Problem 77 - Chemistry Matter and Change

Question

If the concentration of \(\mathrm{H}^{+}\) ions in an aqueous solution decreases, what must happen to the concentration of \(\mathrm{OH}^{-}\) ions? Why?

Step-by-Step Solution

Answer

As the concentration of \(\mathrm{H}^+\) ions decreases, the concentration of \(\mathrm{OH}^-\) ions increases to maintain the constant water dissociation product \(K_w\).

Step 1: Understanding the Relationship Between Ion Concentrations

In an aqueous solution, the concentration of \(\mathrm{H}^+\) ions and \(\mathrm{OH}^-\) ions is related by the water dissociation constant \(K_w\), which is also known as the ion product of water. It is defined as \([\mathrm{H}^+] \times [\mathrm{OH}^-] = K_w\). At 25°C, \(K_w = 1.0 \times 10^{-14}\).

Step 2: Analyzing the Effect of Decreasing \(\mathrm{H}^+\) Concentration

If the concentration of \(\mathrm{H}^+\) ions decreases, in order to keep the product \([\mathrm{H}^+] \times [\mathrm{OH}^-] = K_w\) constant, the concentration of \(\mathrm{OH}^-\) ions must increase. This is because \(K_w\) is a constant at a given temperature, meaning any change in \([\mathrm{H}^+]\) must result in a compensatory change in \([\mathrm{OH}^-]\).

Step 3: Conclusion Based on Water Equilibrium Constant

According to the relationship defined by \(K_w\), increasing \([\mathrm{OH}^-]\) when \([\mathrm{H}^+]\) decreases maintains equilibrium in the solution. Consequently, if the concentration of hydrogen ions declines, hydroxide ions concentration must increase to sustain the constant value of \(K_w\).

Key Concepts

Water Dissociation Constant

The water dissociation constant, commonly symbolized as \( K_w \), is a crucial aspect of understanding aqueous chemistry. It represents the equilibrium between the dissociation and recombination of water molecules into hydrogen ions (\( \mathrm{H}^+ \)) and hydroxide ions (\( \mathrm{OH}^- \)). This constant indicates how much water will naturally ionize at a given temperature.

At 25°C, \( K_w \) has a value of \( 1.0 \times 10^{-14} \). This value tells us that in pure water, the concentrations of \( \mathrm{H}^+ \) and \( \mathrm{OH}^- \) are both \( 1.0 \times 10^{-7} \) M. The simplicity of this constant allows us to predict the behavior of aqueous solutions when different substances are dissolved.

• Represents the balance of water ionization.
• Shows the product of \( \mathrm{H}^+ \) and \( \mathrm{OH}^- \) concentrations.
• Remains constant at given temperatures.

Ion Product of Water

The Ion Product of Water, essentially the same as \( K_w \), provides a snapshot of the ion concentrations in water at equilibrium. Any shift in the concentration of \( \mathrm{H}^+ \) or \( \mathrm{OH}^- \) will inversely affect the other to maintain this constant.

This is fundamentally important in chemistry because alterations in ion concentrations affect pH levels, determining whether a solution is acidic or basic. To keep the balance of \( 1.0 \times 10^{-14} \) in equilibrium, any decrease in hydrogen ions necessitates an increase in hydroxide ions.

• Ensures \( [\mathrm{H}^+] \times [\mathrm{OH}^-] = K_w \).
• Essential for understanding pH balance.
• Critical for predicting solution behavior.

Acid-Base Equilibrium

Acid-base equilibrium is a dynamic balance between acids and bases in solution, deeply rooted in the principles of \( K_w \). When an acid dissolves in water, it increases the \( \mathrm{H}^+ \) concentration, while a base increases \( \mathrm{OH}^- \) concentration. This balance is described by the water dissociation equation.

Understanding this equilibrium helps you predict how changes in \( \mathrm{H}^+ \) or \( \mathrm{OH}^- \) affect the acidity or basicity of a solution. For instance, if the concentration of hydrogen ions in a solution goes down, the equilibrium shifts to maintain the constant \( K_w \), resulting in an increase in hydroxide ions.

• Describes the balance between acids and bases.
• Explains the shift in equilibrium when pH changes.
• Integral for calculating pH levels in solutions.

Hydronium Ions

Hydronium ions, \( \mathrm{H}_3\mathrm{O}^+ \), are essentially hydrogen ions that are more accurately represented in aqueous solutions since \( \mathrm{H}^+ \) ions associate with water molecules. These ions are pivotal in deciding the acidity of a solution.

The presence of more hydronium ions results in a lower pH, signifying an acidic solution. The transformation into hydronium occurs through the reaction: \[ \mathrm{H}^+ + \mathrm{H}_2\mathrm{O} \rightarrow \mathrm{H}_3\mathrm{O}^+ \]

Measuring hydronium ions grants insights into the solution's acidity and aids in maintaining the delicate water equilibrium.

• Represent \( \mathrm{H}^+ \) in water.
• Key to determining a solution's pH.
• Helps in understanding changes in acidity levels.

Hydroxide Ions

Hydroxide ions, \( \mathrm{OH}^- \), significantly influence the basicity of a solution. When you deal with aqueous environments, knowing the concentration of hydroxide ions is essential for understanding shifts in pH levels.

An increase in \( \mathrm{OH}^- \) within a solution results in a rise in pH, creating a more basic or alkaline environment. This is depicted in the ion product of water where any drop in \( \mathrm{H}^+ \) is balanced by an increase in \( \mathrm{OH}^- \), ensuring the equilibrium is never disrupted.

• Increases lead to higher pH values.
• A crucial part of maintaining \( K_w \) balance.
• Indicates shifts in solution's basicity.