Problem 81 - A Complete Resource Book in Chemistry for JEE Main

Question

An acid solution of \(0.005 \mathrm{M}\) has a \(\mathrm{pH}\) of 5 . The degree of ionization of acid is (a) \(0.1 \times 10^{-2}\) (b) \(0.2 \times 10^{-2}\) (c) \(0.5 \times 10^{-4}\) (d) \(0.6 \times 10^{-6}\)

Step-by-Step Solution

Answer

The degree of ionization of the acid is (b) \(0.2 \times 10^{-2}\).

Step 1: Understand the Problem

The problem involves finding the degree of ionization of an acid solution with a known concentration and pH. Given that the concentration of the acid is \(0.005 \ \mathrm{M}\) and the pH of the solution is 5, we will calculate the concentration of hydrogen ions \([\mathrm{H}^+]\) and use this to find the degree of ionization.

Step 2: Calculate Hydrogen Ion Concentration

The pH is given by the formula \(\mathrm{pH} = -\log[\mathrm{H}^+]\). Substituting the pH of 5 into this equation, we find \([\mathrm{H}^+] = 10^{-5} \ \mathrm{M}\).

Step 3: Determine the Degree of Ionization

The degree of ionization is calculated using the formula \(\alpha = \frac{[\mathrm{H}^+]}{C}\), where \([\mathrm{H}^+]\) is the concentration of hydrogen ions and \(C\) is the initial concentration of the acid. Thus, \(\alpha = \frac{10^{-5}}{0.005} = 0.002\).

Step 4: Choose the Correct Answer

The calculated degree of ionization is \(0.002\), which is equivalent to \(0.2 \times 10^{-2}\). This matches option (b).

Key Concepts

pH Calculation

The concept of pH is fundamental in understanding acidity and alkalinity of solutions. The pH scale ranges from 0 to 14, where a lower pH indicates a higher acidity. In this exercise, we are given a pH of 5, which means the solution is slightly acidic. The formula to calculate pH is given by:\[ \mathrm{pH} = -\log_{10} [\mathrm{H}^+] \]Here,

• pH: potential of hydrogen
• [\mathrm{H}^+]: the hydrogen ion concentration in moles per liter

The logarithmic nature of the scale means that a small change in pH implies a significant change in hydrogen ion concentration. For example, a change of 1 pH unit corresponds to a tenfold change in [H⁺]. For the given solution, substituting pH = 5 into our equation, we can determine [H⁺] by calculating as follows:\[ [\mathrm{H}^+] = 10^{-\mathrm{pH}} = 10^{-5} \text{ M} \]This computation shows us that even a weakly acidic solution has significant implications on the concentration of hydrogen ions.

Hydrogen Ion Concentration

Understanding hydrogen ion concentration is crucial for assessing the acidity of a solution. When the pH of a solution is known, the concentration of hydrogen ions can be derived directly using the formula discussed:\[ [\mathrm{H}^+] = 10^{-\mathrm{pH}} \]For example, with a pH of 5, the concentration of hydrogen ions is:\[ [\mathrm{H}^+] = 10^{-5} \text{ Molar} \]Points to remember when dealing with hydrogen ion concentration:

• Lower pH values correspond to higher hydrogen ion concentrations.
• The concentration is often very small and typically expressed in exponential form (e.g., 10^-5).
• Hydrogen ions originate from acidic dissociation, thereby defining the degree of acidity.

This concentration is critical for further calculations, such as determining the degree of ionization or understanding the chemical behavior of the solution.

Degree of Ionization

The degree of ionization (b1) provides insight into how much of an acid is dissociated into ions in a solution. It's an essential parameter when evaluating the strength and behavior of an acid in solution. The formula for degree of ionization is:\[ \alpha = \frac{[\mathrm{H}^+]}{C} \]Where:

• \([\mathrm{H}^+]\): Hydrogen ion concentration
• C: Initial molar concentration of the acid

For the given problem:\[ \alpha = \frac{10^{-5}}{0.005} = 0.002 \]This tells us that the solution's degree of ionization is 0.002, or equivalently, 0.2%. This calculation helps us understand the extent to which the acid has ionized in solution. A higher degree of ionization indicates a stronger acid. In this example, the low degree implies that it is a weak acid.