Derive the relationship between half-life period and rate constant for a first order reaction.

Explanation

`log""(k_(2))/(k_(1))=(E_(a))/(2.303R)((T_(2)-T_(1))/(T_(1)T_(2)))`
`k_(1)=3.46 xx10^(-5)sec^(-1)T_(1)=298K`
`k_(2)=1.35xx10^(-4)sec^(-1)T_(2)=308K`
`log""(1.35xx10^(-4))/(3.46xx10^(-5))=(E_(a))/(2.303xx1.987)((308-298)/(308xx298))`
`E_(a)=(2.303xx1.987xx308xx298)/(10)log""(1.35xx10^(-4))/(3.46xx10^(-5))`
`=2.4830cals.`
`logk_(1)=(E_(a))/(2.303xxRT)+logA`
`log3.46xx10^(-5)=(-24830)/(2.303xx1.987xx298)+logA`
`therefore" "logA=13.7491`
`thereforeA=5.611xx10^(13)sec^(-1)`