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About this Lesson
 Type: Video Tutorial
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 Posted: 07/14/2009
This lesson is part of the following series:
Chemistry: Full Course (303 lessons, $198.00)
Chemistry: Electrochemistry (12 lessons, $19.80)
Chemistry: Galvanic Cells (6 lessons, $11.88)
This lesson was selected from a broader, comprehensive course, Chemistry, taught by Professor Harman, Professor Yee, and Professor Sammakia. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/chemistry. The full course covers atoms, molecules and ions, stoichiometry, reactions in aqueous solutions, gases, thermochemistry, Modern Atomic Theory, electron configurations, periodicity, chemical bonding, molecular geometry, bonding theory, oxidationreduction reactions, condensed phases, solution properties, kinetics, acids and bases, organic reactions, thermodynamics, nuclear chemistry, metals, nonmetals, biochemistry, organic chemistry, and more.
Dean Harman is a professor of chemistry at the University of Virginia, where he has been honored with several teaching awards. He heads Harman Research Group, which specializes in the novel organic transformations made possible by electronrich metal centers such as Os(II), RE(I), AND W(0). He holds a Ph.D. from Stanford University.
Gordon Yee is an associate professor of chemistry at Virginia Tech in Blacksburg, VA. He received his Ph.D. from Stanford University and completed postdoctoral work at DuPont. A widely published author, Professor Yee studies moleculebased magnetism.
Tarek Sammakia is a Professor of Chemistry at the University of Colorado at Boulder where he teaches organic chemistry to undergraduate and graduate students. He received his Ph.D. from Yale University and carried out postdoctoral research at Harvard University. He has received several national awards for his work in synthetic and mechanistic organic chemistry.
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We are so close to understanding all of this with electrochemistry now. We've made the connection between electrochemical information and free energy. We know already this information exists, or this relationship exists. So all we're going to do now is look at the kind of information we get between electrochemical data and K, and how we can use electrochemical information directly to tell us something about an equilibrium constant.
So let's look at an example that's very reallife. This is the reaction that occurs in your car's battery. I'm going to break it down into the two halfreactions. One of the halfreactions is lead metal plus bisulfate, giving us lead 2, plus H^+ plus 2 electrons. So you'll notice, in this case, that this is the oxidation occurring here. And then the reduction is lead 4 plus 3H^+ plus bisulfate plus two electrons goes to lead 2 sulfate plus water. So those are the two halfreactions, which combined together, give us this net equation. And we'll say more about the construction about lead storage batteries shortly. But overall we have lead, which is a solid, lead oxide, which is a solid, H^+  that's going to be something that's going to show up on an equilibrium constant in our reaction quotients, so hold on to that  bisulfate, same thing. That's going to also be important to us. Lead sulfate is a solid. Water's a liquid. It's the liquid in the battery. So all of those terms won't be important to us. But these two guys are very important to us in as far as describing equilibrium constants for this reaction.
Now, whether we talk about a equilibrium constant or a reaction quotient, that value is going to be 1 over the concentration of [H^+]^2 times bisulfate squared. Now, if we're at equilibrium, of course, this is going to correspond to K equilibria. For all other cases, it's going to be just the reaction quotient.
Now before we talk about an equilibrium constant, just briefly, let's go back to our idea of nonstandard state, just because it's an interesting situation here. What happens, when your battery starts to discharge and we start to effectively run that forward reaction? Well, this reaction's going to go and go and go. I'm assuming, for the moment, that it's spontaneous. We've got a voltage for this complete reaction of about 2 volts, if add up those two halfcells  so definitely spontaneous reaction. We let the battery run  or your lights run, let's say, and your battery discharges. Well, what happens is a concentration of H^+ goes down. Concentration of HSo[4] goes down. And as a result of that, Q increases, right? Because these guys are decreasing and they're in the denominator now. So as Q increases, that means that the potential of the battery, according the Nernst equation, decreases. Well, duh! I guess that's pretty obvious that if you let your battery run, the potential is going to decrease. We know that from common experience, but this shows us why, as those potentials drop down, the potential will respond to that. And we move away from standard state conditions.
Okay, now you'll notice the same thing would happen if you put a lot more water in your battery. If those concentrations drop down, you change the potential. We could even talk about what happens if you remove sulfuric acid. This is essentially sulfuric acid. If you remove sulfuric acid, the potential in your battery will drop down. And interestingly enough, what this is saying is that as your reaction moves forward, the concentration of sulfuric acid, which is responsible for giving you this, drops down. And so one way to indicate how much of a charge you actually have in your battery  how much reserve power you've got in your battery  is by looking at the density of the liquid in the battery, because that tells you how much sulfuric acid you have. And if you know how much sulfuric acid you have  what concentration you have  then that's going to tell you whether you're charged and ready to go or whether you've discharged. So that's a nice convenient way to let you know how much storage you've got in your battery  how much charge you've got in your battery.
