Question

R-3-Bromo-3-methylhexane has a rotation of +100 ̊. When placed in 48% aqueous HBr the optical rotation changes rapidly. Within 10 min it is +50 ̊. In 20 min it is +25 ̊. What is the rotation after 1 day? What is the relative amount of R and S isomers at 10 min? (not required but you should be able to write a mechanism for this).

Answer 1

The rate racemization is 10 min it is +50 ̊. In 20 min it is +25 ̊

it is clear that the reaction is first order reaction.

and half life of the reaction is 10 minutes

ln A = -kt + ln A_o

rate constant will be calculate from half life

K = 0.693 / half life = 0.693 / 10 = 0.0693 Min-1

k = rate constant = 0.0693 min-1

t = time = 1 day = 24 hour =  1440 minute

Ao = Initial concentration = 1 (Let us keep)

A = concentration at time t = ?  

Substitute the values in the formula

ln A = -0.0693 x 1440 + ln 1

ln A = -99.79

Log A = -43.33

A = 4.66 x 10^-42 %

Concentration of R-3-Bromo-3-methylhexane is very less ampount after 24 hours. Hence the rotation after 24 hours is almost Zero.

What is the relative amount of R and S isomers at 10 min?

after 10 minutes 50 of compound ger racemized means 75 % of R enantiomer and 25% of S enantiomer is present.