The van't Hoff factor `i` for an electrolyte which undergoes dissociation and association in solvents respectively are:

Explanation

Calculation of degree of dissociation from Van.t Hoff factor.
Suppose I molecule of reactant dissociates to given n molecules or ions of products.
`A hArr ubrace (B + C+ D. . . ) `
`{:(," 1 molecule "," n molecules /ions "),("Initial conc. "," "1," "0),("Eqm. Conc. "," "1 - alpha ," "n alpha ):}`
`:.` Number of particles at equilibrium ` = 1 - alpha + n alpha = 1 + ( n - 1) alpha `
Van.t Hoff factor, ` i =("No. of particles at eqm.")/(" No. of particles originally present ") `
`i = ( 1 + ( n - 1) alpha)/( 1)`
`:. alpha = ( i - 1)/( n - 1) " "` (Here ` n gt 1 and i gt 1`)
calculation of degree of association from Van.t Hoff factor
Suppose n molecules or ions combine to give one molecule ,
`nA hArr A_(n)`
`{:(," n molecules /ions"," 1 molecule "),("Initial conc."," "1," "0),("Eqm. Cone." ," "1 - alpha ," "alpha//n ):}`
`:.` Number of particles at equilibrium ` = 1 - alpha + alpha // n = 1 - ((n - 1)/( n)) alpha `
Van.t Hoff factor, ` i (" No. of particles at eqn. ")/(" No. of particles originally present ")`
`i = 1 - (( n - 1)/( n)) alpha `
`(( n - 1)/( n)) alpha = 1 - i`
`alpha = (( 1 - i) n)/( n - 1) " "` (Here ` n gt 1 and i lt 1`)