Organic Chemistry: Concepts and Applications - Headley Allan D. 2020

Acid—Base Reactions in Organic Chemistry
7.3 Relative Strengths of Acids and Conjugate Bases

The degree to which acids dissociate in water (and other solvents) is different for each acid. Each acid dissociates based on the equilibrium established in a particular solvent. The magnitude of such an equilibrium constant (K_eq) reflects the relative distribution of the dissociated species to the undissociated acid in solution. It is known that nitric acid cannot be ingested; on the other hand, acetic acid (in the form of vinegar in salad dressings) can be ingested! Nitric acid is a much stronger acid than acetic acid and, as a result, is a very dangerous corrosive acid. The relative strengths of acids are typically measured in water. Since water is a base, an acid—base chemical reaction takes place between the acid (HA) and water (the base) to form protonated water, H₃O⁺, and A⁻, which are also known as the conjugate acid and base, respectively, as shown in Reaction (7-3) for an acid HA.

(7-3)

At equilibrium, all the species, H₃O⁺, A⁻, HA, and H₂O, exist in solution, and the concentrations of all the species are used to calculate the equilibrium constant for a particular acid, HA. The expression for the equilibrium constant is shown in Eq. (7-4), where K_eq is the equilibrium constant and the concentrations for the various species are shown in square brackets.

(7-4)

Since water is the solvent making its concentration very high, compared to the other species in solution, its concentration can be considered to be a constant. Thus, the expression in Eq. (7-4) can be modified as shown in Eq. (7-5) and even further to Eq. (7-6) if [H₂O]K made equal to a new constant, K_a, the acidity equilibrium constant in water as a solvent.

(7-5)

(7-6)

The K_a for HCl has been determined experimentally to be 1 × 10⁷, and for acetic acid, the K_a is 1.75 × 10⁻⁵. Since 1 × 10⁷ is a much larger number than 1.75 × 10⁻⁵, HCl is a stronger acid producing more protons (H⁺) in water, compared to acetic acid. Another way of stating this observation is that for an equal concentration of both HCl and acetic acid, the concentration of the protons in a solution of HCl is much greater than that of a solution of acetic acid.

Since these K_a values tend to be either very large or very small and very cumbersome to use, an easier method was devised to compress or expand these numbers, and at the same time convey the same meaning of the relative strengths of acids. The negative log of K_a or pK_a values are routinely used to reflect the relative strength of acids, and the relationship between K_a and pK_a is shown in Eq. (7-7).

(7-7)

Thus, the pK_a for HCl is −7 and for acetic acid is 4.75.

Problem 7.2

i. Determine the pK_a of the acids that have the following K_a values? Which of the acids with the given K_a values would be the weakest?

1. K_a = 1.3 × 10⁻⁵

2. K_a = 1.3 × 10⁵

3. K_a = 1.3 × 10⁻¹⁰

4. K_a = 2.3 × 10²⁵

5. K_a = 7.9 × 10⁻¹²

ii. Given the pK_a values shown below, determine the K_a values? Which of the acids with the given pK_a values would be the strongest?

1. pK_a = 35

2. pK_a = 12

3. pK_a = 4.6

4. pK_a = 24

5. pK_a = −14

A pK_a table gives the pK_a values of common acids used in organic chemistry and the pK_a values of some acids are shown in Table 7.1.

An acid with a pK_a value that is more positive than the pK_a value of another acid means that the acid with the more positive pK_a value is the weaker acid. For example, if two acids have pK_a values of 3.75 and 8.34, respectively, the acid with a pK_a value of 3.75 is a stronger acid than the acid with a pK_a value of 8.34. Also, notice that the pK_a for some of these acids are outside the range of the acidity of water, this means that their pK_a values are not measurable in water, but in other solvents. For example, NH₃ is a weak acid, pK_a = 38, but its conjugate base is extremely strong and will deprotonate water.

The pK_a table is very helpful in predicting the acidity of compounds and equally important, it is also very helpful in predicting the relative strength of conjugate bases. Consider the two acids, HBr and HCN with the acidity in water is shown in Reactions (7-8) and (7-9).

Table 7.1 pK_a for various acids of organic chemistry.

(7-8)

(7-9)

It is known that the conjugate base of a strong acid is weak and as a result, a determination can be made whether a conjugate base of an acid is strong or weak based by just knowing the pK_a value of an acid. Note that the conjugate bases shown in Reactions (7-8) and (7-9) are negatively charged. A stable negative charge has the ability to accommodate that charge. Thus, very electronegative or polarizable species will be better able to accommodate a charge, compared to less electronegative or polarizable species. For the reaction given in Reaction (7-8), the Br⁻ anion is a large atom and hence good at stabilizing the negative charge of the conjugate base. As a result, it is a weak base and its conjugate acid is a strong acid. On the other hand, the CN⁻ anion of Reaction (7-9) is not as polarizable as the bromide anion and is considered to be a harder base as described by the Pearson hard-soft base concept. As a result, the cyanide anion (CN⁻) is a stronger conjugate base than the bromide anion, which makes the conjugate acid, HCN, a weaker acid than HBr. This conclusion that Br⁻ is a weak conjugate base and hence the conjugate acid, HBr is a strong acid is confirmed from the pK_a values in the pK_a table. Similarly, the conjugate base CN⁻ is a strong conjugate base, which makes its conjugate acid, HCN a weak acid. This concept will be utilized throughout this course to predict the relative strengths of conjugate bases and acids.

Problem 7.3

i. Give the structure of the conjugate base of each of the following acids.

1. H₂O

2. CH₃OH

3. HCN

4. CH₃SH

5. H₂S

ii. Utilize Table 7.1 to determine which of the following pairs of acids is stronger and give the structures of the conjugate bases of each acid.

1. CH₃COOH and CH₃OH

2. NH₃ and CH₃OH

3. CH₄ and CH₃OH