Question

State Ostwald’s dilution law.

Answer 1

Hint: Wilhelm Ostwald’s law on dilution was proposed in 1888, which relates the relationship between the dissociation constant (${{\text{K}}_{\text{c}}}$) and the degree of dissociation $\alpha $ of a weak electrolyte. The relation is represented by \[{{\text{K}}_{\text{c}}}\text{=}\dfrac{\left[ {{\text{A}}^{+}} \right]\times \left[ {{\text{B}}^{-}} \right]}{\left[ \text{AB} \right]}=\dfrac{{{\alpha }^{2}}.\text{C}}{1-\alpha }\] .

Complete step by step answer:
Let us understand what is meant by dilution, it is the decrease in the concentration of a solute in a solution simply by mixing with solvent like adding more water to a solution. In diluted solution, the solvent is more than solute.
-Ostwald Dilution law is based on the fact that the ratio of an electrolyte broken into ions at ordinary dilution is completely dissociated into ions at infinite dilution. The derivation for Ostwald dilution law is-
Consider a binary electrolyte which breaks into ions. Ostwald noticed that the law of mass action can be applied to it. The equilibrium state is shown by:
$\text{AB}\rightleftharpoons {{\text{A}}^{+}}+{{\text{B}}^{-}}$
The fraction which is dissociated is $\alpha $ .So, the concentration each ion will be where C is the initial concentration of AB:
  \[\begin{align}
  & \left[ {{\text{B}}^{-}} \right]=C\alpha \\
 & \left[ {{\text{A}}^{+}} \right]=C\alpha \\
 & \left[ \text{AB} \right]=C(1-\alpha ) \\
\end{align}\]
 Now, Substitute the values in the dissociation expression, the dissociation constant becomes
\[{{K}_{\text{c}}}=\dfrac{\left[ {{\text{A}}^{+}} \right]\left[ {{\text{B}}^{-}} \right]}{\left[ \text{AB} \right]}\] ,${{K}_{\text{c}}}=\dfrac{C\alpha \times C\alpha }{C(1-\alpha )}$
${{\text{K}}_{\text{c}}}$ can be resolved into and for weak electrolyte, the degree of dissociation is very low so it will not dissociate completely, thus, $1-\alpha \simeq 1$. Therefore,

${{K}_{\text{c}}}=\dfrac{C{{\alpha }^{2}}}{(1-\alpha )}$ after ignoring $\alpha $,${{\text{K}}_{\text{c}}}$ becomes${{K}_{\text{c}}}=C{{\alpha }^{2}}$.
The concentration of any ion will be given by
$\alpha =\sqrt{\dfrac{{{\text{K}}_{\text{d}}}}{\text{C}}}$ , $\left[ {{\text{A}}^{+}} \right]=\left[ {{\text{B}}^{-}} \right]=\alpha \text{C}=\sqrt{{{\text{K}}_{\text{c}}}\text{C}}$
Thus, the degree of dissociation is proportional to the inverse square root of the concentration or square root of dilution. This is the derivation of Ostwald dilution law.

Additional Information: The Ostwald law of dilution provides a nice description of concentration dependence of the conductivity of weak electrolytes like $\text{C}{{\text{H}}_{3}}\text{COOH}$and$\text{N}{{\text{H}}_{4}}\text{OH}$. The variation of molar conductivity is mainly due to the incomplete ionization of weak electrolytes into ions.

Note: The Ostwald’s dilution law is only applicable when we are dealing with weak bases or acids; it’s not used while we are talking about strong acids or bases which are completely dissociable and ionizable at all dilution. In weak electrolytes, degree of dissociation ($\alpha $) of weak electrolyte is directly proportional to square root of dilution.