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 of the acid is 0.2%.

Step 1: Understand the Problem

We are given a 0.005 M acid solution with a pH of 5. We need to find the percentage ionization of the acid.

Step 2: Calculate the Hydrogen Ion Concentration

The pH is given as 5. We use the formula for pH: \[ \text{pH} = -\log[H^+] \]Rearrange to find \[ [H^+] = 10^{-\text{pH}} = 10^{-5} \]Thus, the concentration of hydrogen ions is \(10^{-5}\) M.

Step 3: Determine the Initial Concentration of the Acid

The initial concentration of the acid before ionization is given as 0.005 M.

Step 4: Calculate the Percentage Ionization

Percentage ionization is calculated using the formula: \[ \text{Percentage Ionization} = \left( \frac{\text{Concentration of ionized acid}}{\text{Initial concentration of acid}} \right) \times 100 \]Substitute the known values: \[ \text{Percentage Ionization} = \left( \frac{10^{-5}}{0.005} \right) \times 100 = \left( \frac{1 \times 10^{-5}}{5 \times 10^{-3}} \right) \times 100 \]Calculate the result: \[ \text{Percentage Ionization} = \left( \frac{1}{500} \right) \times 100 = 0.2\% \]

Step 5: Conclude the Solution

The percentage ionization of the acid is calculated to be 0.2%.

Key Concepts

Understanding Hydrogen Ion Concentration

Hydrogen ion concentration is a key concept in understanding the behavior of acids in solutions. When an acid dissolves in water, it releases hydrogen ions (\[ H^+ \] ), which are responsible for the acidic properties of the solution. The concentration of these ions determines the strength of acidity.

The hydrogen ion concentration is typically expressed in moles per liter (M). This concentration can be calculated using the pH of the solution. The pH is a logarithmic scale, which indicates the acidic or basic nature of a solution.

To find the \[ H^+ \] concentration, we use the formula:\[ [H^+] = 10^{- ext{pH}} \] This mathematical representation allows us to convert a given pH value into the corresponding hydrogen ion concentration. For a solution with a pH of 5, the \[ H^+ \] concentration will be \[ 10^{-5} \] M. This calculation helps in understanding how much of the acid has dissociated in the solution.

The Role of Acid Concentration in Ionization

Acid concentration is the initial concentration of the acid before it undergoes ionization. The degree to which an acid ionizes in solution determines its strength.

In this exercise, we started with an acid concentration of 0.005 M, which represents the amount of acid present in one liter of the solution before it begins to release hydrogen ions.
The percentage ionization is an important factor in evaluating how much of the acid has actually ionized compared to what was originally present. It is calculated with the formula:\[ \text{Percentage Ionization} = \left( \frac{\text{Concentration of ionized acid}}{\text{Initial concentration of acid}} \right) \times 100 \]A higher percentage indicates a stronger acid, which is more likely to ionize completely in solution. Understanding this concept helps students grasp the dynamic nature of acid solutions.

Calculating pH: Its Importance and Application

pH calculation is crucial in the study of chemical properties as it gives insight into the acidity or basicity of a solution.The pH value is derived from the concentration of hydrogen ions, using the equation:\[ \text{pH} = -\log[H^+] \]This expression shows that the pH is inversely related to the concentration of hydrogen ions – the higher the concentration, the lower the pH and, thus, the more acidic the solution.In practical applications, calculating the pH helps predict how an acid behaves in different solutions, which is vital in fields ranging from chemistry to environmental science.For example, with a pH of 5, our solution was slightly acidic. By understanding the pH, one can calculate the hydrogen ion concentration and ultimately determine the degree of ionization and acidity of the solution.This knowledge assists in predicting reactions and ensuring safety in chemical handling.