An optically active compound A undergoes first order conversion to other optically active compounds B and C. From the following data of optical rotation, calculate the time from start at which the solution will become optically inactive :A⟶B+CTime (min)010∞Optical Rotation (°)15°5°-5°

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An optically active compound A undergoes first order conversion to other optically active compounds B and C. From the following data of optical rotation, calculate the time from start at which the solution will become optically inactive :

$A ⟶ B + C$

Time (min)	0	10	$\infty$
Optical Rotation ( $°$ )	$15 °$	$5 °$	$- 5 °$

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answer is A.

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Detailed Solution

It is known that,

$kt = \ln \frac{α_{\infty} - α_{0}}{α_{\infty} - α_{t}}$

Put the values,

$k \times 10 = \ln (\frac{15 + 5}{5 + 5}) \Rightarrow t_{1 / 2} = 10 \min$

$k \times t = \ln (\frac{15 + 5}{5})$

$t = 20 \cdot \min$

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