Equilibrium Constant for the Reaction of a Weak Acid with a Strong Base

Introduction
The equilibrium constant, also known as the acid dissociation constant (Ka), represents the extent to which a weak acid dissociates into its ions in a solution. It is a measure of the acid's strength. In this case, we are given that the dissociation constant of a certain weak acid is 1 × 10^-4.

Explanation

Dissociation of a Weak Acid
When a weak acid (HA) dissolves in water, it partially dissociates into its conjugate base (A-) and hydrogen ions (H+). This can be represented by the following equation:

HA ⇌ H+ + A-

The dissociation constant (Ka) is defined as the ratio of the concentration of the products (H+ and A-) to the concentration of the reactant (HA) at equilibrium. Mathematically, it can be expressed as:

Ka = [H+][A-] / [HA]

Given that the dissociation constant of the weak acid is 1 × 10^-4, we can substitute this value into the equation:

1 × 10^-4 = [H+][A-] / [HA]

This equation represents the equilibrium expression for the dissociation of the weak acid.

Reaction with a Strong Base
When the weak acid reacts with a strong base (such as sodium hydroxide, NaOH), a neutralization reaction occurs. The base accepts the hydrogen ion (H+) from the acid, forming water and the corresponding salt. The balanced equation for the reaction is:

HA + NaOH → H2O + NaA

In this reaction, the weak acid (HA) is converted into its conjugate base (A-), and the strong base (NaOH) is converted into water (H2O) and the salt (NaA).

Equilibrium Constant for the Reaction
The equilibrium constant for the reaction between the weak acid and the strong base can be obtained by considering the balanced equation. Since water (H2O) is a pure liquid, its concentration remains constant and is not included in the equilibrium expression. Therefore, the equilibrium constant (Kc) for the reaction can be expressed as:

Kc = [NaA] / [HA]

The concentration of the salt (NaA) and the weak acid (HA) can be determined experimentally. By substituting these values into the equation, we can calculate the equilibrium constant (Kc) for the reaction.

Conclusion
The equilibrium constant for the reaction of a weak acid with a strong base can be determined by considering the dissociation constant of the weak acid and the balanced equation for the reaction. By substituting the appropriate values into the equilibrium expressions, we can calculate the equilibrium constant.