pKa values correspond to stronger acids because they have higher dissociation constants.

In practice, when comparing different acids, those with lower pKa values will generally be stronger as they dissociate more in solution, making them more capable of donating protons. This basic principle helps us determine the relative strength of acids in any given scenario.

Exploring the Acid Dissociation Constant

The acid dissociation constant, usually denoted as K_a, is a quantitative measure of the strength of an acid in solution. Specifically, it reflects an acid’s ability to give up a proton to water, forming hydronium ions and the conjugate base of the acid. This chemical equilibrium is represented as: \[ HA + H_2O \rightleftharpoons H_3O^+ + A^- \]Where \( HA \) is the acid, \( H_3O^+ \) is the hydronium ion, and \( A^- \) is the conjugate base.

A larger K_a value indicates a stronger acid, as more products (in this case, H_3O^+ and A^-) are formed compared to the reactants (HA). Understanding K_a is crucial because it directly impacts the calculation of pKa. This relationship ties back into acid strength: the stronger the acid, the higher its K_a and consequently, the lower its pKa.

The Role of Chemical Equilibrium in Acid Dissociation

Chemical equilibrium is a dynamic state where the forward and reverse reactions occur at the same rate, meaning the concentrations of reactants and products remain constant over time. In the context of acid dissociation, equilibrium is essential in understanding how acids behave in solution.

When an acid dissolves in water, the equilibrium between the undissociated acid molecules and the ions they form stabilizes. For strong acids, the equilibrium position lies far to the right, indicating substantial dissociation into ions. Conversely, weak acids have an equilibrium position that favors the undissociated acid on the left side of the equation.

This behavior is quantified by the K_a, which tells us about the position of the equilibrium in an acidic solution. Lower pKa values (and thus higher K_a values) tell us that the equilibrium heavily favors dissociation, confirming greater acid strength. Understanding chemical equilibrium and how it relates to K_a helps us predict and explain the behaviors of different acids in solutions.