Problem 17 - Chemistry A Molecular Approach

Question

In most solutions containing a strong or weak acid, the autoionization of water can be neglected when calculating \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right] .\) Explain why this statement is valid.

Step-by-Step Solution

Answer

The contribution of \(H_3O^+\) from water autoionization is negligible compared to that from strong or weak acids due to the much higher concentration of hydronium ions produced by the acids.

Step 1: Understanding the Concept of Autoionization of Water

Water can undergo autoionization where two water molecules react to form a hydronium ion (\(H_3O^+\) and a hydroxide ion (\(OH^-\) ). The equilibrium constant for this reaction is very small (\(K_w = 1 \times 10^{-14}\) at 25°C), indicating it's a rare event at neutral pH.

Step 2: Comparing Acid Ionization and Water Autoionization

For strong acids, they almost completely dissociate in water, contributing a significant concentration of hydronium ions, much greater than what is contributed by autoionization. For weak acids, even though they do not fully dissociate, the equilibrium concentration of hydronium ions is still usually much greater than that from autoionization of water.

Step 3: Neglecting Water Autoionization in Acidic Solutions

Since the contribution of hydronium ions from the strong or weak acid far exceeds that from the water autoionization, the latter's contribution to the overall \(H_3O^+\) concentration can be considered negligible in most cases when calculating the pH of acidic solutions.

Key Concepts

Acid Dissociation

Acid dissociation is a critical concept in chemistry that involves the separation of an acid into its constituent ions in water. The process is represented by the general equation:
\( HA \rightleftharpoons H^+ + A^- \).
Here, \( HA \) is the acid that dissociates into a proton (\( H^+ \)) and its conjugate base (\( A^- \)). The extent to which this dissociation occurs depends on the acid's strength. Strong acids, like hydrochloric acid (\( HCl \)), dissociate almost completely, contributing a significant concentration of hydronium ions (\( H_3O^+ \)) to the solution. Weak acids, like acetic acid (\( CH_3COOH \)), partially dissociate, contributing fewer hydronium ions relative to strong acids. Understanding this principle helps explain why the autoionization of water is often negligible when dealing with solutions of strong or weak acids.

Hydronium Ion Concentration

The concentration of hydronium ions (\( [H_3O^+] \)) in a solution is a key factor in determining the solution's acidity. It directly affects the pH, which is a measure of the solution's acidity or basicity. In pure water at 25°C, the concentration of \( [H_3O^+] \) and hydroxide ions (\( [OH^-] \)) is equal, leading to a neutral pH of 7. When acids are introduced to water, they increase the \( [H_3O^+] \) by releasing more hydrogen ions that combine with water to form hydronium ions. This increase is much more significant when strong acids are dissolved in water due to their high dissociation, which is why the comparatively minimal contribution of \( [H_3O^+] \) from water's autoionization becomes negligible.

Equilibrium Constant

The equilibrium constant of a chemical reaction quantifies the ratio of product concentrations to reactant concentrations at equilibrium. In the context of autoionization of water, the equilibrium constant is known as the ionic product of water (\( K_w \)). At 25°C, \( K_w \) has a value of \( 1 \times 10^{-14} \), calculated as the product of the concentrations of hydronium and hydroxide ions:
\( K_w = [H_3O^+][OH^-] \).
This extremely low value means that, at equilibrium, the concentrations of hydronium and hydroxide ions in pure water are each \( 1 \times 10^{-7} \) M, resulting in a neutral pH. When an acid is added, however, this reaction is shifted, substantially increasing the hydronium ion concentration and thereby reducing the impact of autoionization on the overall acidity of the solution.

Acidic Solutions pH Calculation

Calculating the pH of an acidic solution typically requires knowledge of the hydronium ion concentration. The pH is calculated using the formula:
\( pH = -\text{log}[H_3O^+] \).
In the presence of an acid, the hydronium ion concentration increases, resulting in a lower pH, which indicates a more acidic solution. Since acids contribute more significantly to the \( [H_3O^+] \) than the autoionization of water does, the latter can often be ignored in pH calculations for acidic solutions. In practice, this simplifies calculations and is a useful approximation, given that the contribution from water's autoionization is typically insignificant compared to that from even weak acids in solution.