The thermal decomposition of nitryl chloride NO2Cl,

2NO2Cl---> 2NO2 + Cl2

is thought to occur by the mechanism shown in the following equations:

NO2Cl---> NO2+ Cl
NO2Cl + Cl --> No2+ Cl2

the rate is [NO2][Cl] is this right

Yes, your statement about the rate expression is correct. According to the given mechanism, the rate of the reaction is proportional to the concentrations of both NO2 and Cl.

To understand why the rate expression is [NO2][Cl], we need to analyze the mechanism and look for the rate-determining step (RDS). The RDS is the slowest step in a reaction mechanism and determines the overall rate of the reaction.

In this case, the first step of the mechanism, NO2Cl → NO2 + Cl, is a unimolecular reaction where only one molecule (NO2Cl) is involved. This step does not include Cl as a reactant, so it cannot be the RDS.

The second step, NO2Cl + Cl → NO2 + Cl2, involves a bimolecular collision between NO2Cl and Cl. Since both NO2Cl and Cl are involved in this step, it is likely to be the rate-determining step.

According to the rate-determining step, the rate of the reaction is determined by the concentration of NO2Cl and Cl. The stoichiometry of the reaction tells us that two molecules of NO2Cl are required for the formation of two molecules of NO2 and one molecule of Cl2. Therefore, the rate expression can be written as:

rate = k[NO2Cl][Cl]

where [NO2Cl] represents the concentration of NO2Cl and [Cl] represents the concentration of Cl. The reaction rate is directly proportional to both the concentrations of NO2Cl and Cl, which is consistent with the given rate expression [NO2][Cl].