1st Order Type Parallel Reactions
 |
| 1st order type parallel reactions |
Parallel reactions:
Parallel reactions are also called side reactions. These are the reaction in which a substance reacts or decompose in two or more ways. Parallel reactions follow two or more paths and different types of products are formed. The product in higher yield is called major or main product and the reaction is called major reaction. The product in low yield is called by product or side product and reaction is called by reaction or side reaction of minor reaction.
Here concentration of P1>P2 indicating that P1 is the main product and P2 is the side product or minor product. We can change major products into minor products and vice versa by changing reaction conditions.
1st order parallel reaction: Consider:
R ⇄ P1 + P2
At time t=0 a 0 0
At time t a-x x x
Rate of formation of P1 is R1 ∝ [R] R1 = k1 (a-x) eq.16.1
Rate of formation of P2 is R2 ∝ [R] R2 = k2 (a-x) eq.16.2
Net rate of reaction is equal to sum of both formation rates.
dx/dt = R1 + R2
dx/dt = k1(a-x) + k2(a-x)
dx/dt = a-x (k1 + k2)
Let k1+k2 = Kt (K total) then dx/dt = a-x (Kt)
Integrating the above equation we got
-ln (a-x) = Kt (t) + z eq.16.3
[Note: in above equation the "t" with K is for total while "t" in bracket is the time.]
Click Here To Read More Articles
Equation 16.3 is a straight line equation for 1st order type parallel reactions. To find the value of z we will consider x=0 and t=0 and put in eq.16.3, then z will be equal to
z= -lna
Putting the value of "z" in eq.16.3 we got,
-ln(a-x) = Kt (t) -lna
lna - ln(a-x) = Kt (t) eq.16.4
The graph for eq.16.4 is
After removing the intercept we got,
eq.16.5Also we should know that
R1 = k1(a-x) and R2 = k2 (a-x)
So,
It is to be noted that rate of reaction is proportional to the amount of product. R1 is almost equal to amount of P1 and R2 is almost equal to amount of P2. So,
lets suppose
P1/P2 = z then k1/k2 =z
Then according to above equation
k1 = z.k2 eq.16.6
We also know that here the rate constant will be some of rate constant of both reaction and will be denoted by Kt means total rate constant.
Kt = k1+k2 eq.16.7
putting the value of k1 in eq.16.7 we got,
Kt = z.k2 + k2
Kt = k2 (z+1)
eq.16.8Hence from equation 16.6 and 16.8 we get the values of both constant. The value of Kt can be found from the slope of graph.
The unit of first order parallel reactionparallel reaction is the same as 1st order reaction. Large amount of product will speed up the reaction while small amount of product will decrease the reaction rate.
