Problem 34 - Chemistry The Science in Context

Question

Determine the indicated pH or pOH values: a. \(\mathrm{pH}\) of a solution whose \(\mathrm{pOH}=5.5\) b. \(\mathrm{pH}\) of a solution whose \(\mathrm{pOH}=6.8\) c. pOH of a solution whose \(\mathrm{pH}=9.7\) d. pOH of a solution whose \(\mathrm{pH}=4.4\)

Step-by-Step Solution

Answer

a) pOH = 5.5 b) pOH = 6.8 c) pH = 9.7 d) pH = 4.4 Answer: a) pH = 8.5 b) pH = 7.2 c) pOH = 4.3 d) pOH = 9.6

Step 1: Apply the relationship between pH and pOH

The given pOH value is 5.5. To determine the pH value, we will use the relationship: \(\mathrm{pH} + \mathrm{pOH} = 14\)

Step 2: Calculate the pH value

We will rearrange the equation and plug in the pOH value to find the pH value: \(\mathrm{pH} = 14 - \mathrm{pOH} = 14 - 5.5 = 8.5\) So, the pH of the solution is 8.5. #b: Given pOH value, determine the pH value#

Step 1: Apply the relationship between pH and pOH

The given pOH value is 6.8. To determine the pH value, we will use the relationship: \(\mathrm{pH} + \mathrm{pOH} = 14\)

Step 2: Calculate the pH value

We will rearrange the equation and plug in the pOH value to find the pH value: \(\mathrm{pH} = 14 - \mathrm{pOH} = 14 - 6.8 = 7.2\) So, the pH of the solution is 7.2. #c: Given pH value, determine the pOH value#

Step 1: Apply the relationship between pH and pOH

The given pH value is 9.7. To determine the pOH value, we will use the relationship: \(\mathrm{pH} + \mathrm{pOH} = 14\)

Step 2: Calculate the pOH value

We will rearrange the equation and plug in the pH value to find the pOH value: \(\mathrm{pOH} = 14 - \mathrm{pH} = 14 - 9.7 = 4.3\) So, the pOH of the solution is 4.3. #d: Given pH value, determine the pOH value#

Step 1: Apply the relationship between pH and pOH

The given pH value is 4.4. To determine the pOH value, we will use the relationship: \(\mathrm{pH} + \mathrm{pOH} = 14\)

Step 2: Calculate the pOH value

We will rearrange the equation and plug in the pH value to find the pOH value: \(\mathrm{pOH} = 14 - \mathrm{pH} = 14 - 4.4 = 9.6\) So, the pOH of the solution is 9.6.

Key Concepts

Understanding Acid-Base Chemistry

In acid-base chemistry, pH and pOH are crucial in determining the acidity or basicity of a solution. The pH scale ranges from 0 to 14. A solution with a pH less than 7 is considered acidic, while a pH greater than 7 indicates a basic solution. A pH of exactly 7 describes a neutral solution, like pure water.

• pH: Represents the concentration of hydrogen ions \(\left( \mathrm{H^+} \right)\) in a solution.
• pOH: Indicates the concentration of hydroxide ions \(\left( \mathrm{OH^-} \right)\) in a solution.

Understanding that the sum of pH and pOH is always 14 at standard conditions (at 25°C) is vital. This is due to the relation of the ion product constant of water, represented as \(\mathrm{K_w} = [H^+][OH^-] = 10^{-14}\). Hence, \(\mathrm{pH} + \mathrm{pOH} = 14\).

To compute either value, rearrange the equation to find the unknown. For example, if given pOH, find the pH using the formula \(\mathrm{pH} = 14 - \mathrm{pOH}\), and vice versa.

Chemical Equilibrium in Acid-Base Reactions

Chemical equilibrium is an important concept in acid-base chemistry. It refers to the state in which the concentrations of reactants and products remain constant over time, as their rates of formation are equal. In the context of acids and bases, this occurs when an acid and a base react to form water and a salt.
When considering the equilibrium constant for water, \(\left( K_w \right)\), we can see how it plays into pH and pOH calculations. Since \(K_w = 10^{-14}\), this constant quantifies the concentration of hydrogen and hydroxide ions in any aqueous solution at equilibrium.
It’s crucial to consult this equilibrium constant when titrating acids with bases. This helps us predict how they will neutralize each other to form water, shifting the equilibrium back and forth, thereby affecting the pH and pOH values.

• Remember that balancing the chemical equation is key in these reactions.
• The equilibrium state can be affected by changing concentrations, temperature, or adding catalysts.

Solution Chemistry Fundamentals

In solution chemistry, understanding the concepts of pH and pOH is fundamental to grasping how solutions interact and behave. The concentration of ions in a solution defines its chemical properties, including whether it is acidic or basic.
When discussing solutions:

• A solution is a homogeneous mixture composed of a solute dissolved in a solvent.
• The concentration of a solute in a solution is typically measured in molarity \( (\text{M}) = \dfrac{\text{moles of solute}}{\text{liters of solution}}\).

This concentration directly influences the pH and pOH. For a given acid or base, knowing its concentration helps us predict the resulting pH or pOH. For instance, a higher concentration of hydrogen ions \(\left( \mathrm{H^+} \right)\) will lead to a lower pH, making the solution more acidic. Similarly, a higher concentration of hydroxide ions \(\left( \mathrm{OH^-} \right)\) will increase the pOH, indicating a more basic solution.
This interplay of ions, concentrations, and equilibrium is what you need to consider while determining pH and pOH adjustments in solution chemistry.