Two strong electrolytes AB and CD react with each other, forming a sparingly soluble salt AD. The solution of x(M) AB is mixed with an equal volume of the solution off y(M) CD. If the solubility product of AD be z, then what will be the value of xy (in terms of z) when AD starts precipitating?

Explanation

Reaction: `AB(aq)+CD(aq)toAD(s)+BC(aq)`
Equilibrium that established because of partial ionisation of `AD:AD(s)hArr A^(+)(aq)+D^(-)(aq)`
So, the solubility product of AD, `K_(sp)=[A^(+)][D^(-)]`. If VmL solution of x (M) AB is mixed with the same volume of y(M) CD solution, then in the mixed solution.
`[A^(+)]=(x xxV)/(2V)=(x)/(2)(M) and [D^(-)]=(yxxV)/(2V)=(y)/(2)(M)`
Therefore, `K_(sp)=[A^(+)][D^(-)]=(x)/(2)xx(y)/(2)=(xy)/(4)`
Now, AD will get precipitated when `[A^(+)][D^(-)] gt K_(sp)` i.e., when `(xy)/(4) gtz or, xy gt 4z`.
Therefore, AD will begin to precipitate when xy is greater than 4z.