Question

For a first order reaction A $\rightarrow$B + 2C + 3D (A is optically inactive and B, C and D are dextrorotary), the optical rotation at time t and $\infty$ are rt and$r_{\infty}$ respectively, the expression for rate constant is

• A. $K - \frac{1}{t}In\frac{r_{t}}{r_{\infty} - r_{t}}$
• B. $k = \frac{l}{t}In\frac{r_{\infty}}{r_{\infty} - r_{t}}$
• C. $k = \frac{l}{t}In\frac{r_{\infty} - r_{t}}{r_{t}}$
• D. None of these

Answer 1

Answer: (B)

$k = \frac{l}{t}In\frac{r_{\infty}}{r_{\infty} - r_{t}}$

Answer 2

$\text{A }\overset{\quad\quad}{\rightarrow}\text{ B + 2C + 3D}$

Optical Nrotation – $\theta_{1}\text{ }\theta_{2}\theta_{3}$

$\text{t=0} a \text{ 0 0} \text{ 0}$

Optical rotation at t = 0 is zero.

$\text{t=t} \text{a-x} \text{ x 2x3x}$

Optical rotation at time = t is

(x.q1 + 2x.q2 + 3x.q3).

$\text{t= }\infty 0 \text{ a 2a} \text{ 3a}$

Optical rotation at time = ¥ is

(a.q1 + 2a.q2 + 3a.q3).

$(\text{x.}\theta_{1}\text{ + 2x.}\theta_{2}\text{ + 3x.}\theta_{3})\text{ = }\text{r}_{t};(\text{a. }\theta_{1}\text{ + 2a. }\theta_{2}\text{ + 3a.}\theta_{3})\text{ = }\text{r}_{\infty}x = \frac{r_{t}}{\theta_{1} + 2_{\theta} + 3\theta_{3}};a = \frac{r_{\infty}}{\theta_{1} + 2\theta_{2} + 3\theta_{3}}$

$k = \frac{1}{t}In\left\lbrack \frac{a}{a - x} \right\rbrack = \frac{1}{t}In\left\lbrack \frac{r_{\infty}}{r_{\infty} - r_{t}} \right\rbrack$