Chemistry - Chemical Kinetics Question with Solution | TestHub

Question Explanation: Calculate the rate law for the reaction.

Concept: This question is based on the rate law for a reaction.

Solution:

For the reaction $A+B\to product$, the rate law is given by:

$$r=k[A{]}^x[B{]}^y(1)$$

From experiment 2, when $[B]$ is doubled, the rate doubles:

$$2r=k[A{]}^x[2B{]}^y(2)$$

From experiment 3, when both $[A]$ and $[B]$ are doubled, the rate increases by a factor of 8:

$$8r=k[2A{]}^x[2B{]}^y(3)$$

Dividing equation (2) by equation (1):

$$\frac{2r}{r}=\frac{k[A{]}^x[2B{]}^y}{k[A{]}^x[B{]}^y}$$

$$2=2^y\Rightarrow y=1$$

Dividing equation (3) by equation (2):

$$\frac{8r}{2r}=\frac{k[2A{]}^x[2B{]}^y}{k[A{]}^x[2B{]}^y}$$

$$4=2^x\Rightarrow x=2$$

Therefore, the rate law is:

$$r=k[A{]}^2[B{]}^1$$

or

$$r=k[A{]}^2[B]$$

Final Answer: The correct option is (D).