# Conditions for spontaneity of redox reaction among redox couples with equal standard reduction potentials

A question from the university course:

Could a redox reaction spontaneously occur among the redox couples $$\ce{A_{ox}}/\ce{A_{red}}$$ and $$\ce{B_{ox}}/\ce{B_{red}}$$ within non-standard circumstances if they have the exact same standard reduction potentials? So then, under which conditions?

The lecturer used the Nernst equation as follows for this question:

$$\Delta E = \Delta E^{\circ\prime} + \frac{RT}{zF} \ln{\frac{[\ce{A_{ox}}]}{[\ce{A_{red}}]}} - \frac{RT}{zF} \ln{\frac{[\ce{B_{ox}}]}{\ce{[B_{red}}]}}$$

From my understanding he is calculating the energy that is needed to run the reaction spontaneously, but I don't understand how he came to this equation.

If the reduction potentials of two half-reactions are the same, is it still possible for them to run spontaneously under certain conditions?