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

Explanation

Consider a general zero order reaction R `to` Products.
The differential rate equation is rate `= -(d[R])/(dt)=K[R]^(0)` where K is the rate constant of the zero order reaction.
Rearranging we have `d[R] = - Kdt`
Integrating both sides, we get
`[R]= -Kt+I" "...(1)`
Where, I is the constant of Integration.
When `t = 0, [R] = [R]_(0)`, where `[R]_(0)`, is the initial concentration of the reactant.
Substituting is equation (1) we get
`I=[R]_(0)`
Substituting the value of l in equation (1)
`[R]= -Kt+[R]_(0)" "...(2)`
`Kt=[R]_(0)-[R] " "...(3)`
`K=([R]_(0)-[R])/(t)" "...(4)`
Equation (4) is the expression for the rate constant of a zero order reaction.