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) \(\left(\frac{\mathrm{K}_{1}}{\mathrm{~K}_{2}}\right)\) (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

Option (a) \(\left(\frac{K_1}{K_2}\right)\) compares the relative strengths of acids.

Step 1: Understanding the Problem

To compare the relative strengths of two monobasic acids with the same concentration, we need to find the expression that correctly compares their characteristics. Each option presents a different formula for measuring the relative strengths using different terms: dissociation constant (K), degree of dissociation (\(\alpha\)), and hydrogen ion concentration (\([H^+]\)).

Step 2: Recall Concept of Dissociation Constant

The dissociation constant \(K\) is a measure of the strength of an acid in solution. For a monobasic acid, this is represented as \(K_a\). When comparing two acids of the same concentration, their relative strengths can be directly compared using the ratio of their dissociation constants \(\left(\frac{K_1}{K_2}\right)\).

Step 3: Analyze Option (a)

Option (a) is \(\left(\frac{K_1}{K_2}\right)\). Given that the dissociation constant \(K\) is directly related to the acid strength for acids of equal concentration, this ratio directly compares the strengths of the acids.

Step 4: Consider Other Options

Option (b) \(\left(\frac{\alpha_1}{\alpha_2}\right)\) relates to the degree of ionization but doesn't solely depend on the acid strength if concentrations are different. Option (c) \(\left(\sqrt{\frac{K_1}{K_2}}\right)\), involves a square root, which alters the direct proportionality, making it less straightforward. Option (d) combines hydrogen ion concentrations, but \([H^+]\) also depends on total concentration, not just strength.

Step 5: Determine the Correct Answer

The relative strengths of two acids with the same concentration are best compared by the ratio of their dissociation constants \(\left(\frac{K_1}{K_2}\right)\), which is option (a). This is because \(K\) directly relates to an acid's ability to dissociate and donate protons.

Key Concepts

Acid Strength

Acid strength is a term that refers to an acid’s ability to donate protons, or hydrogen ions, in a solution. The more straightforwardly an acid releases its protons, the stronger it is considered.

• Acids that dissociate completely in solution are termed "strong acids," while those that partially dissociate are "weak acids."
• The dissociation constant, or acid dissociation constant ( K_a ), plays a crucial role here, as it quantifies the degree to which an acid can dissociate.

For acids with the same concentration, comparing their dissociation constants directly enables us to determine which acid is stronger. A higher K_a indicates a stronger acid since it suggests a greater tendency to release hydrogen ions into the solution.

Monobasic Acids

Monobasic acids are a type of acid that can donate only one hydrogen ion (proton) per molecule during the process of dissociation.

• These acids are also known as monoprotic acids because "mono" means one.
• Common examples include hydrochloric acid (HCl) and acetic acid (CH₃COOH).

The concept of monobasic acids is important in calculating and comparing acid strengths because K_a values refer to the dissociation of this single proton. As a result, comparisons based on K_a values are straightforward for monobasic acids. It’s particularly useful since it simplifies calculations and comparisons, focusing only on that one available hydrogen.

Degree of Dissociation

Degree of dissociation ( α ) is the fraction of the original acid molecules that dissociate in solution.

• A higher α value indicates that more acid molecules are ionized, suggesting a stronger acid if the concentration is also taken into account.
• This concept is helpful when evaluating the behavior of weak acids, where the dissociation is not complete.

For comparing acids with the same concentration, looking at the degree of dissociation can provide insights; however, α alone might not directly correlate with acid strength if concentrations differ. This is because the environment of the acid solution can affect the dissociation process.

Hydrogen Ion Concentration

Hydrogen ion concentration ( [H^+] ) directly relates to the acidity of a solution and is usually expressed in terms of pH.

• The pH scale quantifies how acidic or basic a solution is; lower pH means higher hydrogen ion concentration and stronger acidity.
• [H^+] is also pivotal when discussing the strength of acids, as strong acids generate more hydrogen ions compared to weak ones at the same concentration.

Yet, just measuring [H^+] can be misleading when concentrations of the acids differ, because even a weak acid may show similar [H^+] if its concentration is disproportionately higher. So, while hydrogen ion concentration is a component of understanding acid strength, it must be interpreted carefully in context.