Sketch two graphs: (a) percent dissociation for weak acid HA versus the initial concentration of \(\mathrm{HA}\left([\mathrm{HA}]_{0}\right)\) and \((\mathrm{b}) \mathrm{H}^{+}\) concentration versus [HA lo- Explain both.

Weak acids partially dissociate in water, which means that they do not donate all their protons (H⁺ ions) to the solution. The equilibrium constant for this dissociation, Ka, is used to describe the extent of the dissociation. We can represent the dissociation of a weak acid HA as follows: \[HA \rightleftharpoons H^{+} + A^{-}\] The Ka expression for this dissociation is: \[K_{a} = \frac{[H^{+}][A^{-}]}{[HA]}\]

Percent dissociation is the ratio of the dissociated acid concentration to the total initial acid concentration, expressed as a percentage. To calculate this, we divide the concentration of dissociated weak acid [HA] by the initial concentration [HA]₀: \[\text{Percent dissociation} = \frac{[HA]}{[HA]_{0}} \times 100\%\]

As the initial concentration [HA]₀ of the weak acid increases, the percent dissociation decreases. This happens because a greater amount of the weak acid remains undissociated and does not contribute to the proton concentration. Sketch a graph with percent dissociation on the y-axis and [HA]₀ on the x-axis. The curve should start high at lower concentrations and then decrease gradually as the [HA]₀ increases.

To calculate the H⁺ concentration, we can use the Ka expression mentioned in step 1 and the initial concentration of the weak acid, [HA]₀. The relationship can be approximated as follows: \[[H^{+}] \approx \sqrt{K_{a} \times [HA]_{0}}\] The H⁺ concentration increases with an increase in the initial concentration of the weak acid, [HA]₀, but the rate of increase is slower due to the square root term.

To sketch the graph of H⁺ concentration versus [HA]₀, plot the H⁺ concentration on the y-axis and the initial concentration of the weak acid [HA]₀ on the x-axis. The curve should have an increasing trend, starting at low concentrations of H⁺ at low initial concentrations and then gradually increasing with increasing initial concentrations. However, the slope of the curve will be decreasing because of the square root term in the relationship. In conclusion, the first graph (a) illustrates the relationship between the percent dissociation of a weak acid and its initial concentration, showing a decreasing trend as [HA]₀ increases. The second graph (b) demonstrates the relationship between the H⁺ concentration and the initial concentration of the weak acid, displaying an increasing trend but with a decreasing slope as the initial concentration increases. Both graphs provide insight into how the dissociation of a weak acid is affected by its initial concentration.