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 can follow these steps:

### Step 1: Identify the Reaction
The given reaction is \(2AB \xrightarrow{k_1} A_2 + B_2\). This indicates that two moles of \(AB\) react to form one mole of \(A_2\) and one mole of \(B_2\).

**Hint:** Look at the stoichiometry of the reactants and products to understand the relationship between them.

### Step 2: Understand Elementary Reactions
An elementary reaction is a reaction that occurs in a single step. For elementary reactions, the rate law can be directly derived from the stoichiometry of the reaction.

**Hint:** Remember that for elementary reactions, the molecularity is equal to the order of the reaction.

### Step 3: Determine Molecularity
In this reaction, there are 2 moles of \(AB\) on the reactant side. Therefore, the molecularity of this reaction is 2.

**Hint:** Count the number of reactant molecules involved in the elementary step to find the molecularity.

### Step 4: Write the Rate Law
Since the molecularity is 2, the rate law can be expressed in terms of the concentration of the reactant \(AB\). The rate law is given by:

\[ \text{Rate} = k_1 [AB]^n \]

where \(n\) is the molecularity of the reaction. Here, \(n = 2\).

**Hint:** Use the molecularity to determine the exponent in the rate law expression.

### Step 5: Final Rate Law Expression
Substituting \(n = 2\) into the rate law expression, we get:

\[ \text{Rate} = k_1 [AB]^2 \]

This means the rate of the reaction is proportional to the square of the concentration of \(AB\).

**Hint:** Ensure that you include the rate constant \(k_1\) and the correct concentration term in your final expression.

### Conclusion
Thus, the rate law for the elementary reaction \(2AB \xrightarrow{k_1} A_2 + B_2\) is:

\[ \text{Rate} = k_1 [AB]^2 \]