The first order integrated rate equation is

Step-by-step solution

For first order, rate = d[R] d t =k[R] or d[R] [R] =k d t On integrating Eq. (i) array l d[R] [R] =k d t [R]=-k t+C array At t=0,[R]= [R₀ ] [where, R= final concentration, ie, a-x and R₀ is the initial concentration, .i e, a . ] [R₀ ]=C On putting the value of C in Eq. (ii), we get array r [R]=-k t+ [R₀ ] -k t= [R]- [R₀ ] k t= [R₀ ]- [R] array or aligned k &= 1 t [R₀ ] [R] or k&= 1 t a a-x aligned