Question

The polarimeter readings in an experiment to measure the rate of inversion of cane sugar (1st 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]

• A. The half life of the reaction is 75 min
• B. The solution is optically inactive at 120 min
• C. The equimolar mixture of the products is dextrorotatory
• D. The angle would be 7.5${}^o$ at half time

Answer 1

Answer: (A), (B), (D)

The half life of the reaction is 75 min
The solution is optically inactive at 120 min
The angle would be 7.5${}^o$ at half time

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