Ionic Equilibrium — Acids, Bases (Arrhenius, Brønsted, Lewis)

Electrolytes and ionic equilibrium

Michael Faraday classified substances by their ability to conduct electricity in solution: electrolytes conduct in their aqueous solutions, while non-electrolytes do not. He further divided electrolytes into strong and weak. A strong electrolyte is almost completely ionized on dissolution — an aqueous solution of sodium chloride consists entirely of $\ce{Na+}$ and $\ce{Cl-}$ ions. A weak electrolyte is only partially dissociated; acetic acid is less than 5% ionized and its solution is mostly unionized $\ce{CH3COOH}$ molecules with only a little acetate and hydronium ion.

The crucial consequence is that in a weak electrolyte an equilibrium is established between the ions and the unionized molecules. This equilibrium involving ions in aqueous solution is called ionic equilibrium (NCERT §6.9). Acids, bases and salts all fall under the category of electrolytes and may behave as either strong or weak electrolytes.

A vocabulary point that NCERT itself clarifies: dissociation is the separation in water of ions that already exist in the solid (as in $\ce{NaCl}$), whereas ionization is a neutral molecule splitting into charged ions in solution. For acid-base equilibria the two terms are used interchangeably. The strength of ionization depends on the strength of the bond being broken and the extent to which the resulting ions are solvated (hydrated) by the high-dielectric medium, water ($\varepsilon \approx 80$).

The Arrhenius concept

The earliest workable definition came from Svante Arrhenius (1884). According to the Arrhenius concept, an acid is a substance that dissociates in water to give hydrogen ions, $\ce{H+}(aq)$, and a base is a substance that produces hydroxyl ions, $\ce{OH-}(aq)$. The ionization of an acid $\ce{HX}$ and a base $\ce{MOH}$ is written as:

$$\ce{HX(aq) -> H+(aq) + X^-(aq)} \qquad \ce{MOH(aq) -> M+(aq) + OH^-(aq)}$$

A bare proton, $\ce{H+}$, is far too reactive to exist freely in water; it bonds to a lone pair on a water molecule to give the trigonal-pyramidal hydronium ion, $\ce{H3O+}$. NCERT therefore uses $\ce{H+}(aq)$ and $\ce{H3O+}(aq)$ interchangeably to mean a hydrated proton. The neutralisation of acid by base is then simply the combination of these ions to form water.

The Brønsted-Lowry concept

In 1923 the Danish chemist Johannes Brønsted and the English chemist Thomas M. Lowry independently gave a more general definition built around the proton itself. According to the Brønsted-Lowry theory, an acid is a substance capable of donating a hydrogen ion ($\ce{H+}$) and a base is a substance capable of accepting a hydrogen ion. In short: acids are proton donors, bases are proton acceptors. Because the definition makes no mention of water, it removes the solvent restriction of the Arrhenius view.

Consider the dissolution of ammonia in water:

$$\ce{NH3 + H2O <=> NH4+ + OH^-}$$

Here the water molecule donates a proton (so $\ce{H2O}$ is the Brønsted acid) and ammonia accepts it (so $\ce{NH3}$ is the Brønsted base). The basic solution arises from the $\ce{OH-}$ produced — and notice that no hydroxyl group had to come pre-formed inside ammonia, which is exactly what Arrhenius could not handle.

Conjugate acid-base pairs

In the reverse of the ammonia reaction, $\ce{H+}$ is transferred from $\ce{NH4+}$ to $\ce{OH-}$, so $\ce{NH4+}$ acts as a Brønsted acid and $\ce{OH-}$ as a Brønsted base. An acid-base pair that differs by only one proton is called a conjugate acid-base pair. Thus $\ce{OH-}$ is the conjugate base of the acid $\ce{H2O}$, and $\ce{NH4+}$ is the conjugate acid of the base $\ce{NH3}$. The rule is mechanical: the conjugate base has one less proton, the conjugate acid has one extra proton.

The same logic applies to hydrochloric acid in water, where $\ce{HCl}$ donates a proton to $\ce{H2O}$:

$$\ce{HCl + H2O -> H3O+ + Cl^-}$$

Here $\ce{Cl-}$ is the conjugate base of $\ce{HCl}$, and $\ce{H3O+}$ is the conjugate acid of $\ce{H2O}$. The pairing always links a species and its proton-shifted partner across the equation. The worked examples below come straight from NCERT Problems 6.12–6.14.

