Use information from Appendix D to calculate the pH of (a) a solution that is 0.060 M in potassium propionate (C2H5COOK or KC3H5O2) and 0.085 M in propionic acid (C2H5COOH or HC3H5O2). (b) a solution that is 0.075 M in trimethylamine (CH3)3N and 0.10 M in trimethylammonium chloride (CH3)3NHCl. (c) a solution that is made by mixing 50.0 mL of 0.15 M acetic acid and 50.0 mL of 0.20 M sodium acetate.

Verified step by step guidance

1. Step 1: Identify the type of solution in each part of the problem. For (a) and (b), these are buffer solutions, and for (c), it is a buffer solution formed by mixing a weak acid and its conjugate base.
2. Step 2: Use the Henderson-Hasselbalch equation for buffer solutions: \( \text{pH} = \text{pKa} + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \). For part (a), identify \( \text{A}^- \) as potassium propionate and \( \text{HA} \) as propionic acid. For part (b), identify \( \text{A}^- \) as trimethylamine and \( \text{HA} \) as trimethylammonium chloride.
3. Step 3: Look up the \( \text{pKa} \) values for propionic acid and trimethylammonium ion in Appendix D. Use these values in the Henderson-Hasselbalch equation for parts (a) and (b).
4. Step 4: For part (c), calculate the concentrations of acetic acid and acetate ion after mixing. Use the formula \( C_1V_1 = C_2V_2 \) to find the new concentrations, where \( C_1 \) and \( V_1 \) are the initial concentration and volume, and \( C_2 \) and \( V_2 \) are the final concentration and volume.
5. Step 5: Apply the Henderson-Hasselbalch equation to the solution in part (c) using the \( \text{pKa} \) of acetic acid and the concentrations calculated in Step 4 to find the pH.

Key Concepts

Buffer Solutions

Buffer solutions are mixtures of a weak acid and its conjugate base or a weak base and its conjugate acid. They resist changes in pH when small amounts of acid or base are added. In the given question, potassium propionate and propionic acid form a buffer system, as do trimethylamine and trimethylammonium chloride, allowing for the calculation of pH using the Henderson-Hasselbalch equation.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a mathematical formula used to calculate the pH of buffer solutions. It is expressed as pH = pKa + log([A-]/[HA]), where pKa is the negative logarithm of the acid dissociation constant, [A-] is the concentration of the conjugate base, and [HA] is the concentration of the weak acid. This equation is essential for determining the pH in the scenarios presented in the question.

Acid-Base Equilibria

Acid-base equilibria involve the balance between acids and bases in a solution, which can be described by their dissociation constants (Ka for acids and Kb for bases). Understanding these equilibria is crucial for calculating pH, as it helps predict how the concentrations of acids and bases will affect the overall acidity or basicity of the solution. This concept is fundamental in analyzing the mixtures in the question.