Kaplan MCAT General Chemistry Review

Water is a member of a unique class of compounds in the world of acids and bases. The H₂O molecule can act as either an acid or a base, depending on the acid-base nature of the species with which it is reacting. Water acts as an acid by donating one of its hydrogen ions, and it acts as a base by accepting a hydrogen ion. This leads us to the definition of an amphoteric species: one that in the presence of a base reacts like an acid and, in the presence of an acid, reacts like a base. As an amphoteric compound, water can react with itself, in a process called auto-ionization, in the following manner:

One water molecule donates a hydrogen ion to another water molecule to produce the hydronium ion (H₃O⁺) and the hydroxide ion (OH⁺). By the way, some of you may be used to seeing the hydrogen ion represented simply as H⁺, rather than as H₃O⁺. This is fine, but it’s important to remember that the proton is never just “free floating” in the solution; it’s always attached to water or some other species that has the ability to accept it. Auto-ionization of water is a reversible reaction; therefore, the above equation is an equilibrium expression for this reversible reaction. For pure water at 298 K, the water dissociation constant, K_w, has been experimentally determined and is

K_w = [H₃O⁺][OH^-] = 10^-14 at 25°C (298 K)

Because each mole of water that auto-ionizes produces one mole each of hydrogen (or hydronium) ions and hydroxide ions, the concentrations of the hydrogen ions and hydroxide ions are always equal in pure water at equilibrium. Thus, the concentration of each of the ions in pure water at equilibrium at 298 K is 10^-7 mol/L.

The concentrations of the two ions will not always be equal. In fact, they will only be equal when the solution is neutral. Nevertheless, the product of their respective concentrations must always equal 10^-14 when the temperature of the solution is 298 K. For example, if a species is added to pure water and that species donates hydrogen ions to the water (i.e., the species is an acid), then the hydrogen ion concentration will increase, causing the water system to shift to reverse the auto-ionization process. The result is a decrease in the hydroxide ion concentration and a return to the equilibrium state. This is nothing other than Le Châtelier’s principle in action as we’ve seen time and time again: The addition of product to a system at equilibrium (in this case, the addition of H⁺ to the water system at equilibrium) causes the system to shift in direction away from the products, toward the reactants. The shift away from the product side necessarily leads to a decrease in the concentration of the hydroxide ion such that the product of the concentrations of the dissolved ions equals the K_w. The addition of a species that accepts hydrogen ions (i.e., a base), resulting in a decrease in the hydrogen ion concentration, will cause the water system to shift forward to replace the hydrogen ions. The increase in auto-ionization will necessarily lead to an increase in the hydroxide ion concentration and a return to the equilibrium state.

Before we introduce the scales used to measure the concentrations of hydrogen ions and hydroxide ions in different acid-base solutions, we want to emphasize the important thermodynamic principle, often unnoticed by students, contained in the water dissociation constant (K_w) expression. The K_w is an equilibrium constant; unless the temperature of the water is changed, the value for K_w cannot be changed. Thus, the product of the concentrations of the hydrogen ions and the hydroxide ions in the aqueous solution at 298 K must always equal 10^-14. At different temperatures, however, the value for K_w changes. At temperatures above 298 K, the value for K_w will increase, a direct result of the endothermic nature of the auto-ionization reaction.

pH and pOH Scales

The concentrations of hydrogen ions and hydroxide ions in aqueous solutions can vary significantly, and the vastness of the range makes measurements on a linear scale unmanageable. The scales of concentrations for acidic and basic solutions are condensed into something more manageable by being expressed in logarithmic terms, just like the decibel scale for sound intensity. These logarithmic scales are the pH and the pOH scales for the concentrations of the hydrogen and hydroxide ions, respectively.

We find that in many cases, the reactivity of a reaction involving an acid is not a function of hydrogen ion concentration but instead the logarithm of the hydrogen ion concentration (just as loudness of sound is a function of the logarithm of sound intensity). As a result, we often use the logarithmic pH and pOH scales to express the concentrations of the hydrogen and hydroxide ions, respectively.