Aqueous solution of a certain d-sugar has specific rotation $+ 12^{\circ}$ when measured in 1cm polar meter tube and at $4 g m l^{- 1}$ concentration at a given temperature and light. A certain catalyst ‘P’ converts it to meso form. ‘P’ is added so that $1 / 3^{r d}$ of d- sugar is converted to meso form. What will be the observed rotation in $(i n^{\circ})$ if the reaction mixture including optically inactive catalyst is diluted by adding equal volume of water and measured using same Polarimeter under similar conditions?

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answer is 1.6.

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Detailed Solution

$[α] = \frac{θ}{c \times l} \Rightarrow 12 = \frac{θ}{\frac{1}{10} \times 4} \Rightarrow α = {4.8}^{0} [α] = \frac{θ}{c \times l} 12 = \frac{θ}{\frac{2}{3} \times \frac{4}{2} \times \frac{1}{10}} \Rightarrow α = 12 \times \frac{4}{3 \times 10} = \frac{16}{10} = 1.6$