Acid–Base Properties of Water

Recall the structure of the water molecule, with its polar O–H bonds and two lone pairs of electrons on the oxygen atom. Recall that because of its highly polar structure, liquid water can act as either an acid (by donating a proton to a base) or a base (by using a lone pair of electrons to accept a proton). For example, when a strong acid such as HCl dissolves in water, it dissociates into chloride ions (Cl⁻) and protons (H⁺). The proton, in turn, reacts with a water molecule to form the hydronium ion (H₃O⁺):

In this reaction, HCl is the acid, and water acts as a base by accepting an H⁺ ion. The reaction in Equation 16.1 is often written in a simpler form by removing H₂O from each side:

In Equation 16.2, the hydronium ion is represented by H⁺, although free H⁺ ions do not exist in liquid water.

Water can also act as an acid, as shown in Equation 16.3. In this equilibrium reaction, H₂O donates a proton to NH₃, which acts as a base:

Thus water is amphiproticSubstances that can behave as either an acid or a base in a chemical reaction, depending on the nature of the other reactant(s)., meaning that it can behave as either an acid or a base, depending on the nature of the other reactant. Notice that Equation 16.3 is an equilibrium reaction as indicated by the double arrow.

The Ion-Product Constant of Liquid Water

Because water is amphiprotic, one water molecule can react with another to form an OH⁻ ion and an H₃O⁺ ion in an autoionization process:

The equilibrium constant K for this reaction can be written as follows:

When pure liquid water is in equilibrium with hydronium and hydroxide ions at 25°C, the concentrations of the hydronium ion and the hydroxide ion are equal: [H₃O⁺] = [OH⁻] = 1.003 × 10⁻⁷ M. Thus the number of dissociated water molecules is very small indeed, approximately 2 ppb. We can calculate [H₂O] at 25°C from the density of water at this temperature (0.997 g/mL):

With so few water molecules dissociated, the equilibrium of the autoionization reaction (Equation 16.4) lies far to the left. Consequently, [H₂O] is essentially unchanged by the autoionization reaction and can be treated as a constant. Incorporating this constant into the equilibrium expression allows us to rearrange Equation 16.5 to define a new equilibrium constant, the ion-product constant of liquid water (K_w)An equilibrium constant for the autoionization of water, $2{\text{H}}_2\text{O(l)}$ ⇌ ${\text{H}}_3{\text{O}}^{+}\text{(aq)}$ + ${\text{OH}}^{-}\text{(aq),}$ in which the concentration of water is treated as a constant: $K_{\text{w}}$ = $\left[{\text{H}}_3{\text{O}}^{+}\right]\left[{\text{OH}}^{-}\right]$ = $1.006\times {10}^{-14}\text{.}$:

Substituting the values for [H₃O⁺] and [OH⁻] at 25°C into this expression,

Thus, to three significant figures, K_w = 1.01 × 10⁻¹⁴ M. Like any other equilibrium constant, K_w varies with temperature, ranging from 1.15 × 10⁻¹⁵ at 0°C to 4.99 × 10⁻¹³ at 100°C.

In pure water, the concentrations of the hydronium ion and the hydroxide ion are equal, and the solution is therefore neutral. If [H₃O⁺] > [OH⁻], however, the solution is acidic, whereas if [H₃O⁺] < [OH⁻], the solution is basic. For an aqueous solution, the H₃O⁺ concentration is a quantitative measure of acidity: the higher the H₃O⁺ concentration, the more acidic the solution. Conversely, the higher the OH⁻ concentration, the more basic the solution. In most situations that you will encounter, the H₃O⁺ and OH⁻ concentrations from the dissociation of water are so small (1.003 × 10⁻⁷ M) that they can be ignored in calculating the H₃O⁺ or OH⁻ concentrations of solutions of acids and bases, but this is not always the case.

The Relationship among pH, pOH, and pK_w

The pH scale is a concise way of describing the H₃O⁺ concentration and hence the acidity or basicity of a solution. As you recall, the pH and the H⁺ (H₃O⁺) concentration are related as follows:

Because the scale is logarithmic, a pH difference of 1 between two solutions corresponds to a difference of a factor of 10 in their hydronium ion concentrations. Recall also that the pH of a neutral solution is 7.00 ([H₃O⁺] = 1.0 × 10⁻⁷ M), whereas acidic solutions have pH < 7.00 (corresponding to [H₃O⁺] > 1.0 × 10⁻⁷) and basic solutions have pH > 7.00 (corresponding to [H₃O⁺] < 1.0 × 10⁻⁷).

Similar notation systems are used to describe many other chemical quantities that contain a large negative exponent. For example, chemists use an analogous pOH scale to describe the hydroxide ion concentration of a solution. The pOH and [OH⁻] are related as follows:

The constant K_w can also be expressed using this notation, where pK_w = −log K_w.

Because a neutral solution has [OH⁻] = 1.0 × 10⁻⁷, the pOH of a neutral solution is 7.00. Consequently, the sum of the pH and the pOH for a neutral solution at 25°C is 7.00 + 7.00 = 14.00. We can show that the sum of pH and pOH is equal to 14.00 for any aqueous solution at 25°C by taking the negative logarithm of both sides of Equation 16.7:

Thus at any temperature, pH + pOH = pK_w, so at 25°C, where K_w = 1.0 × 10⁻¹⁴, pH + pOH = 14.00. More generally, the pH of any neutral solution is half of the pK_w at that temperature. The relationship among pH, pOH, and the acidity or basicity of a solution is summarized graphically in Figure 16.1 "The Inverse Relationship between the pH and pOH Scales" over the common pH range of 0 to 14. Notice the inverse relationship between the pH and pOH scales.

Figure 16.1 The Inverse Relationship between the pH and pOH Scales

As pH decreases, [H⁺] and the acidity increase. As pOH increases, [OH⁻] and the basicity decrease. Common substances have pH values that range from extremely acidic to extremely basic.