Kaplan MCAT General Chemistry Review

HA (aq) + H₂O (l) H₃O⁺ (aq) + A^- (aq)

Since the system exists in an equilibrium state, we can write the dissociation equation to determine the acid dissociation constant K_a as

The smaller the K_a, the weaker the acid, and consequently, the less it will dissociate. Note that the concentration of water, while not seemingly included in the dissociation constant expression, is actually incorporated into the value of K_a (K_eq [H₂O] = K_a).

A weak monovalent base, BOH, undergoes dissociation to yield B⁺ and OH^- in solution:

BOH (aq) B⁺ (aq) + OH^- (aq)

And the base dissociation constant K_b can be calculated according to

Bridge

Weak acids and bases are often seen on the MCAT in the Biological Sciences section.

The smaller the K_b, the weaker the base, and consequently, the less it will dissociate. As with the acid dissociation expression, the base dissociation expression incorporates the concentration of the water in the value of the K_b itself.

Generally speaking, we can characterize a species as a weak acid if its K_a is less than 1.0 and as a weak base if its K_b is less than 1.0. On the MCAT, molecular (that is, nonionic) weak bases are almost exclusively amines.

CONJUGATE ACID/BASE PAIRS

Since Brønsted and Lowry define an acid-base reaction as one in which a hydrogen ion (proton) is transferred from the acid to the base, the acid and base always occur in pairs called conjugates. A conjugate acid is the acid formed when a base gains a proton, and a conjugate base is the base that is formed when an acid loses a proton. For example,

HCO₃^- (aq) + H₂O CO₃^2- (aq) + H₃O⁺ (aq)

Key Concept

Be aware of the relationship between conjugate acids and bases because you will need to recognize these on the MCAT. Taking a proton from a molecule will give you the conjugate base, and putting a proton on will give you the conjugate acid!

The CO₃^2- is the conjugate base of the HCO₃^- acid, and the H₃O⁺ is the conjugate acid of the H₂O base. To find the K_a, we consider the equilibrium concentrations of the dissolved species:

The reaction between bicarbonate (HCO₃^-) and water is reversible, so we can write it as follows:

CO₃^2- (aq) + H₂O (aq) HCO₃^- (aq) + OH^- (aq)

And write the K_b for CO₃^2- as follows:

In a conjugate acid-base pair formed from a weak acid, the conjugate base is generally stronger than the conjugate acid. Note that this does not necessarily mean that a weak acid will produce a strong conjugate base or that a weak base will produce a strong conjugate acid, although it is always the case that a strong acid will produce a weak conjugate base (e.g., HCl/Cl^-) and a strong base will produce a weak conjugate acid (e.g., NaOH/H₂O). As it turns out, for HCO₃^- and CO₃^2-, the reaction of CO₃^2- with water to produce HCO₃^- and OH^- occurs to a greater extent (that is, is thermodynamically more favorable) than the reaction of HCO₃^- and water to produce CO ₃^2- and H₃O⁺.

When you add the previous two reversible reactions, you see that the net is simply the dissociation of water:

H₂O (l) + H₂O (l) H₃O⁺ (aq) + OH^- (aq)

Since the net reaction is the auto-ionization of water, the equilibrium constant for the reaction is K_w = [H₃O⁺][OH^-] = 10^-14, which is the product of K_a and K_b. Remember: The product of the concentrations of the hydrogen ion and the hydroxide ion must always equal 10^-14 for acid or base aqueous solutions. Because water itself is an amphoteric species (both a weak acid and a weak base), all acid-base reactivity in water ultimately reduces to the acid-base behavior of water, and all acid or base aqueous solutions are governed by the dissociation constant for water. Thus, if the dissociation constant for either the acid or its conjugate base is known, then the dissociation constant for the other can be determined using this equation:

K_a (conjugate acid) × K_b(conjugate base) = K_w = 10^-14

As you can now see, K_a and K_b are inversely related. In other words, if K_a is large, then K_b is small, and vice versa.

APPLICATIONS OF K_aAND K_b

The most common use of the acid and base dissociation constants is for the determination of the concentration of one of the species in the solution at equilibrium. On Test Day, you may be challenged to calculate the concentration of the hydrogen ion (or pH), the concentration of the hydroxide ion (or pOH), or the concentration of either the original acid or base. One such example is provided below to show you the important steps in solving quickly and correctly these types of problems.

To calculate the concentration of H⁺ in a 2.0 M aqueous solution of acetic acid, CH₃COOH (K_a = 1.8 × 10^-5), first write the equilibrium reaction:

CH₃COOH (aq) H⁺ (aq) + CH ₃COO^- (aq)

Next, write the expression for the acid dissociation constant:

Key Concept