A chemical reaction proceeds into the following steps
Step I, `2A hArrX` fast
Step II, `X+B rarr Y` slow
Step III, `Y+B hArr` product fast
The rate law for the overall reaction is

Options

A. Rate `=k[A]^2`
B. Rate `=k[B]^2`
C. Rate = k [A][B]
D. Rate `=k[A]^2[B]`

Answer

To determine the rate law for the overall reaction based on the given steps, we can follow these steps:

### Step 1: Identify the Rate-Determining Step
In the provided reaction mechanism, we note that Step II (`X + B → Y`) is the slow step. The rate law for the overall reaction will be based on this step since it is the rate-determining step.

### Step 2: Write the Rate Law for Step II
The rate law for a reaction is generally expressed as:
\[ \text{Rate} = k[\text{Reactants}] \]
For Step II, the rate law can be written as:
\[ \text{Rate} = k[X][B] \]
where \( k \) is the rate constant for Step II.

### Step 3: Express Concentration of Intermediate X
Since \( X \) is an intermediate, we need to express its concentration in terms of the reactants. From Step I, we have:
\[ 2A \rightleftharpoons X \]
The equilibrium expression for this step can be written as:
\[ K_1 = \frac{[X]}{[A]^2} \]
From this, we can express \( [X] \) as:
\[ [X] = K_1[A]^2 \]

### Step 4: Substitute the Expression for X into the Rate Law
Now, we substitute the expression for \( [X] \) into the rate law from Step II:
\[ \text{Rate} = k[K_1[A]^2][B] \]
This simplifies to:
\[ \text{Rate} = k' [A]^2[B] \]
where \( k' = kK_1 \) is a new rate constant.

### Step 5: Write the Overall Rate Law
Thus, the overall rate law for the reaction is:
\[ \text{Rate} = k' [A]^2[B] \]

### Conclusion
The final rate law for the overall reaction is:
\[ \text{Rate} = k[A]^2[B] \]