Calculate the percent dissociation of the acid in each of the following solutions. a. \(0.50 M\) acetic acid b. \(0.050 M\) acetic acid c. \(0.0050 M\) acetic acid d. Use Le Châtelier's principle to explain why percent dissociation increases as the concentration of a weak acid decreases. e. Even though the percent dissociation increases from solutions a to \(\mathrm{c}\), the \(\left[\mathrm{H}^{+}\right]\) decreases. Explain.

The dissociation reaction of acetic acid (\(CH_3COOH\)) in the water can be written as: \[CH_3COOH \rightleftharpoons CH_3COO^{-} + H^{+}\] The Ka value for acetic acid is \(1.8 \times 10^{-5}\).

We will construct the ICE (Initial, Change, Equilibrium) table for each concentration given in the exercise: | | \(CH_3COOH\) | \(CH_3COO^-\) | \(H^+\) | |----------|--------------|--------------|--------| | Initial | x | 0 | 0 | | Change | -y | +y | +y | | Equilibrium | x-y | y | y | where x is the initial concentration of acetic acid and y is the amount of acetic acid that dissociates.

The Ka expression for acetic acid is given by: \[Ka = \frac{[CH_3COO^-][H^+]}{[CH_3COOH]}\] Using the equilibrium concentrations from the ICE table, we have: \[1.8 \times 10^{-5} = \frac{y^2}{x-y}\] Now, we will solve for the equilibrium concentration of \([H^+]\) (which is equal to y) for each given initial concentration of acetic acid. a. For 0.50 M acetic acid: \(x = 0.50\) b. For 0.050 M acetic acid: \(x = 0.050\) c. For 0.0050 M acetic acid: \(x = 0.0050\) Since the amount of dissociated acetic acid (y) is much smaller than its initial concentration (x), we can assume that \(x \approx x-y\). Thus, for each given initial concentration, we solve the equation: \[1.8 \times 10^{-5} = \frac{y^2}{x}\]

The percent dissociation of acetic acid is given by the formula: Percent dissociation \(= \frac{[H^+]_{equilibrium}}{[CH_3COOH]_{initial}}\times 100\%\) Calculate the percent dissociation for each concentration using the equilibrium concentration values of \([H^+]\) found in Step 3.

d. Le Châtelier's principle states that if a system in equilibrium is subjected to a change in concentration, pressure, or temperature, the system will adjust its state in order to counteract the effect of the change and restore equilibrium. In the case of weak acids, as the concentration of the acid decreases, the equilibrium will shift towards the side of the products (dissociated ions), resulting in a higher percent dissociation. e. Even though the percent dissociation increases from solutions a to c, the concentration of \([H^+]\) decreases. This is because dissociation is still incomplete, and the amount of acetic acid in this case decreases faster than the increase in percent dissociation. Therefore, the overall concentration of \([H^+]\) in the solution will be lower.