Problem 53 - Chemistry The Molecular Science

Question

Write the ionization equation for a weak acid and the equation for its conjugate base reaction with water. Show that adding these two equations gives the autoionization equation for water.

Step-by-Step Solution

Answer

Adding the weak acid ionization and conjugate base reaction gives water's autoionization equation: \( 2\text{H}_2\text{O} \rightleftharpoons \text{H}_3\text{O}^+ + \text{OH}^- \).

Step 1: Write the Ionization Equation for Weak Acid

Consider a weak acid, represented as HA. When it dissolves in water, it partially ionizes into its conjugate base, A⁻, and a H⁺ ion. The equation for this ionization is: \[ \text{HA(aq)} + \text{H}_2\text{O} \rightleftharpoons \text{H}_3\text{O}^+ + \text{A}^- \].

Step 2: Write the Equation for Conjugate Base Reaction

The conjugate base of the weak acid, A⁻, can react with water to reform the weak acid and produce hydroxide ions \( \text{OH}^- \). The equation for this reaction is: \[ \text{A}^- + \text{H}_2\text{O} \rightleftharpoons \text{HA(aq)} + \text{OH}^- \].

Step 3: Add the Two Equations

Add the two equations from Steps 1 and 2 together. The equations are:\( \text{HA(aq)} + \text{H}_2\text{O} \rightleftharpoons \text{H}_3\text{O}^+ + \text{A}^- \) and \( \text{A}^- + \text{H}_2\text{O} \rightleftharpoons \text{HA(aq)} + \text{OH}^- \).When added together, the \( \text{HA(aq)} \) and \( \text{A}^- \) terms cancel each other out, leading to the equation: \[ \text{2H}_2\text{O} \rightleftharpoons \text{H}_3\text{O}^+ + \text{OH}^- \].

Step 4: Interpretation of the Result

The resulting equation, \( \text{2H}_2\text{O} \rightleftharpoons \text{H}_3\text{O}^+ + \text{OH}^- \), is the well-known autoionization of water equation, which shows that water can ionize into hydronium and hydroxide ions, maintaining a balance of hydrogen ion concentration.

Key Concepts

Conjugate Base Reaction

In chemistry, when we talk about a conjugate base, it's the form that remains after an acid has donated a hydrogen ion (H⁺). In the case of a weak acid like HA, when it ionizes in water, it forms its conjugate base, A⁻, along with a hydronium ion (H₃O⁺).
In the conjugate base reaction, this A⁻ doesn't just sit around. Rather, it has the potential to interact with water again. During this interaction, it picks up a hydrogen ion from the water. This gives rise to the original weak acid (HA) and a hydroxide ion (OH⁻).
In simplified terms, think of it as a reversible dance between the acid, its conjugate base, and water. They swap partners and roles, which keeps the system lively and in balance! The equation for this reaction is:

• A⁻ + H₂O ↔ HA(aq) + OH⁻

Autoionization of Water

Water is unique. It has the ability to ionize on its own in a phenomenon known as autoionization. This is where two molecules of water interact with each other.
One water molecule donates a hydrogen ion to the other, forming a hydronium ion (H₃O⁺) and a hydroxide ion (OH⁻). This is a reversible reaction, and thus it's a dynamic process that is constantly occurring in water.

• The overall equation for this process is: 2H₂O ↔ H₃O⁺ + OH⁻

In pure water, this autoionization happens at a very low rate, with equal amounts of H₃O⁺ and OH⁻ being formed. This balance is critical because it lays the foundation for understanding the pH of neutral water. Even though the extent is tiny, it serves as a fundamental basis for acid-base chemistry.

Chemical Equilibrium

Chemical equilibrium is a state where the forward and reverse reactions happen at equal rates. In such a state, the concentrations of the reactants and products remain constant over time.
Take the example of a weak acid in water. The acid, HA, partially ionizes to produce hydronium ions (H₃O⁺) and its conjugate base (A⁻).
Simultaneously, the conjugate base can revert back to the acid by reacting with water, forming hydroxide ions. Even though both reactions continue to happen, they do so at the same rate, leading to a stable balance.

• The reactions can be represented as:
  • HA(aq) + H₂O ↔ H₃O⁺ + A⁻
  • A⁻ + H₂O ↔ HA(aq) + OH⁻
• Adding these equations results in the autoionization of water equation: 2H₂O ↔ H₃O⁺ + OH⁻

The concept of equilibrium is integral in understanding how reactions reach a state where they appear static to an observer, even though molecular happenings are as vibrant as ever. This state helps in predicting the extent of reactions, optimizing conditions, and analyzing yields in chemical processes.