Acetic acid undergoes $25 %$ dissociation and $30 %$ association simultaneously. What will be the value of vant Hoff factor ' $i$ '?

0.65

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0.11

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1.01

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1.10

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Solution

The correct option is D $1.10$
$\begin{matrix} Let total amount of {C H}_{3} C O O H be x . \begin{matrix} 25 % dissociation, α & = \frac{25}{100} x = 0.25 x 30 % association, α & = \frac{30}{100} x = 0.3 x \end{matrix} \end{matrix}$
$\begin{matrix} dissociation {C H}_{3} C O O H \to {C H}_{3} {C O O}^{-} + H^{+} \end{matrix}$
$\begin{matrix} t = 0 & x & 0 & 0 t = t & x - 0.25 x & 0.25 x & 0.25 x t = t & 0.75 x & 0.25 x & 0.25 x \end{matrix}$
$association:-$
$2 C H_{3} C O O H \to C C H_{3} (00 H) 2$
$t = t 0.75 x - 0.30 x \frac{0.30 x}{2} x$
$t = t 0.45 x 0.15 x$
Initial amount $= x$
Final amoun $t = (0.25 + 0.25 + 0.13$
+0.45) $x$
$= 1.10 x$
$\begin{matrix} i = & \frac{initial amount}{Final amount} = \frac{1 \cdot 10 x}{x} = 1.10 \end{matrix}$

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