Question

Consider the following reaction,
\(2H_2(g) + 2NO(g) \rightarrow N_2(g) + 2H_2O(g)\)
which follows the mechanism given below:
\(2NO(g)\underset{k_{-1}}{\stackrel{k_1}{\rightleftharpoons}} N_2O_2(g)\) (fast equilibrium)
\(N_2O_2(g)+H_2(g) \xrightarrow[]{K_2}N_2O(g)+H_2O\)  (slow reaction)
\(N_2O(g)+H_2(g) \xrightarrow[]{K_3}N_2(g)+H_2O\)  (fast reaction)
The order of the reaction is________

Answer 1

Correct Answer: 3

Step 1: Identify the Rate-Determining Step 

The slowest step controls the overall reaction rate. Here, the slow step is:

\[ N_2O_2(g) + H_2(g) \rightarrow N_2O(g) + H_2O(g) \]

Step 2: Express Rate Law in Terms of Intermediate

The rate law for the slow step is:

\[ \text{Rate} = k_2 [N_2O_2] [H_2] \]

Since \( N_2O_2 \) is an intermediate, we express it in terms of reactants using the equilibrium step:

\[ K = \frac{[N_2O_2]}{[NO]^2} \Rightarrow [N_2O_2] = K[NO]^2 \]

Substituting this into the rate equation:

\[ \text{Rate} = k_2 K [NO]^2 [H_2] \]

Step 3: Determine Reaction Order

• The exponent of \([NO]\) is 2.
• The exponent of \([H_2]\) is 1.
• Total order of reaction = 2 + 1 = 3.

Answer 2

To solve the problem, determine the overall rate law based on the given mechanism and identify the order of the reaction.

Given overall reaction:
\[ 2 H_2 (g) + 2 NO (g) \rightarrow N_2 (g) + 2 H_2O (g) \]

Mechanism steps:
1. Fast equilibrium: \[ 2 NO \underset{k_{-1}}{\stackrel{k_1}{\rightleftharpoons}} N_2O_2 \] 2. Slow step (rate-determining step): \[ N_2O_2 + H_2 \xrightarrow[]{k_2} N_2O + H_2O \] 3. Fast step: \[ N_2O + H_2 \xrightarrow[]{k_3} N_2 + H_2O \]

Step 1: Write rate law based on slow step (RDS):
Rate \(r\) is proportional to concentrations of species in slow step: \[ r = k_2 [N_2O_2][H_2] \] But \(N_2O_2\) is an intermediate; express its concentration in terms of reactants using equilibrium in step 1.

Step 2: Expression for \([N_2O_2]\) from equilibrium:
Equilibrium constant for step 1: \[ K = \frac{[N_2O_2]}{[NO]^2} = \frac{k_1}{k_{-1}} \] \[ \Rightarrow [N_2O_2] = K [NO]^2 \]

Step 3: Substitute \([N_2O_2]\) in rate law:
\[ r = k_2 [H_2] \times K [NO]^2 = k [NO]^2 [H_2] \] where \(k = k_2 K\) is the overall rate constant.

Step 4: Determine reaction order:
- Order with respect to \(NO\) is 2
- Order with respect to \(H_2\) is 1
- Total order is \(2 + 1 = 3\)

Final Answer:
The order of the reaction is \(\boxed{3}\).