Calculate the percent ionization of a formic acid solution having the given concentration. b. 0.500 M

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1. Identify the chemical formula for formic acid, which is \( \text{HCOOH} \).
2. Write the ionization equation for formic acid: \( \text{HCOOH} \rightleftharpoons \text{H}^+ + \text{HCOO}^- \).
3. Use the expression for the acid dissociation constant \( K_a \) for formic acid: \( K_a = \frac{[\text{H}^+][\text{HCOO}^-]}{[\text{HCOOH}]} \).
4. Assume the initial concentration of formic acid is \( 0.500 \text{ M} \) and let \( x \) be the concentration of \( \text{H}^+ \) ions at equilibrium. Set up the expression: \( K_a = \frac{x^2}{0.500 - x} \).
5. Calculate the percent ionization using the formula: \( \text{Percent Ionization} = \left( \frac{x}{0.500} \right) \times 100 \% \).

Key Concepts

Ionization of Weak Acids

Weak acids, like formic acid, do not completely dissociate in solution. Instead, they establish an equilibrium between the undissociated acid and its ions. The degree to which a weak acid ionizes is crucial for calculating properties such as pH and percent ionization.

Percent Ionization

Percent ionization is a measure of the extent 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 in understanding the strength of the acid in a given concentration.

Equilibrium Constant (Ka)

The acid dissociation constant (Ka) quantifies the strength of a weak acid in solution. It is defined as the ratio of the concentration of the products (ions) to the concentration of the reactants (undissociated acid) at equilibrium. Knowing Ka allows for the calculation of the degree of ionization and, consequently, the percent ionization.