That's because you left out the need for electricity in addition to the catalyst. However the catalyst could be used for the reaction running the other way, converting the hydrogen and oxygen back to water, and electricity.
—However the catalyst could be used for the reaction running the other way, converting the hydrogen and oxygen back to water, and electricity.—
I just assumed that would be a peripheral function of the motor in the first place, much as a car’s motor runs the alternator.
The reason I called it similar to perpetual motion is that I would think that the hydrogen and oxygen could be converted from water vapor to water with a simple condensation coil and the electricity could be generated by the engine with, well, an alternator.
The impact is that it produces more energy than it takes in and I assume the magic happens in the catalist, producing more hydrogen/oxigen for combustion and power generation than it needs for the chemical reaction in the first place.