Calculate the percent ionization of propionic acid 1C2H5COOH2 in solutions of each of the following concentrations 1Ka is given in Appendix D): (a) 0.250 M

Verified step by step guidance

1. Identify the chemical equation for the ionization of propionic acid: \( \text{C}_2\text{H}_5\text{COOH} \rightleftharpoons \text{C}_2\text{H}_5\text{COO}^- + \text{H}^+ \).
2. Write the expression for the acid dissociation constant \( K_a \) using the concentrations of the products and reactants: \( K_a = \frac{[\text{C}_2\text{H}_5\text{COO}^-][\text{H}^+]}{[\text{C}_2\text{H}_5\text{COOH}]} \).
3. Set up an ICE (Initial, Change, Equilibrium) table to determine the equilibrium concentrations of the species involved.
4. Assume that the initial concentration of \( \text{C}_2\text{H}_5\text{COOH} \) is 0.250 M and that the change in concentration due to ionization is \( x \).
5. Solve for \( x \) using the \( K_a \) expression and calculate the percent ionization using the formula: \( \text{Percent Ionization} = \left( \frac{x}{0.250} \right) \times 100 \).

Key Concepts

Ionization of Weak Acids

Weak acids, like propionic acid, do not fully dissociate in solution. Instead, they establish an equilibrium between the undissociated acid and its ions. The extent of this ionization is characterized by the acid dissociation constant (Ka), which quantifies the strength of the acid and its ability to donate protons (H+) in solution.

Percent Ionization

Percent ionization is a measure of the degree to which an acid dissociates in solution, expressed as a percentage. It is calculated using the formula: (concentration of ionized acid / initial concentration of acid) × 100%. This value helps to understand the strength of the acid in a given concentration and how it changes with dilution.

Equilibrium Calculations

To calculate percent ionization, one must set up an equilibrium expression based on the initial concentration of the acid and the change in concentration due to ionization. This involves using the Ka value to find the concentration of ions at equilibrium, allowing for the determination of how much of the acid has ionized relative to its initial concentration.