Question

Which of the following rate laws represents a reaction that is second order overall?

A. rate = k [A][B]²[C]   

B. rate = k [A]²[B]²[C]²

C. rate = k [A][B]

D. none of these

E. rate = k [A]² [B]      

Answer 1

Suppose, A + B   $\rightarrow$ products

The rate law of the reaction is as follows:

Rate = k [A]^a[B]^b

Here, rate constant is k, [A] is the concentration of A, [B] is the concentration of B, order of reaction with respect to A is "a", order of reaction with respect to B is "b"

The overall order of the reaction is a+b.

A)

The rate law is as follows:

Rate = k[A][B]²[C]

The reaction is first order with respect to A, second order with respect to B and first order with respect to C.

Overall order of the reaction is as follows:

= 1 + 2 +1

= 4

Overall order of the reaction will be 4.

B)

The rate law is as follows:

Rate = k[A]²[B]²[C]²

The reaction is second order with respect to A, second order with respect to B and second order with respect to C.

Overall order of the reaction is as follows:

= 2 + 2 + 2

= 6

Overall order of the reaction will be 6.

C)

The rate law is as follows:

Rate = k[A][B]

The reaction is first order with respect to A, first order with respect to B.

Overall order of the reaction is as follows:

= 1 + 1

= 2

Overall order of the reaction will be 2.

E)

The rate law is as follows:

Rate = k[A]²[B]

The reaction is second order with respect to A, first order with respect to B.

Overall order of the reaction is as follows:

= 2 + 1

= 3

The overall order of the reaction will be 3.

Hence, option C) rate = k[A][B] represents a reaction that is second order overall.