Derive an integrated rate for first order reaction.

Explanation

Consider Ist order reaction `R rarr P`
`"Rate "=(-d[R])/(dt)=k[R]^(1)`
`(d[R])/([R])=-k.dt`
`int(d[R])/([R])=-k int dt`
`ln [R]=-kt+I`
I is integral constant
when `t=0[R]=[R]_(0)`
`ln[R]_(0)=-k(0)+I`
`therefore I =ln[R]_(0)`
`ln[R]=-kt+ln[R]_(0)`
`kt=ln[R]_(0)-ln[R]`
`KT=(2.303)/(t)log""([R]_(0))/([R])`