Problem 98 - A Complete Resource Book in Chemistry for JEE Main

Question

\(0.005 \mathrm{M}\) acid solution has \(5 \mathrm{pH}\). The percentage ionization of acid is (a) \(0.8 \%\) (b) \(0.6 \%\) (c) \(0.4 \%\) (d) \(0.2 \%\)

Step-by-Step Solution

Answer

The percentage ionization is 0.2%, so the correct answer is (d) 0.2%.

Step 1: Understand the relationship between pH and [H+]

The pH of a solution is defined as the negative logarithm (base 10) of the hydrogen ion concentration \([H^+]\). Therefore, if we know that the pH is 5, we can calculate \([H^+]\) using the formula: \[pH = -\log_{10}[H^+]\] Rearranging this gives: \[[H^+] = 10^{-pH}\] Substituting 5 for the pH, we get: \[[H^+] = 10^{-5} = 0.00001 \, \text{M} \]

Step 2: Calculate the degree of ionization

The percentage ionization is calculated by using the formula: \[\text{Percentage Ionization} = \left(\frac{[H^+]}{\text{Initial }[HA]}\right) \times 100\%\] Where \([H^+]\) is the concentration of ionized hydrogen ions and \([HA]\) is the initial concentration of the acid. Here, \([HA] = 0.005 \text{ M}\) and \([H^+] = 0.00001 \text{ M}\). Substituting these values gives: \[\text{Percentage Ionization} = \left(\frac{0.00001}{0.005}\right) \times 100\%\] This simplifies to:\[\text{Percentage Ionization} = 0.2\%\]

Step 3: Choose the correct answer from the options

Based on the calculation, the percentage ionization of the acid is \(0.2\%\). Matching this value with the provided options, we find that option (d) \(0.2\%\) is the correct answer.

Key Concepts

pH Calculation

The pH of a solution is a measure of its acidity or basicity. This value is determined using the concentration of hydrogen ions present in the solution. The relationship between pH and hydrogen ion concentration \([H^+]\) is given by the formula:

• \(pH = -\log_{10}[H^+]\)

The smaller the pH number, the higher the concentration of hydrogen ions, indicating a more acidic solution. Conversely, a higher pH suggests a more basic solution with fewer hydrogen ions.
For example, if the pH of a solution is 5, you can find the hydrogen ion concentration by rearranging the formula to solve for \([H^+]\):

• \([H^+] = 10^{-pH}\)

Substituting the pH value into this formula gives us a hydrogen ion concentration of \(0.00001 \, \text{M}\). Thus, understanding and calculating pH is essential in determining the ionization and strength of an acid.

Percentage Ionization

Percentage ionization refers to the extent to which an acid dissociates in a solution. It provides insight into the strength of the acid: the higher the percentage, the stronger the acid at a given concentration. This is calculated using the formula:

• \[\text{Percentage Ionization} = \left(\frac{[H^+]}{\text{Initial }[HA]}\right) \times 100\%\]

In this formula, \([H^+]\) is the concentration of ionized hydrogen ions, and \([HA]\) is the initial concentration of the non-ionized acid.
For instance, with an initial acid concentration of \(0.005 \, \text{M}\) and \([H^+]\) of \(0.00001 \, \text{M}\), the percentage ionization will be calculated as:

• \[\text{Percentage Ionization} = \left(\frac{0.00001}{0.005}\right) \times 100\%\]

This results in a percentage ionization of \(0.2\%\). Therefore, understanding percentage ionization is crucial for assessing how much an acid ionizes in solution.

Hydrogen Ion Concentration

Hydrogen ion concentration \([H^+]\) is a fundamental aspect of acid-base chemistry. It directly relates to the pH scale, given that the pH is determined by the concentration of hydrogen ions in a solution.

• Higher concentrations of \([H^+]\) result in a lower pH, indicating more acidity.
• Lower concentrations lead to a higher pH, suggesting more basicity.

In practical terms, knowing the hydrogen ion concentration allows chemists to understand how "strong" or "weak" an acid or base may be. For instance, in the original problem, with a calculated \([H^+]\) of \(0.00001 \, \text{M}\) corresponding to a pH of 5, we gain insight into the acid's dissociation in water.
The ability to determine \([H^+]\) is vital in several applications, from laboratory experiments to industrial processes, where precise control of acidity is required.