Question

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

• A. $0.693mi{n}^{-1}$
• B. $0.0693se{c}^{-1}$
• C. $0.0693mi{n}^{-1}$
• D. $0.00693se{c}^{-1}$

Answer 1

The correct option is C $0.0693mi{n}^{-1}$

For the given reaction, $kt=ln\frac{{\theta }_{\infty }-{\theta }_o}{{\theta }_t-{\theta }_o}$

where, ${\theta }_o$= optical rotation on completion,

${\theta }_t$= optical rotation at time $t$ & ${\theta }_o$= initial optical rotation

Since A is not opticallt active, ${\theta }_o=0$ & ${\theta }_t={50}^o,{\theta }_{\infty }={100}^o...$ given

$\therefore K\times 10=ln\frac{100-0}{50-0}$

$\therefore K=\frac{ln2}{10}=0.0693mi{n}^{-1}$