Problem 35 - Chemistry Matter and Change

Question

MAIN Idea Explain why the pH of an acidic solution is always a smaller number than the pOH of the same solution.

Step-by-Step Solution

Answer

In an acidic solution, the concentration of hydrogen ions is greater than hydroxide ions, making the pH smaller and the pOH larger, while maintaining their sum as 14.

Step 1: Understand pH and pOH

The pH of a solution is a measure of its acidity, representing the concentration of hydrogen ions ( H^+). It is defined as \(pH = -\log[H^+]\). The pOH, on the other hand, measures the concentration of hydroxide ions ( OH^-), defined as \(pOH = -\log[OH^-]\). Both pH and pOH are related to the ion product of water, \(Kw = [H^+][OH^-] = 1.0 \times 10^{-14}\) at 25°C.

Step 2: Calculate the Relationship between pH and pOH

Using the ion product of water \(Kw\), we derive a fundamental relation: \(pH + pOH = 14\). This equation means that the sum of the pH and the pOH of the solution always equals 14 in a neutral water solution at room temperature.

Step 3: Analyze Acidic Solutions

For an acidic solution, \([H^+] > [OH^-]\), meaning the concentration of hydrogen ions is greater than that of hydroxide ions. This results in a smaller pH than that of a neutral solution (pH < 7) and, conversely, a larger pOH (pOH > 7) to compensate and maintain the relation \(pH + pOH = 14\). Thus, by definition, the pH is smaller than the pOH in an acidic solution.

Key Concepts

Acidic Solutions

Acidic solutions are characterized by a higher concentration of hydrogen ions (\(H^+\)) compared to hydroxide ions (\(OH^-\)). When a solution is acidic, it means that there is an abundance of \(H^+\) ions, giving the solution its sour taste and ability to react with metals. The pH scale, which ranges from 0 to 14, measures how acidic or basic a solution is.

For acidic solutions, the pH is less than 7. This lower pH results because the \([H^+]\) is higher than in pure water where pH equals 7. Acidity increases as pH decreases, meaning a very low pH indicates a highly acidic solution.

• pH < 7 suggests an acidic solution
• Greater \([H^+]\) than \([OH^-]\) in the solution

Therefore, knowing the pH of a solution can help you determine if a solution is acidic, basic, or neutral.

Ion Product of Water

The ion product of water, commonly expressed as \(K_w\), is a key concept in understanding the balance between hydrogen ions \((H^+)\) and hydroxide ions \((OH^-)\) in water. At 25°C, \(K_w\) is always equal to \(1.0 \times 10^{-14}\).

This constant arises from the self-ionization of water, where water molecules dissociate into the ions:\[ H_2O(l) \leftrightarrow H^+(aq) + OH^-(aq) \] The product of hydrogen ion concentration \([H^+]\) and hydroxide ion concentration \([OH^-]\) is constant for water at given conditions.

• \(K_w = [H^+][OH^-] = 1.0 \times 10^{-14}\)
• This relationship implies that if \([H^+]\) increases, \([OH^-]\) must decrease to maintain equilibrium

Understanding \(K_w\) is essential in predicting how acids and bases will impact the pH and pOH of a solution. The equilibrium condition \(pH + pOH = 14\) is derived from this fundamental property.

Hydrogen Ion Concentration

Hydrogen ion concentration, denoted as\([H^+]\), is a pivotal factor in determining the acidity of a solution. The more \(H^+\) ions a solution has, the more acidic it is. The relationship between \([H^+]\) and pH is inversely logarithmic, captured by the formula:
\[ pH = -\log[H^+] \]In this equation, a high \([H^+]\) corresponds to a low pH value, marking the solution as acidic (<7 on the pH scale).

To further understand:

• As \([H^+]\) increases, the pH decreases
• A tiny change in \([H^+]\) can significantly impact pH, due to the logarithmic nature of the relationship

By knowing \([H^+]\), you can calculate the pH and understand the solution's acidity level. This knowledge is crucial for fields like chemistry and environmental science, where solution acidity needs to be controlled and understood.