Answer to Question #349611 in Inorganic Chemistry for Diu

Question

Derive equation of van't hoff factor when the solute undergo association.

Answer 1

Let's assume A associates to form $A_2$

So,

$\underset{\underset{n(1-a)}{n}}{2A}\to\ \underset{\underset{\frac{an}{2}}{0}}{A_2}$

Now if there were initially n moles of A and 0 moles of $A_2$ then let's assume that ‘a’ times n moles associate so now moles of A=n(1-a) and that of $A_2$ would be $\frac{na}{2}$

So now total no. of moles present

=$n(1-a)+\frac{na}{2}=n-an+\frac{an}{2}\\n-\frac{an}{2}=n(1-\frac{a}{2})$

Van't Hoff factor = $\frac{total ~no.~ of~moles~after~ association}{Initial~ moles}=\frac{n(1-\frac{a}{2})}{n}$

$\ \ \ \ \ \ \ \ =(1-\frac{a}{2})$

where, $a$ is degree of association