Answer to Question #349611 in Inorganic Chemistry for Diu

Question #349611

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




1
Expert's answer
2022-06-10T15:46:01-0400

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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