Editing Law of dilution (section)

==Derivation==

Consider a binary electrolyte AB which dissociates reversibly into A<sup>+</sup> and B<sup>−</sup> ions. Ostwald noted that  the [[law of mass action]] can be applied to such systems as dissociating electrolytes. The equilibrium state is represented by the equation:

:<chem>AB <=> {A+} + B^-</chem>

If ''{{math|α}}'' is the fraction of dissociated electrolyte, then ''{{math|αc<sub>0</sub>}}'' is the concentration of each ionic species. {{math|(1 - ''α'')}} must, therefore be the fraction of ''undissociated'' electrolyte, and {{math|(1 - ''α'')''c<sub>0</sub>''}} the concentration of same. The dissociation constant may therefore be given as

:<math chem>K_d = \cfrac{\ce{[A+ ] [B^- ]}}{\ce{[AB]}} = \cfrac{(\alpha c_0 )(\alpha c_0 )}{(1-\alpha) c_0 } = \cfrac{\alpha^2}{1-\alpha} \cdot c_0 </math>

For very weak electrolytes {{tmath|\alpha \ll 1}}, implying that {{math|(1 - ''α'') ≈ 1}}.

:<math>K_d = \frac{\alpha^2}{1-\alpha} \cdot c_0 \approx \alpha^2 c_0 </math>

This gives the following results;

:<math>\alpha = \sqrt{\cfrac{K_d }{c_0 }} </math>

Thus, the degree of dissociation of a weak electrolyte is proportional to the inverse square root of the concentration, or the square root of the dilution. The concentration of any one ionic species is given by the root of the product of the dissociation constant and the concentration of the electrolyte.

:<math chem>\ce{[A+ ]} = \ce{[B^- ]} = \alpha c_0 = \sqrt{K_d c_0 } </math>