(I)(a) Calculate the boiling point of a solution containing $0.61\;g$ of benzoic acid in $5\; g$ of $CS_2$ .Assuming $84\%$ dimerisation of acid. The boiling point and $K_b$ of $CS_2$ are $46.2^{\circ}0C$ and $2.3\; K\; Kg \;mol^{-1}$ respectively. (b) State Raoult's law for the solution containing non-volatile solute. Give its mathematical expression also. (II) A solution of $KMnO_4$ on reducing yields either a colourless solution or a brown precipitate or a green solution depending on $PH$ of the solution . What different stages of the reduction do these represent and how are they carried out ?

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