Question

Complete and balance the following reaction: Write the equilibrium expression for the \(K_{\mathrm{a}}\) of HOCl.

Short answer

The balanced chemical reaction for the dissolution of HOCl is: HOCl (aq) + H2O (l) \(\leftrightarrow\) H3O+ (aq) + OCl- (aq). And the equilibrium expression for the \(K_{\mathrm{a}}\) of HOCl is \(K_{\mathrm{a}}\) = \([H3O^+][OCl^-] / [HOCl]\).

Step-by-step solution

Write Reaction

First, write the chemical reaction that occurs when HOCl (hypochlorous acid) dissolves in water. It dissociates into H+ ions and OCl- ions. Therefore, the reaction is: HOCl (aq) + H2O (l) \(\leftrightarrow\) H3O+ (aq) + OCl- (aq)

Balance Chemical Reaction

In this case, the chemical reaction is already balanced. There is no need to add any coefficients.

Write Equilibrium Expression

The next step is to write the equilibrium expression for \(K_{\mathrm{a}}\) of HOCl. The \(K_{\mathrm{a}}\) expression for any weak acid is written by placing the concentrations of the products in the numerator and the concentrations of the reactants in the denominator. However, the concentration of water is usually not included in the equation as it essentially remains constant. Therefore, the expression becomes: \(K_{\mathrm{a}}\) = \([H3O^+][OCl^-] / [HOCl]\)

Key concepts

Acid Dissociation Constant

Understanding the acid dissociation constant, usually represented as K_a, is integral to comprehending acid-base chemistry. It's a quantitative measure of the strength of an acid in solution, signifying the acid's ability to donate protons to the solution.

For a general weak acid, represented by HA, the dissociation in water can be written as follows: $$ HA + H_2O \rightleftharpoons H_3O^+ + A^- $$.
The K_a expression for this generic weak acid becomes: $$ K_a = \frac{[H_3O^+][A^-]}{[HA]} $$.
Here, square brackets signify the molar concentrations of the ions and the undissociated acid. A higher value of K_a indicates a stronger acid, implying it donates protons more readily, and thus, a larger amount of the acid is dissociated at equilibrium. On the other hand, a smaller K_a value is characteristic of a weaker acid, with less tendency to part with its proton. Water is omitted from this expression because it is the solvent and its concentration remains relatively constant compared to the changes in concentrations of the acid and its ions.

Balancing Chemical Reactions

Balancing chemical reactions is a foundational skill in chemistry that ensures the law of conservation of mass is maintained. This law states that matter can neither be created nor destroyed.

To balance a chemical reaction, one must make certain that the number of atoms of each element on the reactants side is equal to the number of atoms of that element on the products side. For simple reactions, this often involves adjusting the coefficients of reactants and products to match the atomic inventory. Let's take the previous example of the weak acid HA: $$ HA + H_2O \rightleftharpoons H_3O^+ + A^- $$.
In this case, we can verify, atom by atom, that the reaction is balanced as written: each side has one atom of hydrogen (not counting the water molecule), and one atom from the acid group A. No coefficients need to be adjusted.

For more complex reactions, systematically addressing each element and imposing stoichiometric coefficients becomes necessary. Balancing reactions ensures that the subsequent calculations, such as determining reaction yield or equilibrium concentrations, are grounded in physically meaningful quantities.

Weak Acid Behavior

Weak acids are distinguished from strong acids by their incomplete dissociation in water. Unlike strong acids, which release all of their hydrogen ions into solution, weak acids establish an equilibrium between the undissociated acid and the ions produced.

This behavior can be described in the context of the dissociation reaction: $$ HA_{(aq)} \rightleftharpoons H^+_{(aq)} + A^-_{(aq)} $$.
A weak acid, such as HOCl, only partially dissociates, meaning in a solution of HOCl, a significant amount of the molecules remain intact as HOCl. This continuous dynamic where the dissociated H⁺ (which in presence of water is better referred to as H₃O⁺) and A^- recombine to form HA and vice versa leads to an equilibrium state, characterized by the acid dissociation constant K_a.

In this state, no further net change in the concentration of reactants and products occurs, and the K_a reflects the ratio of the concentrations of products to reactants. The behavior of weak acids is central to buffering capacity and pH stabilization in biological and environmental systems.