Question

The rate law for the reaction \(2\text{NO}(g) + \text{O_2(g) \rightarrow 2\text{NO}_2(g)\) is} \[ \text{rate} = k[\text{NO}]^2[\text{O}_2] \] Then which among the following statements is correct?

• A. The reaction is first order in \(\text{O}_2\), first order in NO and second order overall.
• B. The reaction is second order in NO, zero order in \(\text{O}_2\) and second order overall.
• C. The reaction is second order in NO, first order in \(\text{O}_2\) and third order overall.
• D. The reaction is zero order overall.

Hint:

Overall order of a reaction is always the sum of the exponents of concentration terms in the rate law.

Answer 1

The Correct Option is C

Step 1: Understand the rate law.
The given rate law is: \[ \text{rate} = k[\text{NO}]^2[\text{O}_2] \] The powers of concentration terms indicate the order of reaction with respect to each reactant.

Step 2: Determine individual orders.
Order with respect to NO \(= 2\).
Order with respect to \(\text{O}_2 = 1\).

Step 3: Calculate overall order.
Overall order of the reaction is the sum of individual orders: \[ 2 + 1 = 3 \]

Step 4: Analyze the options.
(A) Incorrect — overall order is not 2.
(B) Incorrect — \(\text{O}_2\) is not zero order.
(C) Correct — it correctly represents individual and overall orders.
(D) Incorrect — the reaction is not zero order.

Step 5: Conclusion.
The reaction is second order in NO, first order in oxygen, and third order overall.