Assertion (A) : The order of the reaction `2NO(g)+2H_(2)(g)rarr2H_(2)O(g)+N_(2)(g)` is 3.
Reason (R) : Order of reaction with respect to a given reactant the power of the reactant's concentration in the rate equation.

Options

A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true but R is not a correct explanation of A
C. A is true but R is false
D. A is false but R is true

Answer

To solve the question, we need to analyze the assertion and reason provided regarding the reaction:

**Assertion (A)**: The order of the reaction \(2NO(g) + 2H_2(g) \rightarrow 2H_2O(g) + N_2(g)\) is 3.
**Reason (R)**: The order of reaction with respect to a given reactant is the power of the reactant's concentration in the rate equation.

### Step-by-Step Solution:

1. **Understanding Reaction Order**:
- The order of a reaction is defined as the sum of the powers of the concentration terms in the rate law expression. It indicates how the rate of reaction depends on the concentration of reactants.

2. **Identifying the Reaction**:
- The given reaction is \(2NO(g) + 2H_2(g) \rightarrow 2H_2O(g) + N_2(g)\).

3. **Determining the Rate Law**:
- For a reaction that is not elementary (which means it occurs in multiple steps), the rate law cannot be directly inferred from the stoichiometry. We need to consider the individual contributions of each reactant.
- Let's denote the rate law as:
\[ \text{Rate} = k[NO]^m[H_2]^n \]
- Here, \(m\) and \(n\) are the orders with respect to \(NO\) and \(H_2\), respectively.

4. **Assuming Reaction Orders**:
- Based on typical reaction mechanisms, we might assume that the reaction is second order with respect to \(NO\) (i.e., \(m = 2\)) and first order with respect to \(H_2\) (i.e., \(n = 1\)).
- Therefore, the rate law can be expressed as:
\[ \text{Rate} = k[NO]^2[H_2]^1 \]

5. **Calculating Total Order**:
- The total order of the reaction is the sum of the individual orders:
\[ \text{Total Order} = m + n = 2 + 1 = 3 \]

6. **Conclusion on Assertion**:
- Since the total order of the reaction is indeed 3, the assertion (A) is correct.

7. **Evaluating the Reason**:
- The reason (R) states that the order of reaction with respect to a given reactant is the power of the reactant's concentration in the rate equation. This is a true statement about reaction kinetics.

8. **Final Evaluation**:
- Both the assertion (A) and the reason (R) are correct, and the reason correctly explains the assertion.

### Final Answer:
Both the assertion and reason are true, and the reason is the correct explanation for the assertion.

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