Chemical Kinetics and Nuclear ChemistryHard

Question

Inversion of sucrose (C12H22O11) is first-order reaction and is studied by measuring angle of rotation at different instant of time
C12H22O11 + H2O C6H12O6
Sucrose           Clucose        Fructose
     d                     d                    l
If (r∞ - r0) = a and (r∞ - rt) = (a - x) (where r0, rt and r∞ 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.r0 = 2rt - r∞
B.r0 = rt - r∞
C.r0 = rt - 2r∞
D.r0 = rt + r∞

Solution

Given      (r∞ - r0) = a ,    (r∞ - rt) = (a - x)
At 50% Inversion
= (a - x)
= (r∞ - r0)
(r∞ - r0 ) = 2r∞ - 2rt
r0 = 2rt - r∞

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