Although the Brønsted–Lowry concept of acids and bases as donors and acceptors of protons is still the most generally accepted one, other definitions are often encountered. Certain of these are adapted for special situations only, but the most important of these other definitions is in some respects more general than the Brønsted–Lowry definition. This definition was first proposed by the American chemist Gilbert N. Lewis in 1923.
According to Lewis, an acid is a species that can accept an electron pair from a base with the formation of a chemical bond composed of a shared electron pair (covalent bond). This classification includes as bases the same species covered by the Brønsted–Lowry definition, since a molecule or ion that can accept a proton does so because it has one or more unshared pairs of electrons, and therefore it also can combine with electron acceptors other than the proton. On the other hand, the typical Lewis acids need not (and usually do not) contain protons, being species with outer electron shells that are capable of expansion, such as boron trifluoride (BF3), sulfur trioxide (SO3), and silver ion (Ag+). Lewis originally based his ideas on the experimental fact that these nonprotonic acids often exhibit the properties regarded as typical of acids, such as neutralization of bases, action on indicators, and catalysis. Such substances often are electron acceptors, but this is not always the case; carbon dioxide (CO2) and nitrogen pentoxide (N2O5), for example, contain completed octets of electrons and, according to usual valence theory, cannot accept any more. In addition, hydrogen-containing substances that have always been regarded as acids (acetic acid, for example) are not obviously electron acceptors, being rather adducts of the proton (a true Lewis acid) and a base such as the acetate ion. They can only be brought logically into the Lewis scheme by appealing to the fact that the reaction between a proton acid, which may be designated as XH, and a base, denoted by B, passes through an intermediate hydrogen-bonded state, X-H…B (in which the dotted line indicates a hydrogen bond, a relatively weak secondary attractive force).
Numerous lengthy polemical exchanges have taken place regarding the relative merits of the Brønsted–Lowry and Lewis definitions. The difference is essentially one of nomenclature and has little scientific content. In the remainder of this article the term acid is used to denote a proton donor (following the Brønsted–Lowry terminology), whereas the term Lewis acid is employed exclusively to refer to electron-pair acceptors. This choice is based partly on the logical difficulties mentioned in the last paragraph and partly on the fact (see below Acid–base equilibria) that the quantitative description of acid–base reactions is much simpler when it is confined to proton acids. It also represents the commonest usage of the terms.
The definition of Lewis acids and bases in terms of the gain or loss of electrons should not be confused with the definition of oxidizing and reducing agents in similar terms. In oxidation–reduction reactions one or more electrons are transferred completely from the reducing agent to the oxidizing agent, whereas in a Lewis acid–base reaction an electron pair on the base is used to form a covalent link with the acid.
Certain other acid–base definitions have been based upon reactions occurring in specific solvent systems. For proton acids in amphoteric solvents these are equivalent to the Brønsted–Lowry definition. It is sometimes convenient to have general terms for the cation and anion derived from the solvent molecule by the addition and removal of a proton, respectively. The terms lyonium and lyate ions are occasionally used in this way. In water, the lyonium and lyate ions are H3O+ and OH−; in ethanol, C2H5OH2+ and C2H5O−; and in liquid ammonia, NH4+ and NH2−. For a given solvent, an acid can then be defined as a substance that increases the lyonium ion concentration (and correspondingly decreases the lyate ion concentration), whereas a base increases the lyate ion concentration (and decreases the lyonium ion concentration). This kind of definition, to be sure, really does not add anything to the concept of acids and bases as proton donors and proton acceptors.
The idea that an acid is a solute that gives rise to cations characteristic of the solvent and that a base is a solute that gives rise to anions characteristic of the solvent has sometimes been extended to solvents where no protons are involved at all—for example, liquid sulfur dioxide, SO2. In this example, the solvent is supposed to ionize according to the equation 2SO2 ⇄ SO2+ + SO32−. Thionyl chloride, regarded as SO2+ + 2Cl−, then can be considered an acid, and potassium sulfite, 2K+ + SO32−, can be considered a base. The species SO2+ and SO32− can certainly be regarded as Lewis acids and bases, but it is doubtful that they exist to any appreciable extent in liquid sulfur dioxide, a situation that makes the discussion somewhat artificial. Although this view of acids and bases has been useful in stimulating work in unusual types of solvent (for example, in carbonyl chloride, selenium oxychloride, antimony trichloride, and hydrogen cyanide), it has not met with general acceptance.
As already mentioned (The Brønsted–Lowry definition), the reaction expressed by the Brønsted–Lowry definition, A ⇄ B + H+, does not actually occur in any solution processes. This is because H+, the bare proton, has an enormous tendency to add to almost all chemical species and cannot exist in any detectable concentrations except in a high vacuum. Apart from any specific chemical interaction, the very small size of the proton (about 10−15 metre) means that it exerts an extremely powerful electric field, which will polarize and therefore attract any molecule or ion it comes into contact with. It has been estimated that the dissociation of 19 grams of the hydronium ion H3O+ to give 1 gram of protons and 18 grams of water would require the expenditure of about 1,200,000 joules (290,000 calories) of energy, and thus it is an extremely unlikely process indeed.
Typical acid–base reactions may be thought of as the combination of two reaction schemes, A1 ⇄ B1 + H+ and H+ + B2 ⇄ A2, leading to the combined form A1 + B2 ⇄ B1 + A2. This represents a proton-transfer reaction from A1 to B2, producing B1 and A2. A large number of reactions in solution, often referred to under a variety of names, can be represented in this way. This is illustrated by the following examples, in each of which the species are written in the order A1, B2, B1, A2.