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Chapter 13: Problem 3

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

Short Answer

Expert verified
In summary, for a weak acid HA, we have two graphs: (a) percent dissociation of HA versus the initial concentration of HA, which shows a decreasing curve, and (b) H+ concentration versus initial concentration of HA, which is a square root curve that increases gradually. The decrease in percent dissociation with increasing initial concentration is due to the equilibrium shift towards the left, while the H+ ion concentration increases at a diminishing rate because of the square root relationship with initial concentration.

Step by step solution

01

Understanding Weak Acids and Dissociation

Weak acids are acids that only partially dissociate in water, meaning they do not fully ionize into H+ ions and their corresponding anions. The dissociation of a weak acid in water can be represented by the following equilibrium: \[HA \rightleftharpoons H^{+} + A^{-}\] The degree to which a weak acid dissociates can be quantified by its percent dissociation, which is the ratio of the equilibrium concentration of dissociated ions to the initial concentration of HA, multiplied by 100.
02

Calculating Percent Dissociation

The percent dissociation of HA can be calculated using the following formula: \[Percent \space Dissociation = \frac{[HA]_{eq}}{[HA]_{0}} \times 100\%\] where, \([HA]_{eq}\) is the equilibrium concentration of HA, and \([HA]_{0}\) is the initial concentration of HA.
03

Sketching the Graph of Percent Dissociation vs Initial Concentration of HA

To plot this graph, we need to understand the relationship between percent dissociation and the initial concentration of HA. Generally, when the initial concentration of a weak acid is increased, the relative amount of dissociation decreases. This happens because, as more weak acid molecules are added to the solution, the equilibrium shifts to the left, reducing the percent dissociation. Thus, the graph will be a decreasing curve.
04

Calculating the Concentration of H+ ions

Since the concentration of H+ ions and A- ions are equal in the solution due to the 1:1 stoichiometry, we can write: \[[H^{+}]_{eq} = [A^{-}]_{eq}\] As a result, we can rewrite the equilibrium expression for the weak acid as: \[[H^{+}]_{eq} = \sqrt{K_a[HA]_{0}}\] where \(K_a\) is the acid dissociation constant.
05

Sketching the Graph of H+ Concentration vs Initial Concentration of HA

This graph shows how the concentration of H+ ions changes as the initial concentration of HA is varied. Following the expression \([H^{+}]_{eq} = \sqrt{K_a[HA]_{0}}\), as the initial concentration of HA increases, the H+ concentration also increases, but at a diminishing rate. This is due to the square root present in the equation, so the graph will have the shape of the square root curve, which increases more gradually as [HA]₀ increases.

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