Q.(a) Give the evidences in favour of Arrhenius theory of electrolytic dissociation.

(a) Conductance, colligative-property, thermochemical, and kinetic evidence all support the existence of free ions in electrolyte solutions, as proposed by Arrhenius. (b) The Nernst equation relates electrode/cell potential to concentration and is derived from the free-energy–EMF relationship $\Delta G = -nFE$ combined with the reaction-isotherm equation $\Delta G = \Delta G^{\circ} + RT\ln Q$.

(a) Evidence for Arrhenius's theory of electrolytic dissociation

Arrhenius proposed that electrolytes, when dissolved in water, spontaneously dissociate (ionise) to a greater or lesser extent into positively and negatively charged ions, even in the absence of an applied electric current. Supporting evidence:

1. Electrical conductivity: solutions of electrolytes (acids, bases, salts) conduct electricity, whereas solutions of non-electrolytes do not. Since conduction requires charge carriers that can move under an applied field, this is direct evidence for the presence of free, mobile ions in solution. Moreover, conductivity (equivalent conductance) increases on dilution, consistent with a greater fraction of the electrolyte dissociating as concentration falls.

2. Abnormal colligative properties: colligative properties (depression of freezing point, elevation of boiling point, osmotic pressure, lowering of vapour pressure) depend on the number of solute particles present. Electrolyte solutions show colligative effects larger than expected from the stated molar concentration (van't Hoff factor $i > 1$), which is explained exactly by dissociation of each formula unit into two or more ions, increasing the effective particle count.

3. Constant heat of neutralisation: the heat evolved when one gram-equivalent of any strong acid is neutralised by one gram-equivalent of any strong base in dilute solution is always very nearly the same (about $57.1\ kJ\,mol^{-1}$ or $13.7\ kcal\,eq^{-1}$), regardless of which particular strong acid and strong base are used. This is explained because, in every such case, the strong acid and strong base are essentially completely ionised, and the only chemical change actually occurring is the combination of the same species in every case: $H^+(aq) + OH^-(aq) \rightarrow H_2O(l)$; all the spectator ions remain unchanged in solution.

4. Characteristic ionic properties (e.g. colour): the colour (and much of the chemical reactivity) of a solution depends only on which ions are present, not on the particular compound that supplied them. For example, every solution containing $Cu^{2+}(aq)$ is blue and every solution containing $MnO_4^-(aq)$ is purple, irrespective of the specific copper or permanganate salt dissolved — showing the ions exist as independent, identifiable entities in solution.

5. Instantaneous ionic reactions: many reactions between electrolytes in solution, such as precipitation reactions (e.g. $Ag^+ + Cl^- \rightarrow AgCl\downarrow$), occur essentially instantaneously on mixing. This is consistent with pre-existing, freely mobile ions simply combining, rather than requiring the breaking of covalent bonds within intact molecules (which would be comparatively slow).

(b) Derivation of the Nernst equation

Consider a general electrode reaction (reduction): $M^{n+} + ne^- \rightarrow M$

From thermodynamics, the free energy change of a reaction at any stage (not necessarily standard conditions) is related to the standard free energy change by the reaction isotherm:

$\Delta G = \Delta G^{\circ} + RT\ln Q$ ... (1)

where $Q$ is the reaction quotient (activities/concentrations of products over reactants), $R$ is the gas constant, and $T$ is the absolute temperature.

The free energy change of an electrochemical process is related to the cell EMF by:

…