Inversion of sucrose `(C_(12)H_(22)O_(11))` is first-order reaction and is studied by measuring angle of rotation at different instants of time
`underset(d)underset("Sucrose")(C_(12)H_(22)O_(11))+H_(2)Ooverset(H^(+))rarrunderset(d)underset("Glucose")(C_(6)H_(12)O_(6))+underset(l)underset("Fructose")(C_(6)H_(12)O_(6))`
If `(r_(oo)-r_(0))=a` and `(r_(oo)-r_(t))=(a-x)` (where `r_(0),r_(t)` and `r_(oo)`) are the angle of rotation at the start, at the time t and at the end of the reaction respectively, then there is `50%` inversion when :

Options

A. `r_(0)=2r_(t)-r_(oo)`
B. `r_(0)-r_(t)-r_(oo)`
C. `r_(0)=r_(t)-2r_(oo)`
D. `r_(0)=r_(t)+r_(oo_`

Answer

A