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I have rather basic knowledge of chemistry (at the level of a first year college class). But maybe somebody can still clarify with some simple words: What makes platinum a good catalyst for the electrodes of fuel cells? And why can't other materials be used?

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Imagine that a fuel cell is like electrolysis - the other way around.

In the electrolysis of water, you'd apply a certain potential (a voltage) to the electrodes and observe hydrogen and oxygen formed at the electrodes.

In theory, you need a particular potential to run the reaction. In reality - and this depends on phenomena on the surface of the electrode material - you often need more.

With platinum, however, this overpotential for hydrogen is zero.

This means that you have no losses, neither in electrolysis, nor in the fuel cell.

This might be oversimplified but I hope it's not completely wrong ;)

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As pointed out in the other answer, platinum makes the oxidation of hydrogen gas to protons occur faster at any given potential, which in general allows you to get more energy out of the system at a given power level.

As for why this happens, it has to do with how platinum metal binds to hydrogen atoms. Hydrogen gas (H2) adsorbs ("sticks") to platinum metal, which causes the H-H bond to break as two H-Pt bonds form. This makes it easier to remove an electron from each H atom, generating two H+ from H2. The thing that makes platinum such a good catalyst for this process is that it binds hydrogen gas strongly enough, but not too strongly. Metals that have weaker interactions with hydrogen gas will not be as effective because the first step won't happen often enough (adsorption of hydrogen gas) and metals that bind hydrogen gas too strongly will not release the products, also resulting in lower rate.

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