Question

For a reaction, $A \to B + C,$ it was found that at the end of $10$ minutes from the start, the total optical rotation of the system was $50^{\circ}$ and when the reaction is complete, it was $100^{\circ}$. Assuming that only $B $ and $C$ are optically active and dextrorotatory. Calculate the rate constant of this first order reaction

• A. $k = 0.695\, min^{-1}$
• B. $k = 0.0693\, sec^{-1}$
• C. $k = 0.0693\, min^{-1}$
• D. $k = 0.00693\, sec^{-1}$

Answer 1

Answer: (C)

$r_{10}=50^{\circ},r_{\infty}=100^{\circ},r_{0}=0$
$\therefore k=\frac{2.303}{10}log \left(\frac{100-0}{100-50}\right)=0.0695\, min^{-1}$