Q.(a) Explain Ostwald's dilution law.

(a) Ostwald's dilution law applies the law of chemical equilibrium to the dissociation of a weak electrolyte, giving $K_a = \dfrac{C\alpha^2}{1-\alpha} \approx C\alpha^2$, so the degree of dissociation rises as the solution is diluted. (b) IUPAC lays down fixed left-to-right, line-notation rules for writing an electrochemical cell diagram unambiguously.

(a) Ostwald's dilution law

Consider a weak, binary electrolyte $AB$ dissociating partially in solution:

$AB \rightleftharpoons A^+ + B^-$

Let $C$ be the initial (stoichiometric) concentration and $\alpha$ the degree of dissociation at equilibrium. At equilibrium:

$[AB] = C(1-\alpha), \qquad [A^+] = [B^-] = C\alpha$

Applying the law of mass action (equilibrium law) to this dissociation gives the dissociation constant $K_a$:

$K_a = \frac{[A^+][B^-]}{[AB]} = \frac{(C\alpha)(C\alpha)}{C(1-\alpha)} = \frac{C\alpha^2}{1-\alpha}$

This relation is Ostwald's dilution law. For a weak electrolyte, $\alpha \ll 1$, so $(1-\alpha) \approx 1$, and the law simplifies to:

$K_a \approx C\alpha^2 \quad \Rightarrow \quad \alpha = \sqrt{\frac{K_a}{C}}$

Since $C = 1/V$ (where $V$ is the volume, in litres, containing one mole of electrolyte, i.e. the dilution), this can also be written as $\alpha = \sqrt{K_a V}$ — showing explicitly that the degree of dissociation increases with dilution (as $C$ decreases, or $V$ increases, $\alpha$ increases), approaching $\alpha \to 1$ at infinite dilution.

Limitation: Ostwald's dilution law holds well for weak electrolytes but fails for strong electrolytes, because it does not account for the inter-ionic attractions between the (nearly fully dissociated) ions of a strong electrolyte, which affect the electrolyte's effective (activity-based) behaviour.

(b) IUPAC conventions for writing a cell diagram

An electrochemical (galvanic) cell is represented in a standardised line-notation form, governed by these IUPAC rules:

1. The anode (oxidation half-cell) is written on the left, and the cathode (reduction half-cell) on the right.
2. A single vertical line ($|$) is used to represent a phase boundary/interface — e.g. between a metal electrode and its electrolyte solution.
3. A double vertical line ($\|$) (or a pair of dashed lines) represents the salt bridge (or any separator) connecting the two half-cells, and indicates that the liquid-junction potential is assumed eliminated.
4. Species that are present in the same phase are separated by a comma rather than a vertical line (e.g. for an inert electrode like Pt dipping into a solution containing both oxidised and reduced forms).
5. The concentration (or activity) of each species is indicated in parentheses immediately after it. …