(a) Derive an integrated rate equation for rate constant of a zero order reaction.
(b) Write (i) Arrhenius equation
(ii) The formula to calculate half life period of zero order reaction.

Explanation

Consider a reaction, where `R to P`
Applying law of mass action
`r prop[R]^(@)`
`r=K[R]^(@)` But `r = -d[[R]]/(dt)`
`(-d[R])/(dt)=K[R]^(@) ,` `[R]^(@) = 1`
`-d[R] = Kdt , d[R] = - Kdt.`
Integrating on both sides
`intd[R]= - K int dt`
`[R] = -Kt+C .......(1)`
put `[R]=[R_(0)] and t=0`
`[R_(0)]= -K(0)+C`
`C=[R_(0)]` ........... (2)
Substituting in eqn (1)
`[R] = -Kt + [R_(0)]`
`Kt=[R_(0)] - [R],`
`K=[[R_(0)]-[R]]/(t)`
(i) `K=Ae^((-Ea)/(RT))`
(ii) `t_(1/2)=[[R_(0)]]/(2K)`