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# Concentration cell

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- [Voiceover] A concentration cell, is a cell that has the same electrodes on both sides. So here we have zinc electrode on the left, and zinc electrode on the right. The only difference is the concentration. On the left side, there is a .10 molar solution of zinc sulfate. On the right side, there is a 1.0 molar solution of zinc sulfate. So the left side is the less concentrated side, and the right side is the more concentrated side. There's a tendency for the concentrations to be equalized, and that's enough to create a small voltage. So how can we make these concentrations more equal? Let's focus on the less concentrated side first. The less concentrated side needs to get more concentrated, so it can do that by increasing the concentration of zinc two plus ions in solution. So how can we increase the concentration of zinc two plus ions? Well, if solid zinc turned into zinc two plus ions, that increases the concentration. Solid zinc turning into zinc two plus is oxidation, so oxidation occurs on the less concentrated side. So let's write that down here. So we have solid zinc, turning into zinc two plus. I'm going to write .10 molar to distinguish this from the other side, plus two electrons, right, so we lose two electrons, solid zinc loses two electrons to turn into zinc two plus. Those two electrons move in our wire here, and we create a current. Now let's think about the more concentrated side. The more concentrated side needs to decrease its concentration. So it needs to decrease the concentration of zinc two plus ions in solution. It can do that if zinc two plus ions come out of solution. So if they gain electrons to form solid zinc. So that's a reduction. So reduction occurs on the more concentrated side, so let's write that, reduction, right here, so this would be zinc two plus ions. I'll write 1.0 molar concentration, once again, to distinguish it from the other one. So this would be gaining two electrons, to form solid zinc. So overall, what is happening overall here, so let's draw a line, so we have solid zinc on both sides. We can cancel that out, we have two electrons on both sides. So on the left side, we would have zinc two plus, at initial concentration of 1.0 molar. And this is going to zinc two plus at .10 molar, so this is zinc two plus at .10 molar. How do we find the voltage of our concentration cell? Remember, from the last few videos that the Nernst equation allows us to calculate the potential of the cell. So let's get some more room down here, and let's write down the Nernst equation. The cell potential, which is what we're trying to find, E, is equal to the standard cell potential E zero, minus .0592, over the number of moles of electrons transferred which is n, times the log of Q. So this is one form of the Nernst equation from the last few videos. Let's think about Q, so what would Q be for our concentration cell? So Q would be equal to the concentration of zinc two plus, this would be the concentration of zinc two plus, on the less concentrated side, so this is the concentration on the less concentrated side, over the concentration of zinc two plus on the more concentrated side. So over the concentration on the more concentrated side. So right now, that would be .10. Right now that's .10 over 1.0, so .10 over 1.0. So this is what Q is equal to. Next, let's think about the standard cell potential, so the standard cell potential E zero. What's the standard cell potential here? Well remember, the standard cell potential is the potential under standard conditions, so one molar concentration of zinc two plus. So let's write down the reduction half-reaction, so zinc two plus, this would be at one molar, so this is a reduction half-reaction, so gaining two electrons to give us solid zinc. If you look at a table of standard reduction potentials, the standard reduction potential for this half-reaction, is negative .76 volts. For the oxidation half-reaction, we need to show solid zinc turning into zinc two plus ions, and this would need to be a one molar concentration of zinc two plus ions, because we're talking about standard cell potential, standard conditions. This is oxidation, so losing two electrons. The standard oxidation potential would be just the negative of the standard reduction potential. So the standard oxidation potential is positive .76. So we've done this several times in earlier videos. Therefore, the standard cell potential, the standard cell potential would be equal to negative .76 plus positive .76, which is equal to zero. So the standard cell potential is equal to zero. That makes sense, because under standard conditions you're starting with the same concentrations. So you shouldn't get a voltage difference. So the standard cell potential is equal to zero, and we're going to plug that into here, in the Nernst equation. All right, let's go ahead and plug everything in. So the cell potential, E, is equal to the standard cell potential which is equal to zero, minus .0592 over n. What is n? We go back up here to remind ourselves that n is equal to two. We're talking about two electrons transferred, so we write n is equal to two. So let me make sure we keep that Nernst equation up there, so n is equal to two times the log of Q. And Q is equal to .10 over 1.0. So .10 over 1.0. So let's solve, let's find the potential of the cell. So let's do the math. So we have, let's see, log of .10, divided by 1.0 and that gives us negative one, so we're multiplying that by negative .0592, and we're going to divide that by two. So we get a cell potential of .0296 volts, so the cell potential is equal to .0296 volts. So that's positive. That's positive, indicating this is spontaneous. So this is our instantaneous cell voltage. So when we're talking about these concentrations, when we're talking about these concentrations right here, this is our instantaneous cell potential, so we get a positive voltage here. It's small, but it is there, and it's due to the difference in the concentrations. It's due to the difference in the concentrations. What happens as the concentrations approach each other? So as time goes on, Q is going to change. Q is going to change. What happens as the concentrations approach each other? Q should increase. So Q increases as the concentrations approach each other, and therefore, the instantaneous cell potential decreases. So the cell potential decreases here, so again, we talked about this in the video on using the Nernst equation. What happens when the concentrations are equal? Let's go back up here to remind ourselves about Q. So what happens when the concentrations are equal? Well, if the same number up here and here, then Q would be equal to one, so when the concentrations are equal, let me go ahead and write that. When the concentrations are equal... Q is equal to one. And what happens when Q is equal to one? We'd be taking the log of one. And the log of one is equal to zero. So let me go ahead and write that down. So E would be equal to zero minus .0592 over two times the log of one. And the log of one is zero, so all of this goes to zero, and therefore, your cell potential would now be zero. And that makes sense because the concentrations are equal, right, so there's no longer any tendency for the concentrations to be equalized and so you're no longer producing a voltage.