A second order reaction between A and B is elementary reaction:
A+B `to` Product
rate law expression of this reaction will be:

Options

A. Rate = K[A][B]
B. Rate = `K[A]^0[B]^2 `
C. Rate = `K[A]^2[B]^0 `
D. Rate = `K[A]^(3//2)[B]^(1//2)`

Answer

To find the rate law expression for the given second order elementary reaction between A and B, we will follow these steps:

### Step 1: Understand the Reaction
The reaction is given as:
\[ A + B \rightarrow \text{Product} \]
This indicates that one molecule of A reacts with one molecule of B to form a product.

### Step 2: Identify the Order of the Reaction
Since this is an elementary reaction, the order of the reaction can be directly determined from the stoichiometric coefficients of the reactants.

### Step 3: Write the Rate Law Expression
The general form of the rate law expression for a reaction is:
\[ \text{Rate} = k [A]^m [B]^n \]
where \( k \) is the rate constant, and \( m \) and \( n \) are the orders of the reaction with respect to A and B, respectively.

### Step 4: Determine the Values of m and n
For the reaction \( A + B \):
- The stoichiometric coefficient of A is 1, so \( m = 1 \).
- The stoichiometric coefficient of B is also 1, so \( n = 1 \).

### Step 5: Combine the Information
Substituting the values of \( m \) and \( n \) into the rate law expression, we get:
\[ \text{Rate} = k [A]^1 [B]^1 \]
This simplifies to:
\[ \text{Rate} = k [A] [B] \]

### Step 6: Conclusion
Thus, the rate law expression for the reaction is:
\[ \text{Rate} = k [A][B] \]