Problem 195 - A Complete Resource Book in Chemistry for JEE Main

Question

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

Step-by-Step Solution

Answer

(b) \(\frac{\mathrm{K}_1}{\mathrm{K}_2}\) compares the relative strengths of weak acids when concentrations are equal.

Step 1: Understanding the Problem

The task is to determine how to compare the relative strength of two weak acids when they have the same molar concentrations.

Step 2: Basic Concept of Acid Strength

The strength of an acid is determined by its dissociation in water. For weak acids, this can be measured in terms of the ionization constant, represented by the acid dissociation constant (\(K_a\)). The larger the \(K_a\) value, the stronger the acid, due to a greater extent of dissociation.

Step 3: Define Molar Concentration Context

Since the molar concentrations of the acids are the same, we can focus on comparing their dissociation constants or degrees of ionization rather than concentration values.

Step 4: Analyzing Given Options

We need to identify which given option correlates directly to the relative strengths of acids based on dissociation. Translating the comparison of strengths, the ratio involving \((\text{K}_1/\text{K}_2)\) directly compares the dissociation constants.

Step 5: Validate Correct Option

Comparing the \(K_a\) values directly: Option (b), \(\frac{\mathrm{K}_1}{\mathrm{K}_2}\), represents this comparison correctly. A greater ratio of \(K_a\) values signifies stronger relative acid strength. The option directly relates to the acid strength comparison metric by conferring the relative dissociation constant values.

Key Concepts

Understanding Weak Acids

Weak acids are acids that do not fully dissociate in solution. This means that, in water, they partially release hydrogen ions

• They have only a small fraction of their molecules transforming into ions.
• This partial dissociation results in an equilibrium between the ionized and undissociated molecules.
• The degree of ionization is important in determining their strength relative to other acids.

For instance, acetic acid is a common weak acid. In solution, it does not completely ionize, which is why vinegar, a dilute solution of acetic acid, does not have the same corrosive properties as stronger acids like hydrochloric acid.

The Importance of Acid Dissociation Constant

The acid dissociation constant, often denoted as \( K_a \), is a critical value when discussing acid strength.

• \( K_a \) measures how well an acid dissociates into its ions in solution.
• The larger the \( K_a \), the stronger the acid because more molecules are ionized.
• In the case of two acids with the same concentration, the one with the higher \( K_a \) will be the stronger acid.

\( K_a \) is crucial for chemists to predict the behavior of an acid in various chemical reactions. This constant provides a quantitative measure allowing scientists to compare different acids regardless of their concentration.

Molar Concentration Defined

Molar concentration, also known as molarity, is an important concept in chemistry, representing the concentration of a solute in a given volume of solution.

• It describes how many moles of a substance are contained per liter of solution (mol/L).
• In the context of acids, molar concentration reflects how much of the acid is present per unit of liquid.
• Molarity allows chemists to prepare solutions with precise acid concentrations for experiments or industrial applications.

When comparing acid strength, having the same molar concentration means that differences in strength are due to other factors, like the dissociation constant, not the number of molecules.

Role of Ionization Constant

The ionization constant is linked to the acid dissociation constant, providing insight into how completely an acid ionizes in solution.

• This constant effectively measures the extent of ionization.
• For weak acids, it is valuable because it indicates the balance between remaining undissociated molecules and ions.
• By comparing ionization constants of acids, it is easy to understand which acid is stronger or weaker relative to others.

In practice, when two weak acids have the same molar concentration, the one with a higher ionization constant is often stronger due to greater ionization. This comparison of constants becomes a crucial method for evaluating acid strength beyond just concentration measures.