Problem 96 - A Complete Resource Book in Chemistry for JEE Main

Question

The dissociation constant of two acids \(\mathrm{HA}_{1}\) and \(\mathrm{HA}_{2}\) are \(3.0 \times 10^{-4}\) and \(1.8 \times 10^{-5}\) respectively. The relative strengths of the acids is (a) \(1: 16\) (b) \(1: 4\) (c) \(4: 1\) (d) \(16: 1\)

Step-by-Step Solution

Answer

The relative strength of \( \text{HA}_1 \) to \( \text{HA}_2 \) is \(16:1\), so the answer is (d) \(16:1\).

Step 1: Understanding Dissociation Constants

The dissociation constant (also known as the acid dissociation constant) is represented as \(K_a\) and provides a measure of the strength of an acid in solution. For two acids \( \text{HA}_1 \) and \( \text{HA}_2 \), their dissociation constants are given as \(K_{a_1} = 3.0 \times 10^{-4}\) and \(K_{a_2} = 1.8 \times 10^{-5}\) respectively. A larger \(K_a\) value indicates a stronger acid.

Step 2: Determine Relative Strengths

The relative strength of two acids can be compared using their dissociation constants. To find the relative strengths, take the ratio of their \(K_a\) values:\[\text{Relative Strength} = \frac{K_{a_1}}{K_{a_2}} = \frac{3.0 \times 10^{-4}}{1.8 \times 10^{-5}}\]

Step 3: Calculating The Ratio

Calculate the ratio:\[\frac{3.0 \times 10^{-4}}{1.8 \times 10^{-5}} = \frac{3.0}{1.8} \times 10^{-4 + 5} = \frac{3.0}{1.8} \times 10^1\]\[= \frac{3.0}{1.8} \times 10 = 1.67 \times 10 = 16.7 \]Rounding to the nearest whole number, the relative strength is approximately 16:1.

Key Concepts

Acid Strength Comparison

When studying acids, it's important to understand how the acids' strength is compared. Acid strength refers to the ability of an acid to donate a proton (H\(^+\)) to a base. A stronger acid dissociates more in solution, meaning it releases more H\(^+\) ions compared to a weaker acid.

This process of dissociation is directly related to the acid dissociation constant, often symbolized as \(K_a\). By examining the \(K_a\) values of two acids, you can effectively compare their strengths. A higher \(K_a\) value indicates a stronger acid because it suggests a greater extent of dissociation. Conversely, a smaller \(K_a\) value points to a weaker acid.

In practice, acid strength comparison is crucial for predicting reactions and understanding the behavior of substances in chemistry. Being able to determine which acid is stronger helps in designing chemical processes where specific degrees of acid strength are required.

Dissociation Constant Calculation

Calculating the dissociation constant of an acid gives insight into how readily an acid donates protons in a solution. The dissociation constant \(K_a\) is calculated from the concentrations of the products and reactants at equilibrium. It's generally expressed in the form:

• \[ K_a = \frac{[H^+][A^-]}{[HA]} \]

Where \([H^+]\) represents the concentration of the hydrogen ions, \([A^-]\) is the concentration of the anion formed, and \([HA]\) is the concentration of the undissociated acid.

With the given dissociation constants of \(\text{HA}_1\) and \(\text{HA}_2\), it's apparent that \(K_{a1} = 3.0 \times 10^{-4}\) is much greater than \(K_{a2} = 1.8 \times 10^{-5}\). The calculation involves inserting these values in equations to evaluate their behavior in solution.

In an educational context, understanding \(K_a\) calculations equips students with the skills to better grasp not just general acid-base equilibria, but also more complex biochemical and industrial applications.

Relative Acid Strength Calculation

To find out how much stronger one acid is relative to another, you determine their relative acid strength.

This is done by taking the ratio of their dissociation constants \(K_a\). For example, if you have two acids \(\text{HA}_1\) and \(\text{HA}_2\) with \(K_{a1} = 3.0 \times 10^{-4}\) and \(K_{a2} = 1.8 \times 10^{-5}\) respectively, you calculate their relative strength using:

• \[ \text{Relative Strength} = \frac{K_{a1}}{K_{a2}} = \frac{3.0 \times 10^{-4}}{1.8 \times 10^{-5}} = 16.7 \]

Rounding 16.7 provides the relative strength as 16:1, which means \(\text{HA}_1\) is approximately 16 times stronger than \(\text{HA}_2\).

This approach is valuable in chemistry, allowing chemists and students to make informed decisions about which acid to use in specific reactions, ensuring the desired reaction outcomes are achieved efficiently.