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The Arrhenius theory of electrolytic dissociation is expressed in Chapter 7.3 of the Physical Chemistry book. The theory stated that electrolytes such as acids, bases and salts dissociated into their component ions in aqueous solution.

Arrhenius further stipulated that some electrolytes dissociated completely (strong electrolytes) and some dissociated only partially (weak electrolytes) (Fig. 7.2 above). The Arrhenius theory was later used to explain the acid-base concept.

Early concepts of acids and bases

Arrhenius defined an acid as a hydrogen-containing compound that when dissolved in water produces a concentration of hydrogen ions (or protons) greater than that of pure water. A base is defined as a substance that when dissolved in water produces an excess of hydroxyl ions, OH⁻. The neutralization reaction can be described as such:

H⁺ (aq) + OH⁻ (aq) →H₂O (l)

However, the Arrhenius theory of acids and bases had limitations.

1. The theory restricts acids to hydrogen-containing species and bases to hydroxyl-containing species
2. The theory applies to aqueous solutions only, while we know that many acid-base reactions can take place in the absence of water
3. The theory is inadequate for gas and solid phase reactions in which H⁺ and OH⁻ may not exist

The Brønsted-Lowry theory of acids and bases

The Brønsted-Lowry theory was developed to eliminate some of the limitations of the Arrhenius concept of acids and bases.
Although the theory states that the acid must still contain hydrogen, it does not require an aqueous medium. E.g. liquid ammonia is a base in aqueous solution but it can act as an acid in the absence of water by transferring a proton to a base and forming the amide anion, NH₂⁻:

NH₃ + base ↔ NH₂⁻ + base + H⁺

In the Brønsted-Lowry theory, acid-base reactions are regarded as proton transfer reactions. This definition enabled the Arrhenius list to include gases such as HCl and NH₃ among many others.
A broader theory of acids and bases was later proposed by the Lewis theory. According to this theory, an acid is any species that acts as an electron pair acceptor (electrophile) and a base is any species that acts as an electron pair donor (nucleophile). Therefore an acid-base reaction is the sharing of an electron pair provided by the base to the acid.
This definition expanded the list to include metal ions and other electron pair acceptors as acids and provides a handy framework for non-aqueous reactions.

Arrhenius’ theory of electrolytic dissociation

We know that the conductivity of a solution is as a result of the mobility of cations and anions in aqueous solution. The greater the number of ions, the greater is the conductivity.
The degree of dissociation is defined as the fraction of the total number of molecules dissociated into ions.
Strong electrolytes are used to express substances that completely ionize when dissolved with no neutral molecules formed in solution. A good example is the ionic solid NaCl. The solute of NaCl is completely ionized because no molecules of NaCl are present in NaCl solid or NaCl solution.

NaCl (s) → Na⁺ (aq) + Cl⁻ (aq)

Some other examples of ionic solids are CuSO₄, NH₄Cl, KBr, NaCH₃COO and NaHCO₃.
Weak electrolytes only partially ionize hence some neutral molecules are still present in their solutions (in this equation below, there are still H₂CO₃ molecules present).

H₂CO₃ (aq) → H⁺(aq) + HCO₃⁻ (aq)

Examples are H₂CO₃, NH₃, NH₄OH, CH₃COOH and most organic acids and bases.
The Arrhenius theory had limitations interpreting for strong electrolytes. Here are some of the anomalies:

1. Arrhenius theory assumes ionization of electrolytes only in aqueous solution but x-ray diffraction studies prove that crystalline alkali halides (e.g. NaCl) exists in ionized forms even in the solid state.
2. Strong electrolytes (e.g. NaOH, KCl) conduct electricity in molten states also which means that their ionization must have taken place in the absence of water
3. Arrhenius theory assumes the existence of ions in solution but it does not explain how or why ions are formed in solution

The behaviour of strong electrolytes is better explained by the Debye-Hückel theory. The theory explains the distribution of positive and negative ions in aqueous solution as a result of electrostatic forces (Fig. 7.3 below). A detailed account of this is covered in Chapter 7.4 of the Physical Chemistry book.

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The importance of electrolytes in our bodies

Electrolyte balance is crucial to maintain bodily functions. The primary electrolytes in bodily fluids are cations (calcium, magnesium, sodium and potassium) and anions (iodide, chloride, phosphates, carbonates, amino acetates). Nutritionally these are called macrominerals.
Extreme imbalance in electrolytes can lead to muscle spasm (as a result of decreased plasma calcium and magnesium), cardiac arrhythmias (as a result of elevated potassium levels) and paralysis (decreased extracellular potassium).