Arrhenius Theory of Acids and Bases

Svante August Arrhenius
(1859-1927)

Svante August Arrhenius, a celebrated Swedish physical chemist, born on February 19, 1859, in Vik, Sweden, faced financial hurdles during his rural upbringing but rose to prominence with his remarkable contributions to science. Completing his Ph.D. in 1884 at the University of Uppsala, he later became a professor there, gaining recognition for his work on electrolytes and his innovative theory of acids and bases. Arrhenius's ground-breaking theory delved into how certain substances conduct electricity when dissolved in water, a concept known as ionization in aqueous solutions. This pioneering work earned him the prestigious Nobel Prize in Chemistry in 1903.

Beyond his impact in chemistry, Arrhenius also left a lasting imprint on climate science. In 1896, he proposed a theory suggesting that alterations in atmospheric carbon dioxide levels could influence Earth's temperature, laying the foundation for our current understanding of climate change. Svante Arrhenius continued his scientific pursuits until his passing on October 2, 1927, in Stockholm, Sweden, leaving behind a significant legacy.

According to Arrhenius's theory, acids are compounds containing hydrogen that can produce protons or H⁺ ions when dissolved in water. Bases, on the other hand, are substances that can produce OH^- ions in water. Some examples of acids and bases include:

Acids: HCl ⇋ H⁺+Cl^- , H₂SO₄ ⇋ 2H⁺ + SO₄^2-

Base: NaOH ⇋ Na⁺+OH^-, NH₄OH ⇋ NH₄⁺+ OH^-

The concentration of acids and bases or acidity and basicity depends on the amount of H⁺ and OH^- a substance can produce. This theory also explains neutralisation which is simply a process that exhibits the combination of H⁺ and OH^- ions. Therefore the heat of neutralization is expected to be an equivalent amount of any acid and bases.

H⁺ + OH^- ⇋ H₂O

In aqueous solutions the concentration of H⁺ is often given in terms of pH, where:

pH = logo₁₀1/[H⁺] = -log10[H⁺]

Where [H+] represents the hydrogen ion concentration, or more precisely, the activity of hydrogen ions should be considered. This logarithmic scale, devised by S. P. L. Sørensen in 1909, proves highly valuable for representing concentrations across various orders of magnitude (e.g., 1 M H⁺ corresponds to pH 0, while 10^-14 M H⁺ corresponds to pH 14).

Before the nineteenth century, it was believed that water was the sole solvent supporting ionic reactions. However, research conducted by Cady in 1897, Franklin and Kraus in 1898 on reactions in liquid ammonia, and Walden in 1899 on reactions in liquid sulphur dioxide, unveiled numerous similarities with reactions occurring in water. These findings hinted at these three solvents being ionizing agents suitable for ionic reactions, with acids, bases, and salts being common to all three systems.

Despite water's prevalence as a solvent, its exclusive usage restricted chemistry to compounds stable in its presence. Consequently, non-aqueous solvents are increasingly employed in inorganic chemistry, as they enable the preparation of many new, water-unstable compounds, including some anhydrous varieties like anhydrous copper nitrate, which exhibit distinct properties from their hydrated counterparts. Thus, the concepts of acids and bases, rooted in aqueous systems, necessitate expansion to encompass non-aqueous solvents.

Acids and Bases in Proton Solvents

Water self-ionizes:

2H₂O ⇋ H₃O⁺ + OH^-

The equilibrium constant for this reaction depends on the concentration of water [H₂O], and on the concentrations of the ions [H₃O⁺] and [OH^-].

K₁ = [H₃O⁺][OH^-]/[H₂O]²

Since water is in large excess, its concentration is effectively constant, so the ionic product of water may be written:

K_w = [H₃O⁺][OH^-] = 10^-14 mol²l^-2

The Value of K_w is 1.00 × 10^-14 mol²l^-2 at 25^oC, but it varies with temperature. Thus at 25^oC there will be 10^-7 mol^-1 of H₃O⁺ and 10^-7 mol^-1 of OH^- in pure water.

K_w of Water in different Temperature

Temperature (oC)	Kw (mol2l-2)
0	0.12 × 10-14
10	0.29 × 10-14
20	0.68 × 10-14
25	1.00 × 10-14
30	1.47 × 10-14
40	2.92 × 10-14
100	47.6 × 10-14

 

Acids such as HA increase the concentration of H₃O⁺:

HA + H₂O ⇋ H₃O⁺ + A^-

In dilute solution water is in such a large excess that the concentration of water is effectively constant (approximately 55 M), and this constant can be incorporated in the constant at the left side. Thus:

K_a = [H₃O⁺][A^-]/[HA]

pH of solutions with different H⁺ and OH^- concentration

pH	[H+] (mol.l-1)	[OH-] (mol.l-1)
0	100	10-14
1	10-1	10-13
2	10-2	10-12
3	10-3	10-11
4	10-4	10-10
5	10-5	10-9
6	10-6	10-8
7	10-7	10-7
8	10-8	10-6
9	10-9	10-5
10	10-10	10-4
11	10-11	10-3
12	10-12	10-2
13	10-13	10-1
14	10-14	100

 

The pH scale is used to measure the activity of hydrogen ions (pH = -log[H+]). In a similar way the acid dissociation constant K_a may be expressed as a pKa value:

pK_a = log [1/K_a] = -log K_a

Thus pK_a is a measure of strength of an acid. If the acid ionizes almost completely (high acid strength) then K_a will be large, and thus pK_a will be small. The pK_a values given below show that acid strength increases on moving from left to right in the periodic table:

 pK_a:   CH₄ = 46                   NH₃ = 35                    H₂O = 16                        HF = 3

Acid strength also increases on moving down a group:

pK_a:    HF = 3                      HCl = -7                      HBr = -9                        HI = -10

With oxoacids containing more than one hydrogen atom, successive dissociation constant rapidly become more positive, i.e., the phosphate species formed on successive removal of H⁺ becomes less acidic:

H₃PO₄ ⇋ H⁺ + H₂PO₄^-    pK_a = 2.15

H₂PO₄^- ⇋ H⁺ + HPO₄^2-     pK_a = 7.20

HPO₄^2- ⇋ H⁺ + PO₄^3-      pK_a = 12.37

If an element forms a series of oxoacids, then the more oxygen atoms present, the more acidic it will be. The reason for this is that the electrostatic attraction for the proton decreases as the negative charge is spread over more atoms, thus facilitating ionization.

Very Weak Acid	Weak Acid	Strong Acid	Very Strong Acid
	HNO2 (pKa =3.3)	HNO3 (pKa =-1.4)
	H2SO3 (pKa = 1.9)	H2SO4 (pKa = -1)
HOCl(pKa =7.2)	HClO2 (pKa = 2.0)	HClO3 (pKa = -1)	HClO4 (pKa =-10)

 

Limitation of Arrhenius concept

However, this theory has limitations. Compounds like SO₃ and CO₂, which lack hydrogen, can still exhibit acidic characteristics by generating H⁺ ions in water. Conversely, compounds like NH₃ and Na₂CO₃ can produce OH^- ions in water. Thus, the Arrhenius concept may not fully explain compounds with acidic and basic properties that do not strictly align with the presence of hydrogen or hydroxide ions. Additionally, the theory confines acid-base interactions to aqueous media, while various interactions are documented in non-aqueous environments.

Reference

1) Concise inorganic chemistry by J. D. Lee.

2) Inorganic Chemistry by James E. Huheey, Ellen A Keither, Richard L. Keither, Okhil K. Medhi.