An optically active drug has one chiral centre and only dextro rotatory isomer is effective. Moreover, it becomes ineffective when its optical activity is reduced to `35%` of original. It was found that mutarotation of this drug was first order reaction with a rate constant of `1 xx 10^(-8) s^(-1)`. Find the expiration time of the drug in years.

Explanation

The optical activity remained `= 35%`
So `65%` optical activity has been lost
It means `35%` of dextro rotatory isomer has been converted to laevo rotatory isomer.
Applying integtrated rate law for first order reaction
`2.303log.(100)/(65) = 1 xx 10^(-18) xx t`
`t = 4.31 xx 10^(7) s`
`= 13.7` years