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My book says that

Since the number of electrons lost must equal the number gained, the half-reactions must be multiplied by integers as necessary to achieve the balanced equation. However, the value of e° is not changed when a half-reaction is multiplied by an integer. Since a standard reduction potential is an intensive property (it does not depend on how many times the reaction occurs), the potential is not multiplied by the integer required to balance the cell reaction.

However, I do not understand why the reduction potential is unaffected by the number of mols. If you have a greater number of mols of the metal, doesn't that allow for a greater potential difference?

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Look at the unit volt. 1 volt = 1 joule per coulomb. If the number of moles is doubled, the coulombs are doubled, as is the number of joules. Think of the volt as the driving force behind an individual electron in an electrochemical system.

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  • $\begingroup$ Good answer. This question is just another example of how physics is dropping the ball by continuing to use outdated units in which coulomb and mole exist as separate units, just reporting electrical potential in J per mole and current in mol per s, etc. $\endgroup$
    – Curt F.
    Jun 19, 2015 at 17:00
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Basically, Imagine that you have a waterfall that is 100 meters high, and 50 meters long, this scenario makes reduction potential an intensive property: now let's say that you have two of the said waterfall--you will have in total (when put side by side) a larger waterfall that is 100 meters high, and 100 meters long. You do not need to multiply it by two because the your "potential" (usually determined by height in physics) is unchanged.

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I'll take a shot at this, so don't insta-hate me. :)

The best way I think I can show you this through is an example. Say we have 2 apples in one bin and 3 oranges in another bin. Assuming the $\ce{E}$ is the difference of the apples and the oranges you get $1.00$.

Even if we doubled the apples and the oranges the difference would be the same. In other words no matter the quantity the voltage will be equivalent.

Now, you might be thinking: what if we just double the apples. Well it doesn't matter because we can consider apples and oranges as reactants to a apple-orange pie. So the more apples we have: it would just be excess.

Take a look at this. Explains it beautifully.

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