Question

why does acetic acid in water show an i value greater than one whereas in benzene is less than one

Answer 1

acetic acid dissociates in water into two ions. i.e.,$CH_3COOH\Leftrightarrow CH_3COO^-+H^+$

now applying Van't Hoff's factor, i = $1-\alpha+n\alpha$

where n = 2 and $\alpha$ is degree of dissociation which is always greater than zero.

so, $i=1-\alpha+2\alpha=1+\alpha$

hence, $i=1+\alpha >1$

while acetic acid associates in benzene. means, it dimerises in benzene.

i.e., $2CH_3COOH\Leftrightarrow (CH_3COOH)_2$

now applying Van't Hoff's factor, $i=1-\alpha+\frac{\alpha}{n}$

where n = 2

so, $i=1-\alpha+\frac{\alpha}{2}=1-\frac{\alpha}{2}$

hence, $i=1-\frac{\alpha}{2}< 1$

therefore it is clear that acetic acid in water show an i value greater than one whereas in benzene is less than one