Rate equation for first order reaction
First order reaction :The rate of the reaction is proportional to the first power of the cocentration of the reactant R is called first order reaction . The rate of first order reaction. The rate of first order reaction ∝ [R] Where ,reaction R →P is first order reaction. The differential rate expression of first order reaction is as under Rate =−d[R]/dt=k[R]..........(i) ∴d[R]/[R]=-kdt.......(ii) Intergrating this equation both side , In [R] =-kt+1 .......(iii) Here,I=Constant of integration When ,t= 0, [R]=[R]° .Where [R]0 is the initial concentration of the reactant.Put this value in eq. (iii) In [R]°=−k×(0)+I ∴In[R]0=I.......(iv) If we put I =In [R]° in equation (iii),we get In [R]=-kt+In [R]°......(VA) ∴ kt =In [R]°-In [R] ∴kt=In[R]°/[R] ∴k=1/t×In[R]°/[R].......(VB) Equation V(A) and V(B) both are integrated rate equation (VA) and (VB) can written in the form log [R]=−kt/2.303+log[R]°......(ViA) K=2.303/t xlog [R]°/[R].....(VIB)