Problem 15 - A Complete Resource Book in Chemistry for JEE Main

Question

A centinormal solution of a monobasic acid is \(100 \%\) ionized. Its \(\mathrm{pH}\) is (a) 2 (b) 4 (c) 3 (d) 1

Step-by-Step Solution

Answer

The pH is 2.

Step 1: Understand the Centinormal Solution

A centinormal ( 1/100 normal) solution means that the molarity is 0.01 M, because normality corresponds to molarity for monobasic acids (one hydrogen ion per molecule).

Step 2: Recognize the 100% Ionization

Since the acid is 100 % ionized, it fully dissociates in water, thus, the concentration of hydrogen ions [ H^+ ] will be equal to the concentration of the acid ( 0.01 M ).

Step 3: Calculate the pH

The pH can be calculated using the formula: \[ ext{pH} = -\log[H^+] \]Given [a=H^+]=0.01 M, substitute to find: ext{pH} = -\log(0.01) = 2.

Key Concepts

Ionization of Acids

Ionization refers to the process by which an acid dissociates in water to produce hydrogen ions (\( H^+ \)) and its corresponding anions. For monobasic acids, each molecule releases exactly one \( H^+ \) ion in solution. This is an important concept, because the degree of ionization determines how much the acid impacts the acidity of a solution.
When an acid is said to be 100% ionized, it means every molecule of the acid has contributed a \( H^+ \) to the solution. Monobasic acids, such as hydrochloric acid (HCl), exhibit complete ionization in water, resulting in a direct representation of their concentration as \( [H^+] \), or the concentration of hydrogen ions.

• Partial Ionization: Weak acids, in contrast, do not fully dissociate, resulting in equilibrium between the undissociated acid and the ions produced.
• Complete Ionization: Strong acids fully dissociate and determine the \( [H^+] \) in the solution.

Fully understanding the ionization of acids is vital for calculating other parameters such as pH and helps predict the reaction behavior of acidic solutions.

Normality and Molarity

Normality and molarity are both measures of concentration, but they are not always equivalent. Understanding the difference is vital, especially when dealing with acid-base reactions.

• Molarity (M): This is defined as the number of moles of solute per liter of solution. For monobasic acids, molarity directly equals the concentration of hydrogen ions it can provide.
• Normality (N): This is the concentration expressed as the number of equivalent weights per liter of solution. For acids, equivalents are determined by the number of \( H^+ \) ions an acid can furnishper molecule.

For monobasic acids, normality and molarity are numerically the same because each molecule contributes exactly one \( H^+ \). In the case of the centinormal solution in the problem, the normality is 0.01 N, which is equivalent to a molarity of 0.01 M. This equivalence eases the calculation of hydrogen ion concentration and further affects pH calculations.

Hydrogen Ion Concentration

Hydrogen ion concentration \( [H^+] \) in a solution is a determinant of the solution's acidity. In the context of pH calculations, it is crucial to know \( [H^+] \) in order to find the pH of a solution.
In the original exercise, the concentration of \( [H^+] \) is directly equal to the molarity of the acid due to complete ionization. Therefore, \( [H^+] = 0.01 \text{ M} \).

• Significance of \( [H^+] \): Knowing \( [H^+] \) is essential for pH calculations. The pH reflects the acidity level of a solution, with lower values indicating higher acidity.
• pH Formula: The pH can be calculated using the formula: \( \text{pH} = -\log[H^+] \). Thus, a higher concentration of hydrogen ions results in a lower pH.

Understanding hydrogen ion concentration facilitates the use of the pH formula and provides insight into the chemical behavior of the solution in various chemical and biological processes.