pK_a and pH

If a strong acid such as HBr is dissolved in water, most of the acid dissociates into hydrogen ions and bromide ions. The products are favored at equilibrium. When a weak acid such as acetic acid, CH₃COOH, is dissolved in water, only a small fraction of the molecules dissociate into ions. In this case, reactants are favored at equilibrium.

The acid dissociation constant, K_a allows us to determine relative acid strengths.

HA + H₂O ⇄ A^– + H₃O⁺   \(\displaystyle \mathrm{K_a}=\frac{[\mathrm{H_3O^+}][\mathrm{A^-}]}{[\mathrm{HA}]}\)
 

The acid dissociation constant for HBr is 1.0 x 10⁹, and Ka for acetic acid is 1.8 x 10^-5. The constant indicates the amount of acid that dissociates into ions. From this information, acetic acid is a weaker acid than HBr. The larger the dissociation constant, Ka, the stronger the acid. In organic chemistry, we use pK_a values. The pK_a is the -log[Ka]. The pK_a for HBr is -9 and the pK_a for acetic acid is 4.74. The smaller the value of the pK_a, the stronger the acid and the larger the value of pK_a, the weaker the acid. The pKa values indicate the strength of an acid in water. We will see in a later study guide how a solvent other than water affects the pK_a value.

The pH of a solution gives the concentration of protons, [H₃O⁺], also written as [H⁺]. The pH is the negative log of the proton concentration.

If the pH of a solution is 7.00, the solution is neutral–there are equal amounts of OH^– and H₃O⁺ ions. When the solution has a pH greater than 7.00, the solution is basic. There is a greater concentration of OH^– ions than H₃O⁺ ions. If the solution pH is less than 7.00, the solution is acidic–a greater concentration of H₃O⁺ ions and a smaller concentration of OH^– ions.

pH = -log [H⁺]

In the figure above, we see that coffee has a pH of about 5 and bleach has a pH of 13. The coffee is acidic while the bleach is basic. Pure water is neutral with a pH of 7.

Organic Acids and Bases

Carboxylic acids are the most common organic acids. The carboxyl group is the COOH group. The carboxylic acids have pK_a values from about 3 to 5. These are weak acids.

Alcohols have an OH group and are much weaker acids than carboxylic acids. Their pK_a values are greater than 15.

Amines are weak bases with nitrogen bonded to a carbon atom. Bonded to the nitrogen atom are either 2 hydrogens, or 1 hydrogen and another organic group, or two organic groups. There is a lone pair of electrons on the nitrogen atom. You can think of amines as derivatives of ammonia. Their pK_a values are very high meaning they do not act as acids, but they do act as bases.

Protonated amines have much lower pK_a values and act as acids. The pK_a values are between 10 and 11. The pK_a of ammonia is 9.2. If we look at the relative strengths of the acids in the figure below, we see that protonated ethylamine is a weaker acid than protonated methylamine or ammonium ion.

Because the protonated ethylamine is the weakest acid of the three, it would have the strongest base. Recall, the weaker the acid, the stronger its conjugate base.

Protonated carboxylic acids and protonated alcohols are very strong acids. Their pK_a values are less than -2.

You should remember the ranges of pK_a values of the types of compounds we have looked at. A summary is below.

Equilibrium: Are Products or Reactants Favored

In the Acid and Base Strengths Study Guide we learned that equilibrium always favors the formation of the weaker acid or weaker base. Both the weaker acid and weaker base are on the same side of the chemical equation. The weaker acid will always have the higher value of pK_a.

The equilibrium constant, K_eq, can be calculated by the following:

pK_eq = pK_a (reactant acid) – pK_a (product acid)
K_a = 10^-pK_a

Exercises

Exercise 1. Order the following acids from weakest to strongest using the pK_a values given. Calculate the acid dissociation, K_a,values.

Check Answer/Solution to Exercise 1

Exercise 2. An acid has a pK_a of 1.8 x 10^-5. What is the equilibrium constant, K_eq, for its reaction in water? (Hint: Write a balanced equation).

Check Answer/Solution to Exercise 2

Exercise 3. Are the following acidic or basic?

Check Answer/Solution to Exercise 3

Exercise 4. Write a chemical equation with CH₃CH₂O^– reacting as a base with HBr. Write another equation with CH₃CH₂OH reacting as an acid with NH₃.

Check Answer/Solution to Exercise 4

Exercise 5. Order the following by increasing acid strength.

Check Answer/Solution to Exercise 5

Exercise 6. What are the conjugate bases for the following? Order the bases by increasing basicity.

Check Answer/Solution to Exercise 6

Exercise 7. Ethene, CH₂CH₂, has pK_a equal to 44. Write an equation, using equilibrium arrows, to show which side equilibrium is favored for the acid-base reaction with OH^–. Write another equation for ethene and ^–NH₂. Which is the better base for removing a proton from ethene? (pK_a NH₃ = 36, pK_a H₂O = 15.7)

Check Answer/Solution to Exercise 7

Exercise 8. What is the equilibrium constant, K_eq for the reaction between CH₃NH₂ and H₂O?

Check Answer/Solution to Exercise 8

Back to Acids and Bases
Back to Organic Chemistry 1 Study Guides