Question

If '$\alpha$' is degree of dimerisation of ${CH}_{3}COOH$ in benzene, then van't Hoff factor '$i$' for circulation of colligative properties is:

• A. $1+\alpha$
• B. $1-\frac{\alpha }{2}$
• C. $1+\frac{\alpha }{2}$
• D. $1+2\alpha$

Answer 1

Answer: (B)

$1-\frac{\alpha }{2}$

For the dimerisation of acetic acid in benzene,

$2C{H}_{3}COOH\rightleftharpoons (C{H}_{3}COOH{)}_2$

$2$ mole of acetic acid associate to from $1$ mole of dimer.

For associate solutes,

$i=1-(1-\frac{1}{n})\alpha$

For association in the absence of dissociation, the van't Hoff factor is:

$i<1$

Now,

$i=1-(1-\frac{1}{n})\alpha$

$=1-(1-\frac{1}{2})\alpha$

$=1-\frac{\alpha }{2}$

Hence, correct option is $B$