Inversion of cane sugar is a pseudo first order reaction.
Rateconstant(k)×t=2.303log((at−a∞)/(a0−a∞))
Rateconstant(k)×t=2.303log(at−a∞)−2.303log(a0−a∞)
t=2.303log(at−a∞)/k−2.303log(a0−a∞)/k
at= optical rotation at time t=t
a0= optical rotation at time t=0
a∞=optical rotation after infinite time
It is of the form x=my+c
x=t
m=2.303/k
y=log(at−a∞)
c=−(2.303log(a0−a∞))/k
Now in the graph, when x=0 ,we obtain x intercept which is equal to c.
We know k,a∞ and c from the graph so using all these in equation (1) we obtain optical rotation at time 0.
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