Power generation through endothermic heat absorption.

I have been toying with an idea that may break the second law of thermodynamics for a while now, but it is basically this; An endothermic reaction is used to convert heat energy into chemical energy, and then the products of that reaction are used as the reactants in an electrochemical reaction to extract the energy captured by the endothermic reaction. The products of that are then used as the reactants for the endothermic reaction in a continual cycle. If the temperature is too low to allow the endothermic reaction to occur, you have a buildup of reactants for that reaction. If the power draw is too low to keep up with the endothermic reaction, you have a build up of reactants for that. Basically turning this system into a battery / fuel cell that recharges by absorbing ambient heat.

I should note that I am only a senior in high school with a fairly limited chemistry/molecular level physics education. - Most of it coming from my research into this idea. My particular expertise instead comes in electrical engineering.

Would this be possible at all? Would it break the second law of thermodynamics as it is skyrocketing past the theoretical maximum efficiency of the Carnot cycle possible in a heat engine? If so, what sort of barrier is stopping this sort of thing from occurring? A theoretical one (The second law - Which could always be disproven as I know of no large parts of physics resting on it. Although please correct me if I'm wrong.) or a chemistry one?

Thank you for any discussion / answer.