An optically active substance decomposes into optically active substances 'B' and ' \( \mathrm{C...

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An optically active substance decomposes into optically active substances 'B' and ' \( \mathrm{C} \) ' as follows.
\[
\mathrm{A} \stackrel{K=0.001 \min ^{-1}}{\longrightarrow} 2 \mathrm{~B}+\mathrm{C}
\]
The specific rotations of \( \mathrm{A}, \mathrm{B} \) and \( \mathrm{C} \) are \( +40^{\circ},+10^{\circ} \) and \( -30^{\circ} \) per mole, respectively. If initially \( A \) and \( \mathrm{C} \) were present in \( 4: 3 \) mole ratio, the time (in min), after which the sample becomes optically inactive is \( (\ln 2=0.7, \ln 5=1.6, \ln 7=2.0, \ln 13=2.5) \)
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