A `20%` solution of cane sugar having dextrorotation of `34.50` inverted by `0.5 N` lactic acid to at `298 K`. The rotations determined are as follows:
`|{:("Time (min)",0,14.55,111.36,oo),("Rotation",34.50,31.10,13.98,-10.77):}|`
Show that the inverison of sugar is a unimolecular reaction.

Explanation

`C_(12)H_(22)O_(11) + H_(2)O overset(H^(o+))rarr C_(6)H_(12)O_(6)+C_(6)H_(12)O_(6)`
`k = (2.303)/(t) log.(r_(0) - r_(oo))/(r_(t)-r_(oo))`
(a) `k = (2.303)/(14.55)log.(34.50 - (-10.17))/(31.1-(-10.77))`
`= (2.303)/(14.55)log.(45.27)/(41.87)`
`= (2.303 xx 0.0339)/(14.55) = 0.0053 min^(-1)`
(b) `k = (2.303)/(111.36) log.(34.50-(-10.77))/(13.98-(-10.77))`
`= (2.303)/(111.36)log.(45.27)/(24.75) = (2.303 xx 0.262)/(111.36) = 0.054 min^(-1)`
The value of `k` is constant. Hence, first order reaction.