Problem 90 - A Complete Resource Book in Chemistry for JEE Main

Question

Ionization constant of acetic acid is \(1.8 \times 10^{-5}\). The concentration of \(\mathrm{H}^{+}\)ions in \(0.1 \mathrm{M}\) solution is (a) \(1.8 \times 10^{-3} \mathrm{M}\) (b) \(1.8 \times 10^{-5} \mathrm{M}\) (c) \(1.3 \times 10^{-3} \mathrm{M}\) (d) \(1.34 \times 10^{-3} \mathrm{M}\)

Step-by-Step Solution

Answer

The concentration of \(\text{H}^+\) ions is \(1.3 \times 10^{-3} \text{ M}\).

Step 1: Write the Ionization Reaction

The ionization of acetic acid (\[ \text{CH}_3\text{COOH} \rightleftharpoons \text{CH}_3\text{COO}^- + \text{H}^+ \]represents the equilibrium where acetic acid dissociates into acetate ions and hydrogen ions.

Step 2: Define the Ionization Constant Expression

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Step 3: Set Up Initial Concentrations

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Key Concepts

Acetic acid

Acetic acid, commonly known by its formula \( \text{CH}_3\text{COOH} \), is a colorless liquid organic compound that imparts the sour taste and pungent smell of vinegar. It is one of the simplest carboxylic acids and plays a critical role in many chemical processes in both organic and inorganic chemistry.
In its aqueous solution, acetic acid can undergo ionization where it dissociates into hydrogen ions (\( \text{H}^+ \)) and acetate ions (\( \text{CH}_3\text{COO}^- \)). This dissociation is fundamental in explaining the acid's weak acidic behavior, meaning it does not completely dissociate in water. Unlike strong acids, only a small fraction of acetic acid molecules release \( \text{H}^+ \) ions into the solution at equilibrium, making it a weak acid.
Useful in a variety of industrial and household contexts, acetic acid's ability to ionize makes it an essential compound for chemical reactions that require a precise pH control.

Hydrogen ions

In chemistry, hydrogen ions (\( \text{H}^+ \)) are fundamental to understanding acidity and pH in solutions. When an acid like acetic acid dissociates, it releases \( \text{H}^+ \) ions which significantly affect the pH of the solution. The concentration of these ions is vital to expressing how acidic a solution is.
Acids, by definition, are substances that can donate \( \text{H}^+ \) ions. The number of \( \text{H}^+ \) ions present in a solution is measured on the pH scale, which typically ranges from 0 to 14. In this scale, a pH less than 7 indicates acidity, while a pH greater than 7 indicates basicity. Acetic acid, as a weak acid, only partially releases its \( \text{H}^+ \) ions.

• The degree of dissociation of these ions is described by the ionization constant.
• This constant helps predict the concentration of \( \text{H}^+ \) ions at equilibrium.

Hence, understanding \( \text{H}^+ \) concentrations allows chemists to calculate the pH and other related properties of solutions.

Equilibrium reaction

An equilibrium reaction occurs when the forward and reverse reactions happen at the same rate, resulting in no net change in the concentration of reactants and products over time. In the ionization of acetic acid, the reaction can be written as:
\[ \text{CH}_3\text{COOH} \rightleftharpoons \text{CH}_3\text{COO}^- + \text{H}^+ \]
This equation shows that acetic acid is in a dynamic equilibrium with its ionized form. At equilibrium, the rate at which acetic acid dissociates into acetate and hydrogen ions is equal to the rate at which these ions recombine to form acetic acid.

• The equilibrium constant for this reaction, known as the ionization constant \( K_a \), quantifies the extent of ionization.
• A small \( K_a \) value, like \( 1.8 \times 10^{-5} \), indicates that only a small fraction of acetic acid is ionized.

This behavior is typical of weak acids, where the equilibrium lies heavily on the side of the non-dissociated acid. Understanding equilibrium reactions is key in predicting how different conditions, like concentration and temperature, affect chemical reactions.