## Acids and Bases

Three Concepts

When learning hydrochemistry, it’s always good (and wise) to start with acid-base theory. Acid-base theory has been known for more than 100 years. Three main concepts were successively developed during this period:

• In 1884, Arrhenius provided the first modern, molecular-based definition: an acid is a substance that releases H+ in water; a base is a substance that releases OH-. In this way, he predicted the dissociation into ions even before charged elementary particles were accepted and established (in the late 1890s). H+ ions are just protons.

• In 1923, Brønsted and Lowry extended the concept with the idea that an acid-base reaction involves a proton transfer from a proton donor (the acid) to a proton acceptor (the base). The solvent no longer has to be water, as the new concept also applies to liquid ammonia, alcohol, benzene, and other non-aqueous solutions.

• About 15 years later, G.N. Lewis went one step further and stretched the “proton-transfer” concept of conventional acids and bases to the much broader concept of “electron-pair transfer”. The latter can also be used for ligand-metal ion coordination reactions and substitution reactions in organic chemistry.

Let’s summarize the concepts as follows:

concept acid base
Arrhenius (1884) contains H+ contains OH-
Brønsted-Lowry (1923) proton (H+) donor proton (H+) acceptor
Lewis (1938) e- pair acceptor e- pair donor

The relationship between all three concepts can be visualized as a Venn diagram where the most general Lewis concept encompasses both Brønsted-Lowry theory and Arrhenius theory.

If one speaks of acids or bases, one inevitably speaks of the pH value. This fundamental quantity, which appears in all formulas, is a measure of the H+ concentration. It is therefore not surprising that we prefer the proton-transfer concept of Brønsted and Lowry for our further discussion.1

Proton Transfer in Acid-Base Reactions

An acid HA is a proton donor; it produces H+ ions (or H3O+) when dissolved in water:

 (1a) HA  =  H+ + A- (1b) HA + H2O  =  H3O+ + A-

For the sake of simplicity we prefer the shorthand notation of 1a, but keep in mind that H+ ions do not exist in a free state; they are extremely reactive and form hydronium ions H3O+.

The definition of acids as proton donors is fully in line with Arrhenius’ notion of acids as substances that contain and release H+ ions. In the case of bases, however, both concepts differ:

 Arrhenius base: contains OH- (e.g.  NaOH, KOH, NH4OH, …) Brønsted-Lowry base: H+ acceptor (e.g.  OH-, Cl-, NH3, …)

This allows all Arrhenius bases2 to be combined into a single H+-acceptor equation:

 (2) OH- + H+ = H2O

Now something new comes into play (that the Arrhenius concept does not have): conjugated acid-base pairs. Adding 1a to 2 yields:

(3a)   HA + OH- = H2O + A-
(3b)   acid + base = conjugate acid + conjugate base
(of base OH-)   (of acid HA)

In this overall reaction, H+ ions do not appear (because they are transferred between conjugate acid-base pairs). H+ ions only appear in “half reactions”, such as 1a or 2.

Autoprotolysis. One very special case of 3 is the self-dissociation of water:

 (4) H2O + H2O  =  H3O+ + OH-

Here, water acts as an acid and a base at the same time. Such substances are named ampholytes.

Acidity Constants Ka (and pKa)

The proton-transfer mechanism makes acid-base reactions very fast, so that chemical equilibrium is always established in the shortest time. This allows the application of a thermodynamic description (while slow reactions, such as redox processes, require more sophisticated kinetic approaches).

The equilibrium constant of reaction (1a) is called ‘acid dissociation constant’ or

 (5) acidity constant: $K_a = \dfrac{\{H^+\}\{A^-\}}{\{HA\}}$

The value of Ka resembles the strength of the acid (large Ka – strong acids, small Ka – weak acids). In practice, it is more convenient to use the (base-10) logarithmic form of 5:

 (6) lg Ka  =  lg {H+} + lg {A-} – log {HA}

The negative decadic logarithm of the acidity constant is then abbreviated by pKa:

 (7) pKa = – lg Ka

which parallels the definition of pH as pH = –lg {H+}. In this notation, 7 converts to

 (8) pKa  =  pH – lg {A-} + lg {HA}

The pKa value allows a classification into strong and weak acids: The smaller the pKa the stronger the acid – quite the opposite to a Ka-based ranking. In literature, several types of classification into strong and week acids exist. One simple classification scheme is described here.

Polyprotic Acids

Acids can donate one, two or more protons (H+). Typical examples are:

Monoprotic acid (HA) Diprotic acid (H2A) Triprotic acid (H3A)
HCl H2CO3 H3PO4
HNO3 H2SO4 H3AsO4
HI H2CrO4 H3BO3
HF H2SeO4 citric acid
formic acid oxalic acid
acetic acid, …

A monoprotic acid is characterized by a single acidity constant K1 (= Ka), a diprotic acid by two acidity constants (K1, K2), and a triprotic acid by three acidity constants (K1, K2, K3):

 1st dissociation step: H3A = H+ + H2A- K1 2nd dissociation step: H2A- = H+ + HA-2 K2 3rd dissociation step: HA-2 = H+ + A-3 K3

The three reaction steps of a triprotic acid can also be written as:

 H3A  =  H+ + H2A- K1 H3A  =  2H+ + HA-2 K1K2 H3A  =  3H+ + A-3 K1K2K3

with equilibrium constants constructed from K1, K2, and K3. In fact, this procedure can be extended to any N-protic acid with N dissociation steps.

Ranking. Protons are released sequentially one after the other, with the first proton being the fastest and most easily lost, then the second, and then the third (which is most strongly bound). This yields the following ranking of acidity constants of a polyprotic acid:3

 (9) K1 > K2 > K3 or pK1 < pK2 < pK3

For example, phosphoric acid has pK1 = 2.147, pK2 = 7.207, and pK3 = 12.346.

Examples. A mathematical description (closed-form formulas) is provided for diprotic acids and for the general case of polyprotic acids.

Remarks & Footnotes

1. A detailed mathematical description is provided as pdf

2. An Arrhenius base can be abbreviated, for example, by BOH where the cation B+ stands for Na+, K+, NH4+ etc.

3. In organic acids, the second and third acidity constant may be similar.

[last modified: 2018-10-23]