Derive an integrated rate equatin for a first order reaction.

Explanation

In first order reactions rate depends on only one concentration term.
`R to P`
Rate `=k [R],(d[R])/(dt)=-k. dt`
Intergration on both sides
ln `[R]=-kt+I" ""_____"(1)`
I = Intergration constant
At `t=0, [R]=[R]_(0)impliesl_(n)[R]_(0)=I`
Substituting `I=ln [R]` in the above equation (1)
`ln [R]=-kt +ln [R]_(0)`
`ln ""([R])/([R]_(0))=-kt" ""____"(2)`
`k=1/tln ""([R_(0)])/([R])`
Taking antilog on both sids of eq. (2)
`R=[R]_(0)e^(-kt)`
This is first order rate equation.