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Chemical Kinetics Complex Reaction Opposing or Reversible Reaction Certain reactions in which product of a chemical change react to form the original reactants are known as reversible or opposing reactions. In opposing reaction, the net rate of the reaction will be influenced by both forward and backward rates and that causes serious disturbance in the measurement of reaction. Ex: 1. Muta rotation of αα -D glucose into β-D β-D glucose 2. Conversion of ammonium cyanate into urea
There are several types of opposing reaction 1) Both forward and backward reactions are of first order 2) First order reaction is opposed by second order 3) Both forward and backward reactions are of second order Let us consider the case when the both forward a nd backward reactions are of first order A
k1 k2
B
Where k 1 and k 2 represents first order rate constants for the forward and backward reactions respectively. Suppose ‘a’ is initial concentration of A, then A, then after time t, x mole of A decomposed to form B. Thus the concentration of A after a time t ime t is a-x and that of B is x. Therefore, the rate of forward and backward reactions equals to k 1(a-x) and k 2x. Thus, the net rate of formation of B is
= 1 ( ) 2 -------(1)
At equilibrium, the net rate is zero,
=0
1( ) 2 = 0--------(2) 2 =
(−)
-------------(3)
is the equilibrium concentration. Substituting the value of k 2 in equation 1, we get
= 1 ( )
1 ( )
On rearranging eqn. 4 we get,
=
( −)
( −)
=
On integrating we get, ln( ) =
-----------(4)
------------(5)
+ ----------(6)
When t=0, x=0, then = l n --------------------(7) Substituting eq.7 in eq.6 we get
1 =
−
-----------(8)
Thus value of k 1 can be calculated by using eqn. 8. If x e, x and t are known, by substituting the value of k 1 in eq.3 k 2 can be calculated.
