Explain why cell potentials are not multiplied by the...

Key Concepts

Intensive vs. Extensive Properties

Cell potentials are intensive properties, meaning they do not depend on the amount of substance involved in the reaction. In contrast, Gibbs free energy is an extensive property that scales with the size or amount of the system. This difference explains why, when a redox equation is balanced and coefficients are introduced, the cell potential remains unchanged while the Gibbs free energy changes proportionally.

Relationship Between ?G and Cell Potential

The equation ?G = -nFE links Gibbs free energy change (?G) with cell potential (E) in electrochemical reactions, where n is the number of electrons transferred and F is Faraday’s constant. Since ?G reflects the total energy change and is dependent on n, scaling the reaction (and thus n) affects ?G but does not change the intrinsic cell potential, which remains an intensive property.

Balanced Redox Reactions and Stoichiometry

Balanced redox reactions require coefficients to conserve mass and charge, ensuring that the chemical equation accurately represents the reaction stoichiometry. However, these coefficients do not influence the measured cell potential because the potential is defined by the intrinsic properties of the half-cells. Multiplying the reaction by a factor alters the overall energy change (?G) while leaving the cell potential the same.

Transcript

00:02 Hello, my name is margaret, and today i'm going to be helping you with zoomdahl, chapter 18, electrochemistry problem 11.

00:10 And the question says, explain why cell potentials are not multiplied by the coefficients in the balanced redox equation.

00:18 Use the relationship between delta g and cell potential to do this.

00:24 So if you want a more in -depth answer than what i'm going to give you right now, i suggest you go look at my solution to problem 27 for this chapter.

00:38 I really get into it in terms of the exact reasoning.

00:43 But i am going to give you a shorter explanation right here.

00:47 And then we'll get into the more specifics for this particular problem.

00:51 But what it really comes down to is the fact that delta g is an intensive, or i'm sorry, is an extensive property, meaning that the amount of matter measured matters, whereas e, which is cell potential, is intensive, and which means that the amount of the amount of the amount of matter measured doesn't matter.

02:07 Okay.

02:08 So basically if, you know, we had stuff right here, you know, if we had a little bit of stuff or a lot of stuff, delta g would change for each of these, but the cell potential wouldn't.

02:24 Okay.

02:26 So this wouldn't change, but this wouldn't change.

02:28 But this would change.

02:30 Okay? but so what in the point where you can really see this in particular is when we're talking about balancing half reactions.

02:44 So i'm going to show you an example.

02:47 And i wrote it all down already so you guys wouldn't have to watch me do it.

02:51 But i'll walk you through what we're talking about.

02:54 So this here is obviously a already balanced.

03:04 Half reaction that we're looking at, but we're going to incorporate another half reaction with it.

03:09 Okay? but we're talking about this is particular chemistry that you might do in the lab, and it's where you can use manganese or potassium per manganate, which is a clear to purple chemical, and you can use that to, because the fact that it reacts with iron, you can use that to determine exactly how much iron is in a solution.

03:37 It's really fun because it's cool to watch something go from colorfulness to purple, but it's not so fun because the purple bits everywhere.

03:46 However, so we have our half reaction of here of how the permanganate looks in the water and how what potential that sits at, and that's right here.

04:02 However, in order for the reaction with the iron to become fully balanced at the end, okay, we have to have three irons present because this reaction with the manganate up here requires three electrons, whereas this iron 2 plus to iron 3 plus reaction only takes up one electron.

04:33 So we have to multiply it by 3...

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