In a polarimetric study of sucrose inversion the rotation is $+ 4 0^{\circ}$ at t = 0, $+ 1 3^{\circ}$ at t = 60 min and $- 1 4^{\circ}$ at infinite time. Assuming first-order kinetics, the time (in min) at which the solution becomes optically inactive (rotation $0^{\circ}$ ), measured from t = 0, is

Answer: B

k = \frac{1}{t} ln \frac{r _{0} - r _{\infty}}{r _{t} - r _{\infty}} = \frac{1}{60} ln \frac{54}{27} = 0.01155 mi n^{- 1}

. For

r_{t} = 0

t = \frac{1}{k} ln \frac{54}{14} = 116.9

min.