Whether or not you understand the laws of thermodynamics, you're going to obey them anyway.
C + O2 --> CO2 produces a fixed amount of energy per reaction, roughly half of which we can turn into electricity.
2CO2 + 6H2 --> C2H5OH + 3H2O takes a fixed amount of energy per reaction, roughly on a par with the amount of energy that came from burning the carbon in the first place. But remember, we've already lost half that energy to heat when generating electricity.
First rule of thermodynamics: you can't get back more than what you put in.
Second rule of thermodynamics: you can't even break even.
If it pans out, this technology may be useful as a means of generating carbon-neutral liquid fuel to store energy from zero-carbon intermittent sources (wind, solar etc.). Using fossil-derived energy to drive it will never make sense - we already have the Fischer-Tropsch process for directly converting carbon sources into liquid fuels, without the wasteful intermediate conversion to electricity.
