A 0.0560-g quantity of acetic acid is dissolved in enough...

A $0.0560-\mathrm{g}$ quantity of acetic acid is dissolved in enough water to make $50.0 \mathrm{mL}$ of solution. Calculate the concentrations of $\mathrm{H}^{+}, \mathrm{CH}_{3} \mathrm{COO}^{-},$ and $\mathrm{CH}_{3} \mathrm{COOH}$ at equilibrium. ($K_{\mathrm{a}}$ for acetic acid $=1.8 \times 10^{-5}$).

Key Concepts

ICE Table Method

An ICE (Initial, Change, Equilibrium) table is a systematic tool used to track the concentrations of species in a reaction as the system shifts from initial conditions to equilibrium. This method helps in setting up the expressions needed to solve for unknown equilibrium concentrations.

Weak Acid Approximation

For weak acids, the degree of ionization is minimal, allowing for the approximation that the change in concentration (due to dissociation) is negligible compared to the initial concentration. This simplification makes it easier to solve the equilibrium expressions without resorting to complex algebra.

Molarity Determination

Calculating molarity involves converting the given mass of a substance to moles using its molar mass and then dividing by the solution's volume. This step is essential for establishing the initial concentration before the system reaches equilibrium.

Acid Dissociation Constant (K?) and Equilibrium Expression

The acid dissociation constant (K?) quantifies the extent of ionization of a weak acid in water. It is defined by the equilibrium expression K? = [H?][A?]/[HA], which relates the concentrations of the hydrogen ions, the conjugate base, and the undissociated acid at equilibrium.