Problem 160 - A Complete Resource Book in Chemistry for JEE Main

Question

If the concentrations of two monobasic acids are same, their relative strengths can be compared by (a) \(\left(\frac{\mathrm{K}_{\mathrm{l}}}{\mathrm{K}_{2}}\right)\) (b) \(\left(\frac{\alpha_{1}}{\alpha_{2}}\right)\) (c) \(\left(\sqrt{\frac{K_{1}}{K_{2}}}\right)\) (d) \(\frac{\left[\mathrm{H}^{+}\right]_{1}}{\left[\mathrm{H}^{+}\right]_{2}}\)

Step-by-Step Solution

Answer

(a) \( \left(\frac{K_1}{K_2}\right) \) compares acid strengths directly.

Step 1: Understanding the Problem

We need to determine which one of the given options can be used to compare the relative strengths of two monobasic acids when their concentrations are the same. Monobasic acids release one proton per molecule.

Step 2: Defining Acid Strength

The strength of an acid is determined by its ability to dissociate into ions. This is quantified by the acid dissociation constant, \( K_a \), where a higher \( K_a \) value means a stronger acid.

Step 3: Analyzing the Options: Part (a)

Option (a) compares the relative strengths using the ratio \( \frac{K_1}{K_2} \), where \( K_1 \) and \( K_2 \) are the dissociation constants of the acids. This is a direct way to compare the strengths because \( K \) values directly indicate the acid's dissociation power.

Step 4: Analyzing the Options: Part (b)

Option (b) involves the ratio \( \frac{\alpha_1}{\alpha_2} \), where \( \alpha \) is the degree of dissociation. The degree of dissociation is also linked to acid strength, but this depends on both \( K_a \) and concentration, making it more complex.

Step 5: Analyzing the Options: Part (c)

Option (c) uses the ratio \( \sqrt{\frac{K_1}{K_2}} \). This transformation doesn’t directly relate to the comparative strength as a simple \( \frac{K_1}{K_2} \) would, and is not typically used for this purpose.

Step 6: Analyzing the Options: Part (d)

Option (d) compares the hydrogen ion concentrations \( \frac{[\text{H}^+]_1}{[\text{H}^+]_2} \). While this can reflect differences in acid strength, it's not solely dependent on \( K_a \) and can be influenced by concentration or other conditions.

Step 7: Conclusion

Since option (a) directly compares the acid dissociation constants \( K_1 \) and \( K_2 \), it is the most straightforward and reliable method for comparing the relative strengths of the acids given the same concentration.

Key Concepts

Monobasic Acids

Monobasic acids are a type of acid that releases only one proton ( H⁺) per molecule when dissolved in water. This proton dissociation is a key feature in understanding the behavior and strength of acids. Basic means 'one' in this context, highlighting that only one hydrogen ion is given away.
For example, hydrochloric acid (HCl) is a common monobasic acid. During its dissociation, HCl splits into H⁺ and Cl⁻ ions. This single release of a proton is what classifies it as monobasic.
Understanding whether an acid is monobasic is important when comparing its strength to other acids. Knowing that it can only lose one proton simplifies calculations around its dissociation and helps in comparing the relative strengths of acids when their concentrations are the same.

• Monobasic acids release one proton per molecule.
• Examples include HCl, HNO₃ and CH₃COOH.

Acid Dissociation Constant (Ka)

The Acid Dissociation Constant, denoted as \( K_a \), is a crucial measure of an acid's strength. It quantifies how well an acid can dissociate into its ions in a solution. A larger \( K_a \) value indicates a stronger acid capable of dissociating more completely, producing more hydrogen ions.
Mathematically, it is expressed as:\[ K_a = \frac{[\text{H}^+][\text{A}^-]}{[\text{HA}]} \]where \([\text{H}^+]\) is the concentration of hydrogen ions, \([\text{A}^-]\) is the concentration of the conjugate base, and \([\text{HA}]\) is the concentration of the undissociated acid.
This formula helps to compare acid strengths when concentrations are equal. The greater the \( K_a \), the more the acid dissociates, and thus, the stronger it is. The \( K_a \) forms the basis for option (a) in the exercise, showing it as a straightforward method to determine which of two acids is stronger, given equal concentrations.

Degree of Dissociation

The degree of dissociation, represented by \( \alpha \), is another way to describe how effectively an acid dissociates into ions. It tells us the fraction or percentage of the original acid that disassociates in solution. A higher \( \alpha \) indicates more dissociation.
It's calculated by:\[ \alpha = \frac{\text{amount of dissociated acid}}{\text{initial amount of acid}} \]While \( \alpha \) provides insight into dissociation, it is influenced by both \( K_a \) and the concentration of the acid. Therefore, it's not as direct a measure of acid strength compared to \( K_a \).
In the exercise, option (b) relates to using \( \alpha \) to compare acid strength. However, unlike \( K_a \), \( \alpha \) varies with concentration, making it a more complex, though still useful, measure.

• Reflects the extent of dissociation in acids.
• Dependent on both the dissociation constant and concentration.
• Best used alongside other measures for full understanding.