Derive an integrated rate equation for the rate constant of a zero order reaction.

Explanation

Consider a zero order reaction
`R rarr P`
`"Rate "=(-d[R])/(dt)=k[R]^(@)`
`(-d[R])/(dt)=k[R]^(@)`
`(-d[R])/(dt)=k`
`d[R]=-k.dt`
Integrating on both sides
`int d[R]=-Kintdt`
`[R]=kt+1" ….(1)"`
where I is called integration constant
`"put "t=0[R]=[R]^(@)`
where I is called integration constant
put `t=0[R]=[R]_(0)`
sub in eq (1)
`[R]_(0)=-K(0)H" "1=[R]_(0)`
Substituting value of 1 in eq (1)
`[R]=-Kt+[R]_(0)`
`Kt=[R]_(0)-[R]`
`K=([R]_(0)-[R])/(t)`