Question

Find the degree of association when $1.0$ gram benzoic acid, dissolved in $25$ gram benzene is having depression in freezing point$0.81K$. The molal depression constant for solvent is $4.9K$ kg ${\text{mol}}{{\text{e}}^{{\text{ - 1}}}}$

Answer 1

Hint : The number of moles of a specific substance associated per more of the substance taken is known as the degree of association.

Complete Step By Step Answer:
From the question it is clear that we should find the degree of association. It is clear from the question that $1.0$ gram benzoic acid, dissolved in $25$ gram benzene is having depression in freezing point$0.81K$. The molal depression constant is given in the question as $4.9K$ kg${\text{mol}}{{\text{e}}^{{\text{ - 1}}}}$. So firstly we are finding molar mass of benzoic acid.
Molar mass of Benzoic acid,

$$= \dfrac{{1000 \times {K_f} \times \,mass\,\,\,of\,\,benzoic\,\,acid}}{{\Delta {T_f} \times \,\,\,mass\,\,\,of\,\,\,solvent}} \\\ = \dfrac{{1000\,\, \times \,\,4.9\,\,\, \times 1}}{{0.81 \times 25}} \\\ 242\,grammol{e^{ - 1}} \\\ van't\,Hoff\,factor(i) = \dfrac{{Theoretical\,\,molar\,\,mass\,\,of\,\,benzoic\,\,acid}}{{Experimental\,\,molar\,\,mass\,of\,benzoic\,acid}} \\\ = \dfrac{{122}}{{242}} \cong 0.5 \\\$$

Initially, we were finding the molar mass of benzoic acid. Then we found the experimental molar mass of benzoic acid as$242\,grammol{e^{ - 1}}$. So here we are using the pre-defined equation of van’t Hoff factor (i) to find the degree of association. The factor I has a value less than 1 when the observed molecular mass is greater than the average. The Van't Hoff's factor is greater than 1 in the case of dissociation because the measured molecular mass is less than the normal molecular mass. In the absence of dissociation, the value of I becomes one. It is possible to calculate the degree of dissociation or association of a material using the value of ‘i.' And finally we found the degree of association as$0.5$.

Note :
The phenomenon of producing current carrying free ions that are dissociated from the fraction of solute at a given concentration is known as the degree of dissociation. The ratio between the actual concentration of particles formed when a substance is dissolved and the concentration of a substance measured from its mass is known as the Van 't Hoff factor.