Question

If \alpha is degree of dimerisation of in benzene, then van’t hoff factor ‘i’ for circulation of colligative properties is:
A. $1 + \alpha \\ $
B. $1 - \dfrac{\alpha }{2} \\$
C. $1 + \dfrac{\alpha }{2} \\$
D. $1 + 2\alpha $

Answer 1

Hint: The concept used in the dimerization of acetic acid when dissolved in benzene is of calculating the degree of association from van’t hoff factor.

Complete step by step solution:
From the question we know that acetic acid has a molecular mass of 120u. The following method is used to determine degree of association using the relation between $\alpha $and i . We know n is the moles of the gas given by weight of the gas by its molecular mass.
There are many organic solutes which in non aqueous solutions undergo association. Thus the number of effective molecules decreases and, consequently the osmotic pressure. Two such examples of this is acetic acid in benzene and chloroacetic acid in naphthalene.

We know that degree of association is the fraction of total number of molecules which combine to form a bigger molecule. Since in the question we are given with dimerization of acetic acid as it gets dissolved in benzene and $\alpha $is the degree of association where van’t hoff factor is
I=observed colligative property/theoretical colligative property
Let us write the above equation in moles, therefore
Number of unassociated moles=1-$\alpha $
Number of associated moles=$\dfrac{\alpha}{n}$
Total number of effective moles=1-$\alpha $+$\alpha $
$
i = 1 - [\alpha (1 - \dfrac{1}{n})] \\
i = 1 - [\dfrac{\alpha }{2}]
$

Hence the correct option is B.

Note:
Since colligative properties depend upon the number of particles of the solute, in some cases where the solute associates or dissociates in solution, abnormal results for molecular masses are obtained.