Lewis Acids and Bases (15.2)

In 1923, G. N. Lewis proposed a generalized definition of acid-base behavior in which acids and bases are identified by their ability to accept or to donate a pair of electrons and form a coordinate covalent bond.

A coordinate covalent bond (or dative bond) occurs when one of the atoms in the bond provides both bonding electrons. For example, a coordinate covalent bond occurs when a water molecule combines with a hydrogen ion to form a hydronium ion. A coordinate covalent bond also results when an ammonia molecule combines with a hydrogen ion to form an ammonium ion. Both of these equations are shown here.

Reactions involving the formation of coordinate covalent bonds are classified as Lewis acid-base chemistry. The species donating the electron pair that compose the bond is a Lewis base, the species accepting the electron pair is a Lewis acid, and the product of the reaction is a Lewis acid-base adduct. As the two examples above illustrate, Brønsted-Lowry acid-base reactions represent a subcategory of Lewis acid reactions, specifically, those in which the acid species is H+. A few examples involving other Lewis acids and bases are described below.

The boron atom in boron trifluoride, BF₃, has only six electrons in its valence shell. Being short of the preferred octet, BF₃ is a very good Lewis acid and reacts with many Lewis bases; a fluoride ion is the Lewis base in this reaction, donating one of its lone pairs:

In the following reaction, each of two ammonia molecules, Lewis bases, donates a pair of electrons to a silver ion, the Lewis acid:

Nonmetal oxides act as Lewis acids and react with oxide ions, Lewis bases, to form oxyanions:

Many Lewis acid-base reactions are displacement reactions in which one Lewis base displaces another Lewis base from an acid-base adduct, or in which one Lewis acid displaces another Lewis acid:

Another type of Lewis acid-base chemistry involves the formation of a complex ion (or a coordination complex) comprising a central atom, typically a transition metal cation, surrounded by ions or molecules called ligands. These ligands can be neutral molecules like H₂O or NH₃, or ions such as CN^– or OH^–. Often, the ligands act as Lewis bases, donating a pair of electrons to the central atom. These types of Lewis acid-base reactions are examples of a broad sub-discipline called coordination chemistry—the topic of another chapter in this text.

The equilibrium constant for the reaction of a metal ion with one or more ligands to form a coordination complex is called a formation constant (K_f) (sometimes called a stability constant). For example, the complex ion Cu(CN)₂ ⁻

is produced by the reaction

Cu⁺(aq) + 2CN⁻(aq) ⇌ Cu(CN)₂ ⁻(aq)

The formation constant for this reaction is

K_f = [latex]\frac{[Cu(CN)_{2} ^{-}]}{[Cu ^{+}][CN^{-}]^{2}}[/latex]

Alternatively, the reverse reaction (decomposition of the complex ion) can be considered, in which case the equilibrium constant is a dissociation constant (K_d). Per the relation between equilibrium constants for reciprocal

reactions described, the dissociation constant is the mathematical inverse of the formation constant, K_d = K_f^–1. A tabulation of formation constants is provided in Appendix K.

As an example of dissolution by complex ion formation, let us consider what happens when we add aqueous ammonia to a mixture of silver chloride and water. Silver chloride dissolves slightly in water, giving a small concentration of Ag⁺ ([Ag⁺] = 1.3 × 10^–5 M):

AgCl(s) ⇌ Ag+(aq) + Cl−(aq)

However, if NH₃ is present in the water, the complex ion, Ag(NH₃)₂ ⁺, can form according to the equation:

Example 15.14

Dissociation of a Complex Ion

Calculate the concentration of the silver ion in a solution that initially is 0.10 M with respect to Ag(NH₃)₂ ⁺.

Solution

Applying the standard ICE approach to this reaction yields the following:

Substituting these equilibrium concentration terms into the K_f expression gives

K_f = [latex]\frac{[Ag(NH_{3})_{2} ^{+}]}{[Ag ^{+}][NH_{3}]^{2}}[/latex]

1.7 × 10⁷ =[latex]\frac{0.10 - x}{(x)(2x)^{2}}[/latex]

The very large equilibrium constant means the amount of the complex ion that will dissociate, x, will be very small. Assuming x << 0.1 permits simplifying the above equation:

1.7 x 107 = [latex]\frac{0.10}{(x)(2x)^{2}}[/latex]

x3 = [latex]\frac{0.10}{4(1.7 \times 10^{7})}[/latex] =1.5 x 10-9

x = [latex]^{3}\sqrt{1.5 \times 10^{-9}}[/latex] = 1.1 x 10^-3

Because only 1.1% of the Ag(NH₃)₂ ⁺ dissociates into Ag⁺ and NH₃, the assumption that x is small is justified.

Using this value of x and the relations in the above ICE table allows calculation of all species’ equilibrium concentrations:

[Ag⁺] = 0 + x = 1.1 × 10⁻³ M

[NH₃] = 0 + 2x = 2.2 × 10⁻³ M

[Ag(NH₃)₂ ⁺] = 0.10 − x = 0.10 − 0.0011 = 0.099

The concentration of free silver ion in the solution is 0.0011 M.

Check Your Learning

Calculate the silver ion concentration, [Ag⁺], of a solution prepared by dissolving 1.00 g of AgNO₃ and 10.0 g of KCN in sufficient water to make 1.00 L of solution. (Hint (see the video below): Because K_f is very large, assume the reaction goes to completion then calculate the [Ag⁺] produced by dissociation of the complex.)

The following Youtube video will help you to better understand the “hint” in the Check Your Learning question above.

Answer: 2.5 × 10^–22 M