Form the data given below for the reaction:`A to B to ` Products
the rate law expression is:

Options

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

Answer

To derive the rate law expression for the sequential reaction \( A \to B \to \text{Products} \), we will follow these steps:

### Step 1: Identify the Reaction Sequence
The reaction involves two steps:
1. \( A \) is converted to \( B \).
2. \( B \) is then converted to the final products.

### Step 2: Write the Rate Law for Each Step
For a reaction, the rate law is generally expressed in terms of the concentrations of the reactants.

- For the first step \( A \to B \), the rate can be expressed as:
\[ \text{Rate}_1 = k_1 [A] \]
where \( k_1 \) is the rate constant for the first step.

- For the second step \( B \to \text{Products} \), the rate can be expressed as:
\[ \text{Rate}_2 = k_2 [B] \]
where \( k_2 \) is the rate constant for the second step.

### Step 3: Determine the Overall Rate Law
Since the product is formed from both \( A \) and \( B \), we need to consider both reactants in the overall rate law expression. The overall rate of formation of the products will depend on the concentrations of both \( A \) and \( B \).

Thus, the overall rate law expression can be written as:
\[ \text{Rate} = k [A][B] \]
where \( k \) is the overall rate constant for the reaction sequence.

### Step 4: Final Rate Law Expression
The final rate law expression for the reaction \( A \to B \to \text{Products} \) is:
\[ \text{Rate} = k [A][B] \]