Question #349611

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

Expert's answer

Let's assume A associates to form "A_2"

So,

"\\underset{\\underset{n(1-a)}{n}}{2A}\\to\\ \n\\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

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