Problem 109 - A Complete Resource Book in Chemistry for JEE Main

Question

If \(0.1 \mathrm{M}\) of a weak monobasic acid is taken and its percentage degree of ionization is \(1.34 \%\), then calculate its ionization constant (a) \(0.8 \times 10^{-5}\) (b) \(1.79 \times 10^{-5}\) (c) \(0.182 \times 19^{-5}\) (d) none of these

Step-by-Step Solution

Answer

The ionization constant is approximately \(K_a = 1.82 \times 10^{-5}\), matching option (b).

Step 1: Understand the Definition of Degree of Ionization

The percentage degree of ionization is the ratio of the concentration of ionized acid to the initial concentration of the acid, expressed as a percentage. Here, the degree of ionization is given as 1.34%.

Step 2: Convert Percentage to Decimal

To work with equations, convert the percentage degree of ionization to a decimal by dividing by 100. Thus, the degree of ionization is \( \alpha = \frac{1.34}{100} = 0.0134 \).

Step 3: Express the Acid Ionization Reaction

For a weak monobasic acid \( HA \), the ionization can be expressed as \( HA \rightleftharpoons H^+ + A^- \).

Step 4: Calculate the Concentration of Ionized Acid

Using the degree of ionization \( \alpha \), calculate the concentration of ionized acid \( [H^+] = [A^-] = \alpha \times C_0 \), where \( C_0 = 0.1 \) M (initial concentration of the acid). Thus, \( [H^+] = [A^-] = 0.0134 \times 0.1 = 0.00134 \) M.

Step 5: Calculate Equilibrium Concentrations

At equilibrium, the concentration of the acid \( [HA] \) is \( C_0 - [H^+] = 0.1 - 0.00134 = 0.09866 \) M.

Step 6: Apply the Ionization Constant Formula

The ionization constant \( K_a \) for the weak acid is given by \( K_a = \frac{[H^+][A^-]}{[HA]} \). Plug in the values, \( K_a = \frac{(0.00134)(0.00134)}{0.09866} \).

Step 7: Evaluate the Ionization Constant

Calculate \( K_a = \frac{(0.00134)^2}{0.09866} \). This simplifies to \( K_a = \frac{1.7956 \times 10^{-6}}{0.09866} \approx 1.82 \times 10^{-5} \).

Step 8: Match with Provided Options

Match the calculated ionization constant \( K_a \approx 1.82 \times 10^{-5} \) with the given options. It matches option (b) \( 1.79 \times 10^{-5} \).

Key Concepts

Degree of Ionization

The degree of ionization is a measure of the fraction of a substance that dually separates into ions in a solution. For monobasic acids, it reflects how much acid dissociates into hydrogen ions \( H^+ \)and conjugate base ions.

• It is often expressed as a percentage of the original substance.
• In this exercise, we have a degree of ionization of \(1.34\%\).

To use this in equations, it must be converted to a decimal, which is done by dividing by \(100\). Thus, the degree of ionization is \(\alpha = \frac{1.34}{100} = 0.0134\).
This value is pivotal when determining how much of the acid starts to ionize compared to its initial concentration.

Weak Monobasic Acid

A weak monobasic acid is an acid that does not completely ionize in solution. This means when dissolved in water, only a small portion of the acid dissociates into ions.

• Monobasic suggests the acid releases one hydrogen ion \( H^+ \) per molecule.
• Common examples include acetic acid \( \text{CH}_3\text{COOH} \).

This concept is relevant in our exercise as we are dealing with a \(0.1 \text{ M}\)solution of a weak monobasic acid.

Acid Ionization Reaction

In the case of a weak monobasic acid \(HA\)it can be expressed as:
\[ HA \rightleftharpoons H^+ + A^- \]Here, equilibrium is reached with a mix of ionized and unionized molecules.

Equilibrium Concentrations

Equilibrium concentrations refer to the balance point in a reversible reaction where both the forward and reverse reactions occur at the same rates.

• The concentrations of reactants and products remain constant.
• In our context, it involves the balance of acid \(HA\), ions \(H^+ \), and \(A^- \).

Calculation of Equilibrium Concentrations

For a weak acid, the degree of ionization helps determine these concentrations:

• Ionized concentration of hydrogen and conjugate base: \( [H^+] = [A^-] = \alpha \times C_0 = 0.00134 \text{ M}\).
• Remaining concentration of acid: \([HA] = C_0 - [H^+] = 0.09866 \text{ M}\).

Ionization Constant Formula

Using equilibrium concentrations, the ionization constant \(K_a\) is calculated:
\( K_a = \frac{[H^+][A^-]}{[HA]} \).
For our calculation: \[ K_a = \frac{(0.00134)^2}{0.09866} \approx 1.82 \times 10^{-5} \].
This indicates the strength of the weak acid in water.