Rate law of binary interaction?

Question

What is the expected rate law of this binary interaction that is dependent on both reactants?

 

2NO(g) + Cl2(g) --> 2NOCl(g)

Answer 1

The rate law is going to have the form:

 

rate = k[NO]^m[Cl₂]ⁿ

 

However, in order to determine the coefficients, you will need more information, such as:

• experimental data (from "initial rate experiments", if you have covered that)
• a reaction mechanism that indicates where the rate determining step (rds) is
• the overall order of the reaction (first, second, or third order)

 

Since you have not provided this information, you cannot give a more detailed information about the rate law.

 

However, for the sake of completeness, a mechanism usually presented for this reaction is:

 

NO + Cl₂ <==> NOCl₂  (fast equilibrium)

NOCl₂ + NO --> 2 NOCl  (rate determining step)

 

Since step 2 is the rds, the rate of formation of one NOCl would correspond to the rate of the reaction.

 

Since we are making two NOCl molecules in this reaction, we need to take that into account when writing the  rate law for that elementary step. So, 

 

rate of reaction = 1/2 (rate of formation of NOCl) = (1/2) d[NOCl]/dt = k₂[NOCl₂][NO].

I am using k₂ for the rate constant to indicate I am working with equation 2.

 

Since NOCl₂ is not a reactant, we cannot use the rate law above as being the final rate law. Intermediates are not allowed in rate laws as their concentrations cannot be measured easily or accurately.

 

What you need to use is the fast equilibrium in the first step and realize that, since you have fast equilibration, the rate forward and the rate backward for the equilibrium are equal. So, you can write:

 

k₁[NO][Cl₂] = k_–1[NOCl₂],

where k₁ and k_–1 represent the rate constants for the forward and reverse reactions, respectively.

 

With simple algebra, you get that: [NOCl₂] = (k₁/k_–1)[NO][Cl₂]

 

Plug the value of [NOCl₂] you just derived into the previous rate law and you get:

 

rate rxn = k₂[NOCl₂][NO]

             = k₂((k₁/k_–1)[NO][Cl₂])[NO]

             = (k₁k₂/k_–1) [NO]²[Cl₂]

 

However, if the reaction mechanism had the first equation as the slow step and the second step as a fast equilibration, the rate law would depend entirely on the first step and you would have:

 

rate = k1[NO][Cl₂]

 

for a mechanism where

NO + Cl₂ --> NOCl₂ (slow, rate determining step)
NOCl₂ + NO <==> 2 NOCl (fast equilibration)

 

Now, which rate law is actually correct? Well, you need to have experimental data (initial rate method) to determine which of the rate laws derived above is actually supported by the data.

 

I hope this helped. If you have more information about this question, please provide it.