[unclebilly]

Electrolysis, or hydrolysis (where hydrogen and oxygen are produced from water) is an endothermic reaction. This means you need to put electricity (or energy) in to make it happen. This is the latent heat of formation.

When the bonds are broken either during combustion or via an electrolytic reaction involving a fuel cell, you get a portion of that energy back.

Les has it right, there is no free ride here.

The theoretical highest efficiency you can theoretically get with a solid oxide fuel cell like the ones I started my career developing is Carnot Efficiency, about 64%. In reality, you might get 40%.