Module 6 : Reaction Kinetics and Dynamics
Lecture 27 : Experimental methods in chemical kinetics
 27.8 Relaxation Methods
  When a reaction system at equilibrium is disturbed by a sudden change in temperature or pressure, the concentrations of the species change in response to this change. After some time, the reactant concentrations reach a new equilibrium from the initial non-equilibrium (caused by pressure/temperature jump, or electric/ magnetic/ultrasonic disturbances) The process of relaxing to a new equilibrium is called the relaxation process. Consider the following process which is at an initial old equilibrium.
  A B
  The ratio of concentrations [ B] eq,old / [A] eq,old is the initial equilibrium constant. This equilibrium is shifted by a change/jump in in one of the reaction conditions mentioned above. Let the rate constants after this jump be kf (forward reaction) and kb (reverse reaction) and [ A ] eq,new and [B] eq,new be the new equilibrium values of A
   
 
   
  Figure 27.8
   
  x = [ A] - [A] new, eq, x 0 = [A]eq,old - [ A] eq,new, [ B] = [ B] eq,new - x (27.8)
  d [A] /dt = - ka [ A] + kb [ B]  
  = - ka { x + [A] eq,new } + kb { [ B] eq,new -x } (27.9)
  But since [ B] eq,new / [A] eq,new = ka / kb
  kb [ B] eq,new = ka [ A] eq,new and
  d [ A] / dt = - (ka + kb)x = dx / dt
  or - dlnx = (ka + kb) dt (27.10)
  or x = x0 e - t /
 

Where 1/ = (ka + kb)

(27.11)
   
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