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:

The three concepts can be summarized 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

Venn diagram of acid-base concepts

The Venn diagram on the right shows how the Lewis concept encompasses both Brønsted-Lowry and Arrhenius theories.

When one talks about acids, one inevitably talks about pH. The pH is a measure of the H+ concen­tration (to be more precise: the H+ activity). It is therefore not surprising that we prefer the proton-transfer concept of Brønsted and Lowry for our further discussion.2

Proton Transfer in Acid-Base Reactions

An acid HA is a proton donor; it releases H+ ions (more precisely: 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, the concepts of Arrhenius and Brønsted-Lowry differ:

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

This allows all Arrhenius bases3 to be combined into a single H+-acceptor equation:

(2) OH- + H+ = H2O ,

but the Brønsted-Lowry concept has something more up its sleeve.

Conjugate Acids.  Something new comes into play with the Brønsted-Lowry concept (that the Arrhenius concept does not have): conjugate 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 disappeared (because they are transferred between conjugate acid-base pairs). H+ ions only appear in “half reactions”, such as 1a or 2:

(3c)         \(\boxed{ \quad \left. \begin{array}{c} \mathsf{acid} \\ \mathsf{(proton\ donor)} \end{array} \right. =\ \ \mathsf{\ce{H+}}\ + \left. \begin{array}{c} \mathsf{conjugate\ base} \\ \mathsf{(proton\ acceptor)} \end{array} \right. \quad}\)

3c is a general concept that applies to any polyprotic acid, namely for each individual dissociation step (as shown here).

Autoprotolysis.  One very special case of 3a 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”.

Justification of the Equilibrium Approach

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

The framework was established long ago in form of the “Law of mass action” (by Guildberg and Waage in 1864), where the equilibrium state is characterized by one single quantity — the equilibrium constant K. In modern-day chemistry this is derived from the Gibbs energy (originally established in 1873 by J.W. Gibbs).

Acidity Constants Ka (and pKa)

The equilibrium constant of reaction (1a) is called “acid dissociation constant” or

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

The value of Ka signifies the strength of the acid:

In practice, it is more convenient to use the (base-10) logarithmic form of 5:

(6) lg Ka  =  lg {H+} + lg {A-} – lg {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 the 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 citric acid
  HF H2SeO4
  formic acid oxalic acid  
  acetic acid, …  

A monoprotic acid is characterized by 1 acidity constant K1 (= Ka), a diprotic acid by 2 acidity constants (K1, K2), and a triprotic acid by 3 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:4

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

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

Examples.  Analytical formulas are provided for diprotic acids and for the general case of polyprotic acids.

Remarks & Footnotes

  1. While acid-base reactions interchange electron-pairs, redox reactions are based on the exchange (of a sequence) of single electrons. 

  2. A detailed math description is provided in the form of a review article (2021) and/or lecture (2023). 

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

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

[last modified: 2023-11-26]