Problem 126 - Introductory Chemistry Atoms First

Question

True or false? Even in a very basic aqueous solution, there are some \(\mathrm{H}_{3} \mathrm{O}^{+}\) ions present. Explain your answer.

Step-by-Step Solution

Answer

True. Even in a very basic aqueous solution, there are some H3O+ ions present. This is because the autoionization of water results in the formation of both H3O+ and OH- ions, maintaining a constant ion product (Kw) at a specific temperature. Even when the concentration of OH- ions is high, the concentration of H3O+ ions cannot become zero, as it would violate the constant Kw value.

Step 1: Understand Water Autoionization (Dissociation)

In aqueous solutions, water molecules can undergo a process called autoionization or dissociation. In this process, a water molecule loses a proton (H+) to another water molecule, leading to the formation of a hydroxide ion (OH-) and a hydronium ion (H3O+). The reaction can be represented as follows: \[2H_{2}O \rightleftharpoons H_{3}O^{+} + OH^{-}\]

Step 2: Discuss the Equilibrium Constant for Water Dissociation

Since the dissociation of water is a reversible process, it has an equilibrium constant called the ion product of water (Kw). Kw is the product of the concentrations of H3O+ and OH- in a neutral aqueous solution at a specific temperature. At 25°C, the value of Kw is approximately \(1 \times 10^{-14}\). So: \[K_{w} = [H_{3}O^{+}][OH^{-}] = 1 \times 10^{-14}\]

Step 3: Evaluate H3O+ and OH- Concentrations in a Basic Solution

A basic aqueous solution has a greater concentration of OH- ions than H3O+ ions, hence making the solution basic. Since the ion product of water (Kw) must remain constant at a specific temperature: \[[H_{3}O^{+}] = \frac{K_{w}}{[OH^{-}]}\] Even when the concentration of OH- ions is high in a basic solution, the concentration of H3O+ ions cannot become zero because then, the ion product of water (Kw) would not be constant.

Step 4: Conclusion

It is true that even in a very basic aqueous solution, there are some H3O+ ions present. The autoionization of water always results in the formation of both H3O+ and OH- ions, maintaining a constant ion product (Kw) at a specific temperature.

Key Concepts

Hydronium Ion

In aqueous solutions, hydronium ions, represented as \(\mathrm{H}_{3} \mathrm{O}^{+}\), are a key player in understanding the acidity and basicity of the solution. When water autoionizes, it self-ionizes to form both \(\mathrm{H}_{3} \mathrm{O}^{+}\) and hydroxide ions \(\mathrm{OH}^{-}\). This implies that even in pure water, without any added acids or bases, these ions are present in equilibrium.

To visualize this, consider the interaction between water molecules: a proton \(\mathrm{H}^{+}\) is transferred from one molecule to another, creating \(\mathrm{H}_{3} \mathrm{O}^{+}\). This dynamic process showcases why water acts as both a very weak acid and a weak base.

• The concentration of hydronium ions in neutral water at 25°C is approximately \(1 \times 10^{-7} \text{M}\).
• The presence of \(\mathrm{H}_{3} \mathrm{O}^{+}\) determines the acidity of a solution.
• More \(\mathrm{H}_{3} \mathrm{O}^{+}\) than \(\mathrm{OH}^{-}\) results in an acidic solution, and vice versa.

Equilibrium Constant

The concept of equilibrium constant is crucial in the context of chemical reactions that reach a state where the reactants and products are no longer changing in concentration over time. For water autoionization, the equilibrium is particularly noteworthy. The balanced equation for this process is \[ 2\mathrm{H}_2\mathrm{O} \rightleftharpoons \mathrm{H}_3\mathrm{O}^+ + \mathrm{OH}^- \], indicating both forward and reverse reactions happen simultaneously.

The equilibrium constant for this reaction is termed the ion product of water, denoted as \(K_w\). At 25°C, \(K_w\) has a value of \(1 \times 10^{-14}\). This illustrates that the product of the concentrations of \(\mathrm{H}_{3} \mathrm{O}^{+}\) and \(\mathrm{OH}^{-}\) remains constant, regardless of changes in individual ion concentrations:

• Applies to all aqueous solutions, including neutral, acidic, and basic water.
• Reflects water's capacity to maintain balance between ion concentrations.
• In neutral solutions, \([\mathrm{H}_3\mathrm{O}^+] = [\mathrm{OH}^-] = 1 \times 10^{-7} \text{M}\).

Ion Product of Water

The ion product of water, \(K_w\), is a fundamental concept in describing how water maintains its chemical balance. Regardless of whether the water solution is neutral, acidic, or basic, \(K_w\) at 25°C is always \(1 \times 10^{-14}\). This constancy forms the backbone for understanding pH levels and solution properties in chemistry.

In a basic solution, although the concentration of \(\mathrm{OH}^{-}\) ions exceeds that of \(\mathrm{H}_{3} \mathrm{O}^{+}\), \(K_w\) ensures that \(\mathrm{H}_{3} \mathrm{O}^{+}\) never drops to zero. This ensures that basic solutions still contain \(\mathrm{H}_{3} \mathrm{O}^{+}\) molecules:

• \(K_w\) helps predict concentration changes when conditions shift.
• Highlights why even basic solutions have \(\mathrm{H}_{3} \mathrm{O}^{+}\) present.
• Links directly to the pH scale, where pH + pOH = 14 due to the logarithmic nature of \(K_w\).

This equilibrium makes water an excellent medium for many chemical reactions, being able to adapt to different concentrations while retaining stability.