Question

Which is the correct expression of van't Hoff factor for association of electrolyte?
Here,
n is the number of molecules associate to form n-mer
$\beta$ is the degree of dissociation

• A. $i=2+\left[\frac{1}{n}-1\right]\beta$
• B. $i=1+\left[\frac{1}{n}-1\right]\beta$
• C. $i=1+\left[\frac{1}{n}+1\right]\beta$
• D. $i=1+[n-1]\beta$

Answer 1

The correct option is B $i=1+\left[\frac{1}{n}-1\right]\beta$

Association of electrolyte:
$nA\rightleftharpoons A_n$
$t=0:C0$
$t=t_{eq}:C(1-\beta )\frac{c\beta }{n}$

At equilibrium,
$\text{Net concentration}=C-C\beta +\frac{c\beta }{n}$
$=C[1+\left[\frac{1}{n}-1\right]\beta ]$

$i=\frac{C[1+\left[\frac{1}{n}-1\right]\beta ]}{C}$
$i=1+\left[\frac{1}{n}-1\right]\beta$