Optically pure (R)-Z racemises by a first-order process in solution (the observed rotation alpha is proportional to the ee). The observed rotation falls from +9.60 deg to +2.40 deg in 40.0 min. The percentage of (R)-Z present after 60.0 min is

JEE Advanced levelSingle correct optionDifficulty 3 of 3st145

Optically pure (R)-Z racemises by a first-order process in solution (the observed rotation $α$ is proportional to the ee). The observed rotation falls from $+ 9.6 0^{\circ}$ to $+ 2.4 0^{\circ}$ in 40.0 min. The percentage of (R)-Z present after 60.0 min is

α

falls to one quarter in 40.0 min, so

k = ln 4/40.0 = 0.0347 mi n^{- 1}

. At 60.0 min ee =

e^{- k t} = 4^{- 1.5} = 0.1250

(12.5%). %(R) = 50 + ee/2 = 56.25%. The value 62.50% is the (R) content after 40.0 min, and 51.56% corresponds to 100 min.