Question

Fora 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 ${50}^o$ and when the reaction is complete, it was ${100}^{o}C$ Assuming that only B and C are optically active and dextro rotatory, the rate constant of this first order reaction would be ?

• A. $0.069mi{n}^{-1}$
• B. $0.69mi{n}^{-1}$
• C. $6.9mi{n}^{-1}$
• D. $6.9\times {10}^{-2}mi{n}^{-1}$

Answer 1

Answer: (A)

$0.069mi{n}^{-1}$

Let the rotation of Sucrose be $r_1^o$ per mole and the initial moles of Sucrose be a.
$⟹r_0=a{r}_1^0$

Let the moles converted be x.
$⟹r_t=(a-x)r_1^0$
$⟹\frac{a}{a-x}=\frac{r_o}{r_t}$
$⟹k=\frac{1}{t}\ln \frac{a}{a-x}=\frac{1}{t}\ln \frac{r_o}{r_t}$
$⟹k=\frac{2.303}{10}\log \frac{100}{50}$
$⟹k=0.069mi{n}^{-1}$