Chemistry - Chemical Kinetics Question with Solution | TestHub

The integrated rate equation for first order
Reaction,$A\to$product is$k=\frac{1}{t}In\frac{{\left[A\right]}_t}{{\left[A\right]}_0}.$
For 1^storder reactions,$R\to P$
Rate =$\frac{-d\left[R\right]}{dt}=\stackrel{·}{k}\left[R\right]$
On integrating this equation, we get
In$\left[R\right]=-kt+l...\left(i\right)$
At$t=0,R={\left[R\right]}_0=-k\times 0+l$
In${\left[R\right]}_0=l$
Substituting the value of l in (i) and on rearrangement, we get
In$\left[R\right]=-kt+In{R}_0$
And,$k=\frac{1}{t}In\frac{\left[R_0\right]}{\left[R\right]}$