- A concentration cell is a cell which on both sides has the same electrodes.
But here we have an electrode of zinc on the left, and an electrode of zinc on the right. The only distinction is concentration. There's a .10 molar zinc sulfate solution on the left side. There's a 1.0 molar zinc sulfate solution on the right side. So, the less focused side is the left side, and the more focused side is the right side. There is a tendency to equalize the concentrations, and that's enough to produce a tiny voltage.
But how do we equalize these concentrations? Let us focus first on the less focused side. It is necessary for the less concentrated side to get more concentrated. So, by rising the zinc concentration to plus ions in the solution, it can do that. Then how can the concentration of zinc plus two ions be increased? Well, if solid zinc has converted two plus ions into zinc, that increases the concentration. Oxidation is solid zinc transforming to zinc two plus, so oxidation happens on the less concentrated side.
So let's just write it down here. So we've got strong zinc converted into two plus zinc. To differentiate this from the other hand, plus 2 electrons, I'm going to write a .10 molar. But we're losing 2 electrons. To turn into zinc two plus, solid zinc loses two electrons. In our wire, those two electrons are moving here, and we are making a current. Let's think on the more oriented side now.
The more concentrated side has to reduce its concentration, so the concentration of zinc in the solution must be decreased by two plus ions. When zinc two plus ions come out of the solution, it will do so if they accumulate electrons to form solid zinc. That's a reduction, therefore. So on the more focused sides, reduction happens. Let's write that down right here. Reduction. So this would have been zinc plus two 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's happening here in general? So let's draw a line, so we've got both sides of strong zinc. We should cancel it out. In both sides, we've got two electrons. So we'd have zinc two plus on the left side, zinc two plus at an initial 1.0 molar concentration, and this is going to be zinc two plus at 0.10 molar. So this is zinc 2 plus at a molar of .10. How can we locate our concentrator's voltage?
From the last few images, note that the nearest equation helps us to measure the cell's potential. So let's go down here to get some more space. Let's write down the equation that comes closest. The cell potential we are trying to find, E, is equal to the normal cell potential E zero minus .0592 over the number of transmitted moles of electrons, which is N, times Q's log.
So, from the last few images, this is one form of the closest equation. Let's think of Q. Then what will Q be to our cell of concentration? So Q would be equal to zinc two plus concentration, which would be zinc two plus concentration, on the less concentrated side. So this is the concentration on the less concentrated side, on the more concentrated side, over the concentration of zinc two plus, and on the more concentrated side, over the concentration.
So right now, that would be .10, which is .10 right now, over 1.0.0. So .10 over 1.0, so that's what equals Q. Next, let's think about the potential for standard cells. So the standard potential of the cell, zero E. What's the potential for standard cells here? Well, remember, under standard conditions, the standard cell potential is the potential, so one molar of zinc concentration is two plus.
So, let's write down the half-reaction reduction. So this would be at one molar, zinc two plus, so this is a half-reaction reduction, so gaining two electrons to give us solid zinc. The standard reduction potential for this half reaction is negative .76 volts, if you look at a table of standard reduction potential. We need to show solid zinc for the oxidation half reaction, turning into zinc two plus ions, and if zinc two plus ions, this would need to be a single molar concentration, because we're talking about standard cell potentials, standard conditions.
This is oxidation, so two electrons are lost. Just the negative of the standard reduction potential would be the standard oxidation potential. The standard potential for oxidation is therefore positive .76. So we did this in earlier videos several times. The normal cell potential, therefore, would be equal to negative .76 plus positive .76, which is equal to zero, the standard cell potential.
So the potential for the standard cell is equal to zero. That makes sense, because you're starting with the same concentrations under standard conditions, so you shouldn't get a voltage difference. So the potential for the standard cell is equal to zero. We're going to plug that into the closest equation here. Okay, let's go ahead and plug it all in. Therefore, E's cell potential is equal to the standard cell potential, equal to zero, minus .0592 over N.
What is N?
To remind ourselves that N is equal to two, we are going back up here. We're talking about two transferred electrons. So N is equal to two, we write. So let me make sure that we keep the nearest equation up there, so N is equal to two times Q log, and Q is equal to .10 over 1.0, so .10 over 1.0, so .0296 volts is equal to the cell potential. That's positive, therefore. It is positive, it is spontaneous to indicate this
So this is our instantaneous voltage from the cell. So when we're talking about these concentrations, when we're talking right here about these concentrations, that's our instantaneous potential for cells. So we're getting the positive, we're getting the positive voltage. It's small, but there it is. And that's because of the difference between the concentrations. It's because of the difference between the concentrations.
When the concentrations approach each other, what happens? So, Q is going to change as time goes on. Q is going to change. As the concentrations approach each other, what happens? Q ought to rise. So, as the concentrations approach each other, Q increases, and the instantaneous cell potential therefore decreases. So the potential of the cells decreases here. So, again, this is what we talked about in the video using the closest equation.
What happens when there are equal concentrations? Okay, well, let's go back to this place to remind ourselves of Q. So what happens when there are equal concentrations? If there's the same number up here and down here, then Q is equal to one. So, if the concentrations are equal, let me go ahead and write that Q is equal to one when the concentrations are equal. And when Q is equal to 1, what happens? We would take the log of one and the log of one would be equal to zero.
So let me go ahead and write down this. So E will be 2 times the log of one, equal to zero minus .0592 over 2. And one log is zero, so all of this goes to zero, so your cell potential is now zero, so your cell potential is zero. And because the concentrations are equal, that makes sense. But there's no longer a tendency to equalize the concentrations, and so you no longer generate a voltage.
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