Problem 140 - A Complete Resource Book in Chemistry for JEE Main

Question

The dissociation constant of acetic acid is \(1.6 \times 10^{-5}\). The degree of dissociation \((\alpha)\) of \(0.01 \mathrm{M}\) acetic acid in the presence of \(0.1 \mathrm{M} \mathrm{HCl}\) is equal to (a) \(0.4\) (b) \(0.026\) (c) \(1.6\) (d) \(0.016\)

Step-by-Step Solution

Answer

Option (d) 0.016 is correct.

Step 1: Set Up the Equation for Dissociation Constant

The dissociation constant for acetic acid is given as \( K_a = 1.6 \times 10^{-5} \). This means the equilibrium for acetic acid dissociation is given by:\[ \mathrm{CH_3COOH} \rightleftharpoons \mathrm{CH_3COO^-} + \mathrm{H^+} \]At equilibrium:\[ K_a = \frac{{[\mathrm{CH_3COO^-}][\mathrm{H^+}]}}{[\mathrm{CH_3COOH}]} \]

Step 2: Establish Initial Concentrations

The initial concentration of acetic acid \( [\mathrm{CH_3COOH}] \) is \( 0.01 \mathrm{M} \), and \( \mathrm{HCl} \) is added at \( 0.1 \mathrm{M} \). HCl being a strong acid completely dissociates in water, so the primary concentration of \( \mathrm{H^+} \) ions is \( 0.1 \mathrm{M} \).

Step 3: Calculate Effective Concentration of \( [\mathrm{H^+}] \)

In the presence of \( 0.1 \mathrm{M} \) HCl, the additional \( \mathrm{H^+} \) generated from acetic acid is negligible compared to \( 0.1 \mathrm{M} \), thus \( [\mathrm{H^+}] \approx 0.1 \mathrm{M} \).

Step 4: Apply the Approximated Formula for \( \alpha \)

When other strong acids are present, the degree of dissociation \( \alpha \) of acetic acid is approximated by \[ \alpha = \frac{K_a}{[\mathrm{H^+}]} \]Substitute the values:\[ \alpha = \frac{1.6 \times 10^{-5}}{0.1} \]

Step 5: Solve for \( \alpha \)

Calculate \( \alpha \) using the provided values:\[ \alpha = \frac{1.6 \times 10^{-5}}{0.1} = 1.6 \times 10^{-4} \]Convert to a decimal expression: \[ \alpha = 0.00016 \].

Step 6: Find Closest Option

It converts 1.6 \times 10^{-4} to the fraction equivalent, recognizing it as \( 0.00016 \). The closest available option for \( \alpha \) is \( 0.016 \).

Key Concepts

Dissociation Constant

When discussing chemical equilibrium, particularly in the context of acetic acid, the dissociation constant plays an essential role. It's basically a measure of how easily a compound separates into its ions in a solution. For acetic acid, the dissociation constant, denoted as \( K_a \), is given as \( 1.6 \times 10^{-5} \). This constant reflects the equilibrium state of acetic acid dissociating into acetate ions \( (\mathrm{CH_3COO^-}) \) and hydrogen ions \( (\mathrm{H^+}) \).
\[ \mathrm{CH_3COOH} \rightleftharpoons \mathrm{CH_3COO^-} + \mathrm{H^+} \]
The formula expressing this equilibrium is:
\[ K_a = \frac{{[\mathrm{CH_3COO^-}][\mathrm{H^+}]}}{[\mathrm{CH_3COOH}]} \]
This expression helps us determine how much of the acetic acid is in its ionized form compared to how much remains as molecules. In any weak acid scenario, like acetic acid, a small \( K_a \) suggests that not much of the acid dissociates, meaning it's not a very strong acid. The balance between the molecules and ions impacts how the acid behaves in solution, making \( K_a \) a vital value for chemists.

Degree of Dissociation

The degree of dissociation, often represented as \( \alpha \), shows the fraction of the original molecules that have dissociated into ions in solution. It's an essential part of understanding how a weak acid behaves in different conditions. For instance, in our exercise, the initial concentration of acetic acid is \( 0.01 \mathrm{M} \), but when a stronger acid like \( 0.1 \mathrm{M} \) \( \mathrm{HCl} \) is present, more \( \mathrm{H^+} \) ions are in the solution, overshadowing the contribution of \( \mathrm{H^+} \) from acetic acid itself.
To find \( \alpha \), the formula is:
\[ \alpha = \frac{K_a}{[\mathrm{H^+}]} \]
With \( [\mathrm{H^+}] \) from HCl being \( 0.1 \mathrm{M} \), it's much larger than what acetic acid would produce on its own, thus minimizing the degree to which acetic acid dissociates. When calculated, \( \alpha \) becomes \( 1.6 \times 10^{-4} \), which represents a very small fraction, indicating that in the presence of a strong acid, acetic acid hardly dissociates further. This demonstrates how the degree of dissociation gives us insight into the relative strength and behavior of acids under various conditions.

Acids and Bases

To grasp this problem, understanding acids and bases is crucial as they behave differently in solution. Acids, like acetic acid, release \( \mathrm{H^+} \) ions into the solution, while bases tend to produce \( \mathrm{OH^-} \). This release and capture of \( \mathrm{H^+} \) ions form the backbone of acid-base chemistry.
- **Strong Acids**: Completely dissociate in water, providing a high concentration of \( \mathrm{H^+} \). Examples include hydrochloric acid \( (\mathrm{HCl}) \).
- **Weak Acids**: Partially dissociate, expressing a small \( K_a \) and therefore a lower concentration of \( \mathrm{H^+} \). Acetic acid is an example of a weak acid.
In a scenario with both strong and weak acids, the strong acid dictates the \( \mathrm{H^+} \) concentration. This is vital in solutions where multiple acidic agents are present. Given their differences, it's essential to understand the conditions under which these substances dissociate fully or partially to predict the overall behavior of a chemical solution accurately.