Sucrose inversion is followed polarimetrically. The initial rotation is +10.0 deg, the rotation at complete inversion is -6.0 deg, and after 40 min it is +2.0 deg. Assuming first-order kinetics and using ln2=0.693, ln(16/6)=0.981, the solution is optically inactive after

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Sucrose inversion is followed polarimetrically. The initial rotation is $+ 10. 0^{\circ}$ , the rotation at complete inversion is $- 6. 0^{\circ}$ , and after 40 min it is $+ 2. 0^{\circ}$ . Assuming first-order kinetics and using $ln 2 = 0.693$ , $ln (16/6) = 0.981$ , the solution is optically inactive after

\frac{r _{0} - r _{\infty}}{r _{t} - r _{\infty}} = \frac{16}{8} = 2

, so

t_{1/2} = 40

min and

k = 0.693/40 = 0.01733 mi n^{- 1}

. Rotation

0

means

r_{t} - r_{\infty} = 6

, so

t = \frac{1}{k} ln \frac{16}{6} = \frac{0.981}{k} = 56.6

min.