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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30 min

100 min

5 min

20 min

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