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# The degree of dissociation of a weak electrolyte is proportional to its molar conductance. Explain.

Last updated date: 12th Sep 2024
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Hint: The degree of dissociation is the fraction of original solute molecules that have dissociated. It is usually dissociated by Greek symbol $\propto$. More accurately, degree of dissociation refers to the amount of solute dissociated into ions or radicals per mole.

The second class of category of compounds, referred to as weak electrolytes, are those where ionization is incomplete. The ionization will increase with dilution and hence the molar conductivity increases with dilution. Thus, we can say that the conductivity is directly proportional to the degree of dissociation of electrolyte..
For weak electrolytes, the graph plotted between molar conductivity $\sqrt C$ (where $C$ is the concentration) is not a straight line. This is because weak electrolytes have lower molar conductivities and lower degree of dissociation at higher concentration which increases steeply at lower concentration. Hence, we use Kohlrausch law of independent migration of ions for determining to limit molar conductivity $E_n^\circ$ for weak electrolyte.

Let us consider weak electrolyte $AB$.
$AB \rightleftharpoons {A^ + } + {B^ - }$
$l = 0,{\text{ C 0 0}}$ $\propto \to {\text{degree }}of{\text{ }}dissociation$
$t = t,{\text{ }}C - C \propto {\text{ }}C \propto {\text{ }}C \propto$
$K = \dfrac{{\left[ {{A^ + }} \right]\left[ {{B^ - }} \right]}}{{\left[ {AB} \right]}} = \dfrac{{\left( {C \propto } \right)\left( {C \propto } \right)}}{{C\left( {1 - \propto } \right)}} = \dfrac{{{ \propto ^2}C}}{{1 - \propto }}$
For weak electrolyte, $\propto \ll 1$
This implies that $\left( {1 - \propto } \right) \approx 1$
$K = \dfrac{{{ \propto ^2}C}}{{1 - \propto }} = { \propto ^2}C$
So, from this we can say that
$\propto = \sqrt {\dfrac{K}{C}}$
Thus, it is clear that the degree of dissociation of weak electrolyte is proportional to the inverse square root of the concentration, or the square root of dilution. The concentration of any one ionic species is given by the root of the product of the dissociation constant and concentration of electrolyte.
$\left[ {{A^ + }} \right] = \left[ {{B^ - }} \right] = \propto C = \sqrt {KC}$

Note:
Weak electrolyte, like weak acids and bases partially ionize in solution. On the other hand, strong electrolytes completely or almost completely ionize or dissociate and have many ions.