You need to determine if the bimetallic component on your catalyst is in alloy form. If it exists as an alloy, you can assume same type of catalytic site for CO and O2 in LHHW calculations. However, if they exist as individual metals you need to assume adsorption of CO and O2 on different catalytic sites. The alloy formation can be determined by XPS analysis of catalyst with monometallic and bimetallic loading.

@S Patankar: What you mean by "alloy form" and "individual metals"? An alloy is a physical solution of the individual metal atoms. Perhaps you mean to compare homogeneous mixtures versus heterogeneous mixtures?

In any case, I am also not certain that homogeneous versus heterogeneous mixtures is what immediately distinguishes the behavior at the binding sites of the two metals. Since either case is a physical mixture, to a first approximation, the elements behave (essentially) the same as their bulk cases regardless. So, we are left with just the consideration of what one element does versus the other. The mechanism may change on each element. That will change the rate law expressions in each element. If so or if not, the rates will be different on the two elements. The final rate law expression will be a complicated mixture law of the two expressions.

This does not even consider spill-over effects. Also, when you want to present arguments about electronic effects for one metal on the other in comparison of homogeneous versus heterogeneous solutions of the bimetallic systems ... that is an entirely different and more complex beast.

I would wonder whether any literature work has been done on this topic? I would also wonder whether the original poster appreciates the model as it stands for just one element, let alone that we discuss a bimetallic system.

@ J J Weimer: Yes I meant homogeneous and heterogeneous mixtures. The reaction mechanism and hence mathematical model will be different in these two cases. I agree that its essential to study the role of individual metals on the rate of reaction. 

Thank you Saurabh Patankar and Jeffrey J Weimer for the informative discussion.

This systems exist as alloy that homogeneously mixed.

As, lets the alloy of that systems is AB. After the optimization, CO is most stable on top site of A, whereas O atom is on fcc hollow site that consists of atom A and B. Then, I need to calculate the coverage of CO on the top of A and the coverage of O atom on that fcc site, separately? After that, by using their coverage values, then I may calculate the reaction rate as a role of individual atoms? With the same equation as metallic case?

Thank You very much for the help.

By the way, I have a reference that discussing the same topic.

Feng Gao, Yilin Wang and Wayne Goodman; J.Phys. Chem. C, 2010, 114, 4036-4043

As indicated in previous answers, it is difficult to know a priori if adsorptions take place on the same sites or on different sites. The best criteria are always the experimental results! I advise you to use two equations and see which looks best, your equation or r = kr kCOPCO /(1 + kCOPCO) * (kO2PO2)1/2/(1 + (kO2PO2)1/2 ).

Many Thanks Dr. Guy Schmitz.

I will try to use both and see the results, and compare with experimental.

It is very important atomic ratio of Pt and Pd in solution.Mechanism of adsorption CO and O2 can be change 

The reaction mechanisms for a bimolecular reaction on a solid surface are of two types :

Langmuir-Hinshelwood mechanism and Langmuir-Rideal mechanism.

In the Langmuir-Hinshelwood reaction mechanism, the rate of the surface reaction is proportional to the probability that the two molecules are adsorbed on neighbouring sites on the solid surface.

For a reaction  A  +  B  ------>  products, the two molecules should first get adsorbed on adjacent sites, form an activated complex which then will break up into products.

Rate = k SA SB where the S terms represent the areas occupied by the respective reactants.

For unit area of the solid surface, the free or bare area available for adsorption is (1-SA-SB)

rate of adsorption of A =kAa [A] (1-SA -SB) and rate of desorption of A =kBdSA where the k terms are the rate constants for adsorption and desorption.

At equilibrium , the two rates are equal and hence, SA/ 1-SA -SB =KA[A]  where KA=kAa/kAd

A similar equation can be worked out for reactant B.

These are simultaneous equations which can be solved to give the following equations:

SA = KA[A]/ 1+ KA[A] + KB[B]  and SB=KB[B] / 1+ KA[A] +KB[B]

Rate = k SASB . Substituting for the surface area terms

we get rate =k KAKB[A] [B]  / { [1+KA[A] + KB[B] }2

The rate of the bimolecular surface reaction is maximum when maximum number of A-B pairs are adsorbed on the surface.

Case1 At low concentrations of both reactants, the reaction if of second order

Case 2 If one reactant  say A is weakly adsorbed  and the other say B is strongly adsorbed then, rate = k KA[A]  / KB [B] and the order is 1 with respect to A.

Example:for the reaction between CO and Oxygen on quartz the rate is proportional to pressure of oxygen but inversely proportional to pressure of CO. CO is strongly adsorbed on quartz.

Hi

Can you please find the attached image that shows the equation I used during the calculation of reaction rate of conversion of butene

Have a very good day and best of luck