Question

(a) Given that \(K_{a}\) for acetic acid is \(1.8 \times 10^{-5}\) and that for hypochlorous acid is \(3.0 \times 10^{-8}\), which is the stronger acid? (b) Which is the stronger base, the acetate ion or the hypochlorite ion? (c) Calculate \(K_{b}\) values for \(\mathrm{CH}_{2} \mathrm{COO}^{-}\) and \(\mathrm{Cl} \mathrm{O}^{-}\)

Short answer

(a) Acetic acid is the stronger acid. (b) The hypochlorite ion (\(\mathrm{ClO}^-\)) is the stronger base. (c) The \(K_b\) values for the acetate ion (\(\mathrm{CH}_{2}\mathrm{COO}^-\)) and the hypochlorite ion (\(\mathrm{ClO}^-\)) are \(5.56 \times 10^{-10}\) and \(3.33 \times 10^{-7}\), respectively.

Step-by-step solution

Determine the stronger acid

To determine the stronger acid, we will compare the \(K_a\) values of the given acids. The larger the \(K_a\) value, the stronger the acid. Given that \(K_a\) for acetic acid is \(1.8 \times 10^{-5}\) and that for hypochlorous acid is \(3.0 \times 10^{-8}\), we can determine which acid is stronger. Since \(1.8 \times 10^{-5} > 3.0 \times 10^{-8}\), acetic acid is the stronger acid.

Determine the stronger base

To determine the stronger base, we will use the knowledge that the conjugate base of a weaker acid is a stronger base. Since we have determined acetic acid is the stronger acid, the hypochlorous acid is the weaker acid. Therefore, the stronger base is the conjugate base of the weaker acid, which is the hypochlorite ion (\(\mathrm{ClO}^-\)).

Calculate \(K_b\) values for \(\mathrm{CH}_{2}\mathrm{COO}^-\) and \(\mathrm{ClO}^-\)

To calculate the \(K_b\) values, we will use the relationship between \(K_a\), \(K_b\), and \(K_w\). The ion product constant of water, \(K_w\), is \(1.0 \times 10^{-14}\). The relationship between the constants is as follows: $$K_a \times K_b = K_w$$ Let's first calculate the \(K_b\) for \(\mathrm{CH}_{2}\mathrm{COO}^-\) (the acetate ion): $$K_b = \frac{K_w}{K_a} = \frac{1.0 \times 10^{-14}}{1.8 \times 10^{-5}} = 5.56 \times 10^{-10}$$ Now, let's calculate the \(K_b\) for \(\mathrm{ClO}^-\) (the hypochlorite ion): $$K_b = \frac{K_w}{K_a} = \frac{1.0 \times 10^{-14}}{3.0 \times 10^{-8}} = 3.33 \times 10^{-7}$$ In conclusion, (a) Acetic acid is the stronger acid. (b) The hypochlorite ion (\(\mathrm{ClO}^-\)) is the stronger base. (c) The \(K_b\) values for the acetate ion (\(\mathrm{CH}_{2}\mathrm{COO}^-\)) and the hypochlorite ion (\(\mathrm{ClO}^-\)) are \(5.56 \times 10^{-10}\) and \(3.33 \times 10^{-7}\), respectively.

Key concepts

Acid Strength

Acid strength refers to the propensity of an acid to donate a proton (H⁺) to a base. In an aqueous solution, a strong acid almost completely ionizes, releasing a large number of hydrogen ions, while a weak acid only partially ionizes. The acid dissociation constant (Ka) is a quantitative measure of the strength of an acid in solution. The larger the Ka value, the stronger the acid, because it denotes a greater tendency to lose a proton. For instance, acetic acid with a Ka value of 1.8 x 10^-5 is a stronger acid than hypochlorous acid with a Ka value of 3.0 x 10^-8, because it is more willing to part with its hydrogen ion.

Understanding acid strength is important not only for predicting the behavior of acids in chemical reactions but also in understanding the balance of substances in the environment and in our bodies.

Conjugate Base Strength

The strength of a conjugate base is intrinsically linked to the strength of its counterpart acid. In an acid-base reaction, the acid donates a proton to become a conjugate base. The weaker the acid, the stronger the resulting conjugate base. This is because a weak acid holds onto its proton more tightly, and upon losing it, the remaining base retains more of the original acid's strength. Conversely, a strong acid donates its proton easily, leaving behind a weak conjugate base that is less likely to re-accept a proton.

In the case of acetic acid and hypochlorous acid, since acetic acid is the stronger acid, its conjugate base (acetate ion) is the weaker base compared to the hypochlorite ion, which is a stronger base as it comes from the weaker hypochlorous acid. The tendency of a conjugate base to accept a proton is represented by its base dissociation constant (Kb).

Acid Dissociation Constant (Ka)

The acid dissociation constant (Ka) is essential for understanding acid strength. This constant quantifies the degree of dissociation of an acid into its conjugate base and a proton. Expressed in terms of concentrations, the larger the Ka, the more the acid dissociates, which indicates a stronger acid. The dissociation equation for an acid (HA) going to its conjugate base (A^-) and a proton can be written as follows:

Ka = [A^-][H⁺]/[HA]

Where [A^-] is the concentration of the conjugate base, [H⁺] is the concentration of the hydrogen ion, and [HA] is the concentration of the acid. In other words, the higher the concentration of A^- and H⁺ produced, the greater the Ka.

Base Dissociation Constant (Kb)

The base dissociation constant (Kb) is an indicator of base strength and is particularly valuable for predicting the behavior of bases in solution. It measures the extent to which a base forms its conjugate acid by accepting a proton from water. Analogous to the acid dissociation constant, the larger the Kb, the stronger the base, indicative of a higher degree of ionization in solution. The formula for the dissociation of a base B into its conjugate acid HB⁺ can be expressed as:

Kb = [HB⁺][OH^-]/[B]

Where [HB⁺] is the concentration of the conjugate acid, [OH^-] is the concentration of hydroxide ions, and [B] is the concentration of the base. When comparing bases, if one base has a higher Kb than another, it more readily accepts a proton and is therefore considered stronger.

Ion Product Constant of Water (Kw)

The ion product constant of water (Kw) is pivotal for understanding acid-base equilibria, especially in aqueous solutions. It represents the propensity of water molecules to disassociate into hydrogen ions (H⁺) and hydroxide ions (OH^-). At 25°C, Kw is always 1.0 x 10^-14.
This constant equilibrium expression can be represented as follows:

Kw = [H⁺][OH^-]

Kw also underpins the relationship between Ka and Kb. Since the product of the dissociation constants for an acid (Ka) and its conjugate base (Kb) should always be equal to Kw, we can calculate one if we know the other. This relationship allows us to maintain an understanding of the balance between acids and bases in a given solution.