A possible reaction mechanism for the reaction-

2H2+2NO-----> N2+ 2H2O is

1. 2NO--->N2O2 (fast)
2. N2O2+H2----> N2O+ H2O (slow)
3. N2O + H2---> N2+ H2O

What is the rate law for the reaction?

To determine the rate law for the reaction 2H2 + 2NO → N2 + 2H2O, we analyze the proposed reaction mechanism you provided. The mechanism consists of three steps, with the first step being fast and the second step being slow. The rate law is primarily influenced by the slow step, as it is the rate-determining step in the mechanism.

Understanding the Reaction Steps

The proposed mechanism is as follows:

• Step 1: 2NO → N2O2 (fast)
• Step 2: N2O2 + H2 → N2O + H2O (slow)
• Step 3: N2O + H2 → N2 + H2O (fast)

In this mechanism, the second step is the slowest, which means it will dictate the overall rate of the reaction. The rate law can be derived from the reactants involved in this step.

Identifying Rate Law from the Slow Step

In the slow step (N2O2 + H2 → N2O + H2O), we see that the rate depends on the concentration of both N2O2 and H2. Therefore, we can express the rate law based on this step:

Rate = k[N2O2][H2]

Relating Intermediates to Reactants

However, we notice that N2O2 is an intermediate in the mechanism. To eliminate intermediates from the rate law, we need to express N2O2 in terms of the original reactants, H2 and NO. From Step 1, we have:

• 2NO → N2O2

This implies that the concentration of N2O2 can be expressed as:

[N2O2] = k'[NO]^2

Substituting this back into the rate law gives:

Rate = k[NO]^2[H2]

Final Rate Law Presentation

In conclusion, the overall rate law for the reaction 2H2 + 2NO → N2 + 2H2O, based on the proposed mechanism, is:

Rate = k[NO]^2[H2]

This indicates that the reaction rate is dependent on the square of the concentration of nitrogen monoxide (NO) and the first power of hydrogen (H2). Understanding the relationship between reaction mechanisms and rate laws is crucial in mastering kinetics in chemistry.