Problem 62 - Chemistry Matter and Change

Question

Use the symbols \(<,>,\) and \(=\) to express the relationship between the concentrations of \(\mathrm{H}^{+}\) ions and \(\mathrm{OH}^{-}\) ions in acidic, neutral, and basic solutions.

Step-by-Step Solution

Answer

Acidic: \([\mathrm{H}^{+}] > [\mathrm{OH}^{-}]\), Neutral: \([\mathrm{H}^{+}] = [\mathrm{OH}^{-}]\), Basic: \([\mathrm{H}^{+}] < [\mathrm{OH}^{-}]\).

Step 1: Understand the Relationship of pH and Ion Concentrations

In any solution, the concentration of hydrogen ions (\(\mathrm{H}^{+}\)) and hydroxide ions (\(\mathrm{OH}^{-}\)) are related by the water dissociation constant \( K_w = 1 \times 10^{-14}. \) The pH indicates the acidity or basicity of the solution, influencing these concentrations.

Step 2: Acidic Solution Characteristics

For an acidic solution, the pH is less than 7, indicating a higher concentration of \(\mathrm{H}^{+}\) ions compared to \(\mathrm{OH}^{-}\) ions. Thus, we can express this relationship as \([\mathrm{H}^{+}] > [\mathrm{OH}^{-}].\)

Step 3: Neutral Solution Characteristics

A neutral solution has a pH of exactly 7, which means the concentrations of \(\mathrm{H}^{+}\) ions and \(\mathrm{OH}^{-}\) ions are equal, thus \([\mathrm{H}^{+}] = [\mathrm{OH}^{-}].\)

Step 4: Basic Solution Characteristics

In a basic solution, the pH is greater than 7, which means the concentration of \(\mathrm{OH}^{-}\) ions is greater than that of \(\mathrm{H}^{+}\) ions. So, the relationship is expressed as \([\mathrm{H}^{+}] < [\mathrm{OH}^{-}].\)

Key Concepts

pH Scale

The pH scale is crucial for understanding the nature of a solution, whether it’s acidic, neutral, or basic. It ranges from 0 to 14 and is a logarithmic scale used to specify the acidity or basicity of an aqueous solution. A pH level below 7 indicates acidity, meaning there are more hydrogen ions ( H^+ ) present, while a pH above 7 indicates a basic or alkaline solution, with more hydroxide ions ( OH^− ). When the pH is exactly 7, it signifies neutrality, where hydrogen ion concentration is equal to hydroxide ion concentration.

• Acidic Solutions: Have a pH less than 7. More H^+ ions mean fewer OH^− ions.
• Basic (Alkaline) Solutions: Have a pH greater than 7. More OH^− ions mean fewer H^+ ions.
• Neutral Solutions: Have a pH of exactly 7. H^+ and OH^− ions are equal.

Understanding the pH scale helps in various practical applications, such as titration, agriculture, water treatment, and the food industry.

Hydrogen Ion Concentration

Hydrogen ion concentration ([H^+]) is a measure of how many hydrogen ions are present in a solution. It is an essential factor in determining the acidity of a solution. The concentration of hydrogen ions is expressed in moles per liter (M).
In acidic solutions, there is a high concentration of H^+ ions, resulting in a lower pH value. The more hydrogen ions present, the stronger the acid.
In neutral solutions, H^+ ions are balanced by OH^− ions, resulting in a neutral pH of 7. In basic solutions, the concentration of H^+ ions decreases as it is suppressed by the higher concentration of OH^− ions.
To calculate [H^+], you can use the formula:\[ [H^+] = 10^{-pH} \]This equation shows the inversely proportional relationship between pH and hydrogen ion concentration: lower pH equates to higher [H^+] and vice versa.

Hydroxide Ion Concentration

Hydroxide ion concentration ([OH^-]) plays a significant role in determining the basicity of a solution. Similar to hydrogen ion concentration, hydroxide ion concentration is also expressed in moles per liter (M).

• In a basic solution, there is a high concentration of OH^- ions, resulting in a higher pH over 7. This indicates less presence of H^+ ions.
• In neutral solutions, OH^- ions are balanced with H^+ ions, giving a neutral pH of 7.
• In acidic solutions, the amount of OH^- ions is lower than H^+, thus resulting in a lower pH.

The relationship between OH^- concentration and pH can be calculated using:\[ [OH^-] = \frac{1 \times 10^{-14}}{[H^+]} \]This equation shows how decreases in [H^+] cause increases in [OH^-] and vice versa, due to the inverse relationship.