Question

Explain Ostwald's dilution law.

Answer 1

Step 1: Concept of Ostwald's dilution law

1. Ostwald's dilution law describes the dissociation constant of the weak electrolyte with the degree of dissociation $\mathrm{\alpha }$ and the concentration of the weak electrolyte.
2. It is applicable only for weak electrolyte such as Acetic acid (${\mathrm{CH}}_3\mathrm{COOH}$)

Step 2: Derivation of Ostwald's dilution law

1. Consider a binary electrolyte AB which dissociates into ${\mathrm{A}}^{+}$ and ${\mathrm{B}}^{-}$ ions, $\mathrm{AB}\left(\mathrm{l}\right)\rightleftharpoons {\mathrm{A}}^{+}\left(\mathrm{l}\right)+{\mathrm{B}}^{-}\left(\mathrm{l}\right)$.
2. At t=0 when no reaction is going on Concentration of AB= C and Concentration of ${\mathrm{A}}^{+}$ and ${\mathrm{B}}^{-}$ ions= 0 since there is no product formed.
3. At equilibrium Concentration of AB= $\mathrm{C}-\mathrm{C\alpha }$, Concentration of ${\mathrm{A}}^{+}$and ${\mathrm{B}}^{-}$ ions= $\mathrm{C\alpha }$
4. $\mathrm{AB}\left(\mathrm{l}\right)\rightleftharpoons {\mathrm{A}}^{+}\left(\mathrm{l}\right)+{\mathrm{B}}^{-}\left(\mathrm{l}\right)$ putting the values of an reactants and products concentration the equilibrium constant can be written as: $\mathrm{K}=\frac{\left[{\mathrm{A}}^{+}\right(\mathrm{l}\left)\right]\left[{\mathrm{B}}^{+}\right(\mathrm{l}\left)\right]}{\left[\mathrm{AB}\right(\mathrm{l}\left)\right]}$ which is also written as: $\mathrm{K}=\frac{\left[\mathrm{C\alpha }\right]\left[\mathrm{C\alpha }\right]}{\mathrm{C}-\mathrm{C\alpha }}=\frac{{\left(\mathrm{C\alpha }\right)}^2}{\mathrm{C}(1-\mathrm{\alpha })}$
5. For very weak electrolytes since $\mathrm{\alpha }<<<1,(1-\mathrm{\alpha })\approx 1$ therefore the expression of equilibrium constant can be written as: $\mathrm{K}={\mathrm{C\alpha }}^2$ then $\mathrm{\alpha }=\sqrt{\frac{\mathrm{K}}{\mathrm{C}}}$ where K= dissociation constant of weak acid, $\mathrm{\alpha }$= degree of dissociation, C= concentration.
6. Ostwald's dilution law states that only at infinite dilution the weak electrolyte undergoes complete ionization.

Therefore, Ostwald's dilution law relates dissociation constant with degree of dissociation and concentration.