Overview Activity Chem Equilibrium Acids Carbonate System Mineral Phases

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”: Acids are substances able to “accept” a lone pair of electrons from another molecule, designated as a base.¹ This concept can also be used for ligand-metal ion coordination reactions and substitution reactions in organic chemistry.

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

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 K_a (and pK_a)

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 K_a signifies the strength of the acid:

• large K_a   ⇔   strong acids
• small K_a   ⇔   weak acids

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 pK_a:

(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 pK_a value allows a classification into strong and weak acids: The smaller the pK_a the stronger the acid – quite the opposite to a K_a-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 (= K_a), 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