What is Van't Hoffs factor 'i' and how is it related to `'alpha'` in the case of a binary electrolyte (1 : 1) ?

Explanation

Van't Hoffs factor (i) : "It is defined as the ratio of the observed value of colligative property to the theoretical value of colligative property".
`"I"=("experimental values of colligative property")/("calculated value of colligative property")`
Solute dissociation or ionization process : If a solute on ionization gives 'n' ions and `'alpha'` is degree of ionization at the given concentration, we will have `[1+(n-1)alpha]` particles.
`(1-alpha)iff n alpha`
Total `1-alpha+n alpha=[1+(n-1)alpha]`
`:." i"=([1+(n-1)alpha])/(1)`
`alpha=("i"-1)/(n-1)" "alpha_("ionization")=("i"-1)/(n-1)`
Solute association process :
If 'n'A molecules combine to give `A_(n)`, we have
`nA iff A_(n)`
If `'alpha'` is degree of association at the given concentration.
`1-alpha=(alpha)/(n)" "=1-alpha+(alpha)/(n)`
`"i"=(1-alpha+(alpha)/(n))/(1)`
Or
`alpha=(1-i)/(1-(1)/(n))" "alpha_("dissociation")=(1-i)/(1-(1)/(n))`