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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?

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Yes, it is possible to construct two half cells with the same standard reduction potentials. For example, we can half cells made of copper dipping in copper sulfate solution. The caveat is that if both the cells are under standard conditions, the resulting electrode potential would be zero.

The trick is to use different concentration of copper ions in each half cell. With the help of Nernst equation you can determine which side will be the anode and which side will be the cathode. Read more about "concentration cells" as they are called.

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