Rate law for the elementary reaction `2AB to^(k_1) A_2+B_2` will be:

Options

A. Rate =`-(d[AB])/(dt)=k_1[AB]^2`
B. Rate =`-(d[A_2])/(dt)=k_1[AB]^2`
C. Rate =`(d[B_2])/(dt)=k_1[AB]^2`
D. Rate =`-(d[A_2])/(dt)=(k_1[AB]^2)/2`

Answer

To determine the rate law for the elementary reaction \( 2AB \xrightarrow{k_1} A_2 + B_2 \), we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Reaction**:
The given reaction is \( 2AB \xrightarrow{k_1} A_2 + B_2 \). Here, \( AB \) is the reactant, and \( A_2 \) and \( B_2 \) are the products.

2. **Understand Elementary Reactions**:
An elementary reaction is a single-step reaction where the reactants convert directly to products in one step. The rate law for such reactions can be derived directly from the stoichiometry of the reaction.

3. **Write the Rate Law**:
For an elementary reaction, the rate law can be expressed in terms of the concentrations of the reactants raised to the power of their stoichiometric coefficients.
- In this case, the stoichiometric coefficient of \( AB \) is 2.
- Therefore, the rate law can be written as:
\[ \text{Rate} = k_1 [AB]^2 \]

4. **Determine the Overall Order of the Reaction**:
The overall order of the reaction is the sum of the powers of the concentration terms in the rate law. Since we have \( [AB]^2 \):
- The overall order = 2.

5. **Final Expression**:
Thus, the rate law for the reaction \( 2AB \xrightarrow{k_1} A_2 + B_2 \) is:
\[ \text{Rate} = k_1 [AB]^2 \]