## Chemistry: Molecular Approach (4th Edition)

1. Draw the ICE table for this equilibrium: $$\begin{vmatrix} Compound& [ HC_2H_3O_2 ]& [ C_2H_3{O_2}^- ]& [ H_3O^+ ]\\ Initial& 0.250 & 0 & 0 \\ Change& -x& +x& +x\\ Equilibrium& 0.250 -x& 0 +x& 0 +x\\ \end{vmatrix}$$ 2. Write the expression for $K_a$, and substitute the concentrations: - The exponent of each concentration is equal to its balance coefficient. $$K_a = \frac{[Products]}{[Reactants]} = \frac{[ C_2H_3{O_2}^- ][ H_3O^+ ]}{[ HC_2H_3O_2 ]}$$ $$K_a = \frac{(x)(x)}{[ HC_2H_3O_2 ]_{initial} - x}$$ 3. Assuming $0.250 \gt\gt x:$ $$K_a = \frac{x^2}{[ HC_2H_3O_2 ]_{initial}}$$ $$x = \sqrt{K_a \times [ HC_2H_3O_2 ]_{initial}} = \sqrt{ 1.8 \times 10^{-5} \times 0.250 }$$ $x = 2.1 \times 10^{-3}$ 4. Calculate the percent ionization: $$\frac{ \sqrt{ 1.8 \times 10^{-5} \times 0.250 } }{ 0.250 } \times 100\% = 0.85 \%$$