Okay, anyway, I started this discussion now wanting to talk about equilibrium constants, so I'd better do that. But again, this nice application again of the Nernst equation. Okay, so let's let this thing go and go and go until it reaches equilibrium. Okay, well where is equilibrium? Well, this says it's way to the side, but just how far is it to this side? It's going to run and run and run until we have gotten about as far over here as we can get, and it won't stop until what happens? Well, it won't stop until  again, you know from common experience  the potential goes to zero. The voltage drops to nothing. Well at that point, what's got to be true, when we're at equilibrium, is the cell voltage will be zero. So just remember that. You're always at equilibrium if your cell electromotive force is zero. That's an important point. And at that stage, just rearranging this equation here, moving this guy over to the other side, the standard state cell potential has got to be equal to positive . Remember Q now, since you're at equilibrium, is the equilibrium constant. So I can solve for equilibrium constant as long as I know my standard state. And I know that is about 2 volts, I said. So I can plug in the numbers, putting in 2 volts here and whatever our values are for these guys. These are just constants again. Our n is going to be, in this case, 2. And what we're looking for is the equilibrium constant and it will turn out to be that the equilibrium constant is 3.7 x 10^67. That is huge! That says you're down to the last molecule and then some, running in this direction. So equilibrium constants can be really, really big.
But the point I want to make here is that what seems to us like not so huge of a voltage, translates to an absolutely enormous equilibrium constant, because there's a log relationship here. Again, this is a log of the equilibrium information.
So let's look at one more example of this, actually going through and finding an equilibrium constant. And we'll do something a little different this time. We talked a little earlier about standard reduction potentials. And in particular, we talked about silver's reduction potential and silver chloride's reduction potential. And let me be careful here. What I'm pointing at is not a reduction potential at all. This is the reverse of a reduction potential. It's the oxidation potential. So remember, to get an oxidation potential from a HHhhhhjjj^
reduction potential, I just flip the equation around, but I also have to change that sign. So don't forget that.
So I've got these values that I'm just reading off our collection of reduction potentials. And the reason I'm interested in this is that if I combine those two halfreactions together, I actually end up with kind of an interesting equation that involves no electrons at all. In fact, it involves no change in oxidation states at all. But it doesn't make any difference. It's just an equilibrium. It's silver chloride  my silvers cancel out, my electrons cancel out  goes to silver plus plus chloride minus. Well, isn't that interesting. That's just a K[sp] expression. So I could get information about a K[sp]  a solubility situation  by knowing electrochemical information. I can measure those things. Those are easy to measure. And by measuring those numbers, I could get information out about how soluble, ultimately, silver chloride is. Remember, we did that? We talked about K and solubility. You might want to review that if that's a little rusty.
So I know that my potential for this overall reaction, if I combine those two halfreactions, is minus .578 volts. What does that tell me? Not a spontaneous reaction, right? Well, I knew that. I knew silver chloride was really insoluble. Just how insoluble is it? So, nFE is RTlnK. If you remember before, we talked about that relationship, combining equilibrium and standard state. And in particular  I have to be careful here remember  this is at standard state that that's going to be true. So let's make sure to mark that.
Okay, so then just rearranging then, we have our equilibrium constant is equal to natural log over equilibrium constants  . And so our equilibrium constant, then, we just convert this now to solve for K and we end up with . So I know all of this stuff. My number of moles of electrons, in this case, is one. Again faradays. Standard state potential. So let's, again, put in our standard state sign there, and it will be here for you on the side. And so we end up with a value of 1.6 x 10^10. Well, that is indeed the K[sp] of silver chloride.
So, how convenient. I mean, we said you can measure potentials with a volt meter. And you can get two halfcells, measure their potential, and from that, figure out, versus some reference point, or even directly, in this case. We don't even need to measure it versus a reference. All I want to know is are those two cells connected together? And by knowing that voltage, I can figure out how soluble silver chloride is. That's pretty cool, that I can make such a big connection between electrochemical information and solubility information. But you know what, this is all just equilibria. That's all we're talking about here. And by connecting equilibria with free energies and being able to talk about free energies in terms of potentials, we've completed that cycle. And so we've made another really important bridge between, in this case, electrochemical information and, in this particular example, the equilibrium involving solubility.
Electrochemistry
Galvanic Cells
Electrochemical Determinants of Equilibria Page [2 of 2]
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