The correct equation for the degree of association `'alpha'` of an associating solute, 'n' molecules of which undergoes association in solution, is

Options

A. `alpha = (n(i-1))/(1-n)`
B. `alpha =(i(n-1))/(1 + n)`
C. `alpha = (i(1+n))/(1-n)`
D. `alpha = (i(n+1))/(n-1)`

Answer

A

Explanation

Consider following association reaction,
`nA hArr (A)_n`
`{:("Initial mole","1 mole","0"),("Associated change",-alpha"mole",+alpha//n"mole"),("Equilibrium mole",(1-alpha)"mole",alpha//n"mole"):}`
Total number of moles after association of 1 mole of A
`=(1 - alpha) + (alpha //n)`mole
Total no. of moles `=1 - alpha + alpha/n`
van.t Hoff factor (i)
`=("Number of moles after association")/("Normal number of mole taken")`
`=(1-alpha + alpha/n)/1`