Some species sit in the middle and can swing either way. These amphoteric (amphiprotic) species act as a Brønsted acid in one reaction and a base in another. NCERT Problem 6.14 lists $\ce{H2O}$, $\ce{HCO3^-}$, $\ce{HSO4^-}$ and $\ce{NH3}$ as species that do both:

Water's dual personality is the cleanest illustration. Faced with $\ce{HCl}$ it accepts a proton (acts as a base); faced with $\ce{NH3}$ it donates a proton (acts as an acid). The same molecule, opposite roles, decided entirely by the partner.

The Lewis concept

The Brønsted view still cannot describe acidity in species that have no proton to give, such as $\ce{AlCl3}$, nor the basicity of proton-free bases. In 1923 G. N. Lewis proposed the broadest definition of all, framed in terms of electron pairs rather than protons. A Lewis acid is any species that can accept an electron pair; a Lewis base is any species that can donate an electron pair.

For bases there is little practical difference between the Brønsted and Lewis pictures — in both, the base supplies a lone pair. The real expansion is on the acid side: many Lewis acids carry no proton at all. The textbook example is electron-deficient $\ce{BF3}$ reacting with ammonia:

$$\ce{BF3 + :NH3 -> BF3:NH3}$$

$\ce{BF3}$ has no proton, yet it acts as an acid by accepting the lone pair on nitrogen to complete boron's octet. The same behaviour is shown by other electron-deficient species — $\ce{AlCl3}$, $\ce{Co^{3+}}$, $\ce{Mg^{2+}}$ — which act as Lewis acids, while $\ce{H2O}$, $\ce{NH3}$ and $\ce{OH-}$, all able to donate a lone pair, act as Lewis bases. A proton itself, $\ce{H+}$, is a Lewis acid because it accepts a lone pair from bases such as $\ce{OH-}$ or $\ce{F-}$. The NIOS supplement (§12.2.3) frames the same idea around $\ce{AlCl3}$: it accepts the lone pair of $\ce{NH3}$ to give the adduct, so $\ce{AlCl3}$ is the Lewis acid and $\ce{NH3}$ the Lewis base.

The pattern worth memorising is the source of acidity in each theory. Arrhenius and Brønsted acidity both trace back to a hydrogen atom that can be released as a proton, so neither can label a proton-free species an acid. Lewis acidity instead arises from an empty orbital or electron deficiency, which is why it admits boron and aluminium halides, transition-metal cations and the proton alike. Because lone-pair donation underlies basicity in all three pictures, the Lewis and Brønsted definitions of a base coincide in practice — the genuine broadening is confined to the acid side.

Comparing the three concepts

The three theories are not rivals but a widening sequence. The comparison below is the single most testable block of this subtopic: definition, what counts as the acid and base, an example, and the limitation each new theory overcomes.

Relative strength and conjugates

Acid-base dissociation is a dynamic equilibrium of proton transfer in both directions, so the natural question is which direction is favoured. The driving principle is that the equilibrium shifts towards the formation of the weaker acid and weaker base: the stronger acid donates its proton to the stronger base. For the generic weak acid $\ce{HA}$,

$$\ce{HA + H2O <=> H3O+ + A^-}$$

if $\ce{HA}$ is a stronger proton donor than $\ce{H3O+}$, the position lies to the right and the solution is rich in $\ce{A-}$ and $\ce{H3O+}$. From this follows the inverse-strength relationship between an acid and its conjugate base.

Because a strong acid dissociates almost completely, the conjugate base it leaves behind has almost no tendency to recapture the proton — it is a very weak base. NCERT spells this out: the strong acids $\ce{HClO4}$, $\ce{HCl}$, $\ce{HBr}$, $\ce{HI}$, $\ce{HNO3}$ and $\ce{H2SO4}$ give the conjugate bases $\ce{ClO4^-}$, $\ce{Cl^-}$, $\ce{Br^-}$, $\ce{I^-}$, $\ce{NO3^-}$ and $\ce{HSO4^-}$, all much weaker bases than water. The NIOS supplement (§12.3) states the converse rule generally: the weaker an acid, the stronger is its conjugate base, and the weaker a base, the stronger is its conjugate acid.