The Polarimeter readings in an experiment to measure the rate of inversion of cane sugar (1^st order reaction) were as follows
Time (min) : 0 30 $\infty$
Angle (degree) : 30 20 -15
Identify the true statement(s)?
$[\log 2 = 0.3, \log 3 = 0.48, \log 7 = 0.84, \log_{e} 10 = 2.3]$

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The solution is optically inactive at 120 min

The half life of the reaction is 75 min

The equimolar mixture of the products is dextrorotatory

The angle would be ${7.5}^{0}$ at half time

answer is A, B, D.

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Detailed Solution

Ans: ABD
0 30 $\infty$
30 20 -15
$k = \frac{1}{30} 2.3 \log \frac{30 - (- 15)}{20 - (- 15)} = \frac{1}{30} 2.3 \log \frac{45}{35}$
$t_{1 / 2} = 75 \min$
$k = \frac{1}{t} 2.3 \log \frac{45}{0 - (- 15)}$
$t = 120 \min$
$\frac{30 - (- 15)}{x - (- 15)} = 2$ at half time
$\Rightarrow \frac{45}{x \times 15} = 2$ $\Rightarrow x + 15 = \frac{45}{2}$ $\Rightarrow x = 22.5 - 15 = {7.5}^{0}$