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I am looking at the effects of increasing the surface area of which the flowing hydrogen fuel is in contact with the anode in a fuel cell.

At the anode the hydrogen is catalytically split into protons and electrons. The catalyst used is most commonly platinum. So, for a fixed flow rate of hydrogen, increasing the contact surface area with the anode will increase the number of hydrogen atoms in contact with the catalyst, and the duration that they are in contact with it. Therefore the number of oxidization half cell reactions will increase. But what is the mathematical relationship that governs the number of reactions that will occur? Is it just a linear relationship, i.e doubling the surface area doubles the number of reactions, or is it more complex?

If it is impossible to get an exact mathematical relationship, what is a good approximation on how these variables will scale with each other? Also, how do chemist usually predict the number of reactions/reaction rate, and could this be applied to my example?

Thanks!