Question

The data set below was collected from a differential, isothermal PFR analyzing the conversion of A +B

Answer 1

This reaction is FIRST ORDER with respect to the reactant A and SECOND ORDER withrespect to the reactant B so that the order (total) of the reaction is 1+2 = 3

The rate expression is    rate = k[A]¹[B]²

                                             rate = k[A][B]²

EXPLANATION:

In a FIRST ORDER reaction, if the concentration of a reactant is doubled, the rate will be doubled (2¹ NOTE THE POWER which is the order)

In a first order reaction, if the concentration of of a reactant is tripled, the rate will be tripled (3¹ NOTE THE POWER which is the order)

In a first order reaction, if the concentration of of a reactant is increased 4 times, the rate will become by 4 times (4¹ NOTE THE POWER which is the order)

and so on

In a SECOND ORDER reaction, if the concentration of of a reactant is doubled, the rate will become 4 times (2²=4 NOTE THE POWER which is the order)

In a SECOND ORDER reaction, if the concentration of of a reactant is tripled, the rate will become 9 times (3²= 9 NOTE THE POWER which is the order)

In a SECOND ORDER reaction, if the concentration of of a reactant is increased 4 times, the rate will become 16 times (4²= 16 NOTE THE POWER which is the order)

and so on

The given data conforms to these conditions

P_A =10   P_B = 10    rate =1    at 500K

P_A =20   P_B = 10    rate =2    at 500K

The concentration of A has been doubled keeping the concentration of B constant. The rate is doubled. The reaction is first order with respect to A

This confirmed by the next data

P_A =10    P_B = 10    rate = 1    at 500K

P_A = 40 P_B = 10    rate = 4    at 500K

The concentration of A has been increased 4 times keeping the concentration of B constant. The rate becomes 4 times. The reaction is first order with respect to A

P_A =10    P_B = 10    rate =1    at 500K

P_A = 10 P_B = 20    rate = 4    at 500K

The concentration of B has been increased 2 times keeping the concentration of A constant. The rate becomes

4 = (2²) times. The reaction is second order with respect to B

This confirmed by the next data

P_A =10    P_B = 10    rate =1    at 500K

P_A = 10 P_B = 40    rate = 16 at 500K

The concentration of B has been increased 4 times keeping the concentration of A constant. The rate becomes

16 = (4²) times. The reaction is second order with respect to B

Therfore

This reaction is FIRST ORDER with respect to the reactant A and SECOND ORDER withrespect to the reactant B so that the order (total) of the reaction is 1+2 = 3

The rate expression is    rate = k[A]¹[B]²