$\begin{array}{1 1}(a)\;\large\frac{i-1}{N-1}\\(b)\;\large\frac{i-1}{N+1}\\(c)\;\large\frac{N+1}{i-1}\\(d)\;\large\frac{N-1}{i-1}\end{array}$

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Let, AX be a weak electrolyte whose dissociation is shown below:.

$AX\rightarrow A^++X^-$

At t=0, [AX]=1, [$A^+$]=0, and [$X^-$]=0

At t=t', [AX]=1, [$A^+$]=N$\alpha$, and [$X^-$]=1-$\alpha$

Van't Hoff factor, $i=\large\frac{1-\alpha +N\alpha}{1}$

$i=1-\alpha[1-N]$

$\Rightarrow \alpha [1-N]=1-i$

$\alpha =\large\frac{1-i}{1-N}$

$\Rightarrow \large\frac{i-1}{N-1}$

Hence (a) is the correct answer.

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