Here is my understanding. If you have an endergonic reaction (m) with $\Delta G_m=-m$ and you couple it to an exergonic reaction (n) with $\Delta G_n=n$, where $n>m$, then the endergonic reaction can proceed as the overall $\Delta G$ for the system is negative. I understand why having the endergonic reaction occurring is not a violation of the second law of thermodynamics and why it is made possible in that sense.
I was recently studying electrolysis and they talked about hooking up an electrochemical cell to a power supply and using electrical energy to drive a nonspontaneous redox reaction. If you include the power supply in the system, then the $\Delta G$ is negative, as the power supply gives a lot of energy.
This is my confusion: if the redox reaction is nonspontaneous (let’s call it R1), then it must be spontaneous if the opposite direction (let’s call it R2). However, in the presence of electrical energy… R1 is made spontaneous? Therefore it can occur? But what of R2? Shouldn’t that reaction be even more spontaneous, as it were? Shouldn’t the system try to minimize its energy by preferentially allowing R2 to proceed, even in the presence of an energy source? Thus, why would R1 occur? Why does shoving energy into a system cause a nonspotaneous reaction to occur when it would be more favorable to continue having it occur in the opposite direction?
I would also appreciate it if anyone could extend this to general energy coupling, say with hydrolyzing ATP and a nonspontaneous biological reaction. Why is the original spontaneous reaction not made more spontaneous?