Q.

An optically active substance decomposes into optically active substances ‘B’ and ‘C’  as follows
 Ak=0.001minute12B+C
 The  specific rotations of A,B and C are +400,+100and  300   per mole, respectively. If initially A and C were present in 4:3 mole ratio, the time (in min), after  which the sample becomes optically inactive is  ln2=0.7,ln5=1.6,ln7=2.0,ln13=2.5
 

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answer is 500.

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Detailed Solution

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ANS-500
SOL-
 A2B+C t=0            4a         0          3a t=t             4ax   2x         3a+x
 From the question 
4ax40°+2x10°+3a+x30°=0°
 x=75a
Now,  
t=1K×ln4a4a75a=10.001,ln2013=500min

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