I don't really study chemistry so while my question may be very obvious, its not obvious to me:

If we take an electrochemical reaction like

$$\ce{2Fe^2+ + Au^3+ -> 2Fe^3+ + Au+}$$

We can find its standard potential and standard Gibb's energy by summing half reactions whose are known, and can be consulted in tables.

Its intuitive for me that the standard Gibb's energy will be given by a sum of the corresponding reactions. Its even intuitive for me that I can multiply a reaction by minus one, or whatever, and use that to construct my complete reaction.

The reason I see Gibbs energy as intuitive is because you're essentially just taking $\sum_{products} \mu_{products} - \sum_{reactants} \mu_{reactants}$ and this will prove the additive property of "summing up reactions".

But I don't see any reason for additivity being true when considering standard potentials. I don't even see why inverting the reaction should invert my potential if my half cell is in equilibrium and is a kind of "whole" that is compared to the standard hydrogen electrode and should therefore have the same potential no matter how I write it.

How am I screwing up here? Why can we add up potentials?

I don't really study chemistry so while my question may be very obvious, its not obvious to me. If we take an electrochemical reaction like

$$\ce{2Fe^2+ + Au^3+ -> 2Fe^3+ + Au+}$$

we can find its standard potential and standard Gibb's energy by summing half reactions whose are known, and can be consulted in tables.

It's intuitive for me that the standard Gibb's energy will be given by a sum of the corresponding reactions, and that I can multiply a reaction by minus one, or whatever, and use that to construct my complete reaction.

The reason I see Gibbs energy as intuitive is because you're essentially just taking

$$\sum_{\mathrm{products}} \mu_{\mathrm{products}} - \sum_{\mathrm{reactants}} \mu_{\mathrm{reactants}}$$

and this will prove the additive property of "summing up reactions".

But I don't see any reason for additivity being true when considering standard potentials. I don't even see why inverting the reaction should invert my potential if my half cell is in equilibrium and is a kind of "whole" that is compared to the standard hydrogen electrode and should therefore have the same potential no matter how I write it.

How am I screwing up here? Why can we add up potentials?

I don't really study chemistry so while my question may be very obvious, its not obvious to me:

If we take an electrochemical reaction like

2Fe(2+) + Au(3+) --> 2Fe(3+) + Au(+)

We can find its standard potential and standard Gibbs energy by summing half reactions whose are known, and can be consulted in tables.

Its intuitive for me that the standard Gibbs energy will be given by a sum of the corresponding reactions. Its even intuitive for me that I can multiply a reaction by minus one, or whatever, and use that to construct my complete reaction.

The reason I see Gibbs energy as intuitive is because you're essentially just taking $\sum_{products} \mu_{products} - \sum_{reactants} \mu_{reactants}$ and this will prove the additive property of "summing up reactions".

But I don't see any reason for additivity being true when considering standard potentials. I dont even see why inverting the reaction should invert my potential if my half cell is in equilibrium and is a kind of "whole" that is compared to the standard hydrogen electrode and should therefore have the same potential no matter how I write it.

How am I screwing up here? Why can we add up potentials?

I don't really study chemistry so while my question may be very obvious, its not obvious to me:

If we take an electrochemical reaction like

$$\ce{2Fe^2+ + Au^3+ -> 2Fe^3+ + Au+}$$

We can find its standard potential and standard Gibb's energy by summing half reactions whose are known, and can be consulted in tables.

Its intuitive for me that the standard Gibb's energy will be given by a sum of the corresponding reactions. Its even intuitive for me that I can multiply a reaction by minus one, or whatever, and use that to construct my complete reaction.

The reason I see Gibbs energy as intuitive is because you're essentially just taking $\sum_{products} \mu_{products} - \sum_{reactants} \mu_{reactants}$ and this will prove the additive property of "summing up reactions".

But I don't see any reason for additivity being true when considering standard potentials. I don't even see why inverting the reaction should invert my potential if my half cell is in equilibrium and is a kind of "whole" that is compared to the standard hydrogen electrode and should therefore have the same potential no matter how I write it.

How am I screwing up here? Why can we add up potentials?