Problem 163 - A Complete Resource Book in Chemistry for JEE Main

Question

The dissociation constant of monobasic acids \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) are \(10^{-4}, 10^{-6}\) and \(10^{-10}\) respectively. The concentration of each monobasic acid is \(0.1 \mathrm{M}\). Which of the following has been arranged in increasing order of \(\mathrm{pH}\) ? (a) \(\mathrm{C}<\mathrm{B}<\mathrm{A}\) (b) \(\mathrm{B}<\mathrm{A}<\mathrm{C}\) (c) \(\mathrm{A}<\mathrm{B}<\mathrm{C}\) (d) \(\mathrm{B}<\mathrm{C}<\mathrm{A}\)

Step-by-Step Solution

Answer

The correct answer is (c) \(\mathrm{A} < \mathrm{B} < \mathrm{C}\).

Step 1: Understanding pH and Dissociation Constant

To solve this problem, it's important to recognize that the pH of a solution is influenced by the degree of dissociation of acids. Stronger acids dissociate more, resulting in lower pH, while weaker acids dissociate less, causing higher pH. The dissociation constant (Ka) serves as a measure of acid strength.

Step 2: Relating Dissociation Constant to Acid Strength

The given dissociation constants for acids A, B, and C are \(10^{-4}, 10^{-6},\) and \(10^{-10}\) respectively. A larger Ka value indicates a stronger acid with a greater ability to donate protons, leading to a lower pH.

Step 3: Ranking Acids by Strength Based on Ka

Based on the dissociation constants, acid A (\(K_a = 10^{-4}\)) is the strongest, acid B (\(K_a = 10^{-6}\)) is weaker than A, and acid C (\(K_a = 10^{-10}\)) is the weakest. Therefore, in decreasing order of strength, the acids are: A > B > C.

Step 4: Arranging Acids in Increasing Order of pH

Since stronger acids have lower pH, and weaker acids have higher pH, the increasing order of pH for acids is the reverse of their acid strength. Hence, the correct arrangement in increasing order of pH is: \(\text{A} < \text{B} < \text{C} \).

Step 5: Matching with Given Options

The arrangement \(\text{A} < \text{B} < \text{C} \) corresponds to option (c).

Key Concepts

Dissociation Constant

The dissociation constant, denoted as \(K_a\), is crucial for understanding how acids behave in solution. It quantifies the extent to which an acid releases its protons into the solution. When an acid dissociates, it separates into ions, and \(K_a\) provides a numerical value of this equilibrium. Higher \(K_a\) values indicate a higher degree of dissociation, meaning the acid releases more protons. This makes the acid stronger. A dissociation constant, therefore, allows us to compare different acids and predict their strength.

• A higher \(K_a\) means a stronger acid because it dissociates more.
• A lower \(K_a\) indicates a weaker acid with less dissociation.

Understanding \(K_a\) is essential as it is directly related to acid strength and the calculation of pH.

Acid Strength

Acid strength refers to an acid's ability to donate protons to the surrounding solution. This characteristic is vitally linked to its dissociation constant. In essence, strong acids dissociate completely or almost completely, whereas weak acids remain largely undissociated in solution. Acid strength can be understood better through these points:

• Strong acids: These have high \(K_a\) values, indicating a high proton donation ability.
• Weak acids: These have low \(K_a\) values and donate fewer protons.

Knowing the strength of an acid helps predict how it will impact the pH of the solution it's in, making it a fundamental concept in chemistry.
Examining how acids such as A, B, and C behave in solution based on their \(K_a\) values reveals their respective strengths and the potential for altering the solution's pH.

pH Calculation

The term pH is a numerical representation of how acidic or basic a solution is. It's calculated using the concentration of hydrogen ions (\[\text{pH} = -\log_{10}[\text{H}^+]\] where \([\text{H}^+]\) is the hydrogen ion concentration. Stronger acids contribute more hydrogen ions to the solution, meaning lower pH values.When calculating pH, consider the following:

• High \(K_a\): Corresponds to high [\(\text{H}^+\)] and low pH.
• Low \(K_a\): Results in low [\(\text{H}^+\)] and high pH.

Understanding pH calculation is vital as it directly connects to the concept of acid strength and dissociation constant. In the problem scenario, knowing that stronger acids lower the pH helps us organize the acids A, B, and C in order of pH.

Monobasic Acids

Monobasic acids are a type of acid that can donate only one hydrogen ion (proton) per molecule to an aqueous solution. This characteristic simplifies calculations and thus the understanding of key concepts like dissociation constant and pH.

• Monobasic: Can release one proton in a series of reactions.
• Useful for pH calculations as they have a straightforward dissociation behavior.

In the context of the exercise with acids A, B, and C, each having the same concentration, the differences in pH arise solely from their respective dissociation constants due to their monobasic nature. The focus, therefore, is firmly on how these acids dissociate, as this determines the overall pH of the solution.