Did you determine the rate equations for catalysts? What is the equation order for the concentration of the catalysts ?

Dear F. Javier Lopez-Jaramillo this is certainly an interesting and important technical question. For some basic information about this topic please have a look at the following useful links:

THE EFFECT OF CATALYSTS ON REACTION RATES

https://www.chemguide.co.uk/physical/basicrates/catalyst.html

and

Approximating Catalyst Effectiveness Factors with Reaction Rate Profiles

Article Approximating Catalyst Effectiveness Factors with Reaction R...

This article has been posted by the authors as public full text on RG. Thus it can be freely downloaded as pdf file.

You can also retrieve more helpful information by searching the "Publications" of RG. For example, search for the term "effect of catalysts on reaction rates" and then click on "Publications":

https://www.researchgate.net/search.Search.html?type=publication&query=EFFECT%20OF%20CATALYSTS%20ON%20REACTION%20RATES

This will provide you with a rather long list of relevant references which have been posted by RG members. Some of these articles are even available as public full texts.

I hope this helps. Good luck with your research and best wishes!

We did few reactions using catalyst and observed that reaction getting faster with increasing concentration of catalyst. i.e using for 10%w/w catalyst reaction completed in 2h where as for 5%w/w same reaction taken 4-5h.

Thanks to all of you for your time and your interest in my question. After reading may papers (most of them just reporting the improvement of the reaction rate as the concentration of catalyst is increased) I came to the conclusion that the catalyst I have worked on are too different to be comparable.

There is Relationship between concentration of catalyst and reaction rate. As the catalyst conc. increases the rate of the reaction also increases as per the definition of the catalyst.