We've already seen that the change in free energy, delta G, can be related to the cell potential E by this equation. Under standard state conditions, this would be the standard change in free energy, so delta G zero, which is related to the standard cell potential E zero, by the same equation. This equation down here comes from thermodynamics, and we're gonna plug in for delta G and delta G zero. So we're gonna plug this in for delta G, and we're gonna plug this in for delta G zero. So that gives us negative N, F E is equal to negative N F E zero plus R T natural log of Q, where Q is the reaction quotient.
Let's divide everything by negative NF. So we're gonna divide everything in here by negative NF, and let's see what cancels out. So all of this would cancel out, all of that would cancel out, and we get the Nernst equation.
So let me go ahead and write it. The cell potential E is equal to the standard cell potential. potential E zero minus RT over N.
F times the natural log of Q, where Q is the reaction quotient. So this is the Nernst equation. Alright, we'll talk about why the Nernst equation is so important, we'll talk more about that at the end of the video. Right now, let's go ahead and derive another form of the Nernst equation. So I should say the form when you're talking about a certain temperature.
So at 25 degrees C, right, most of our reactions take place at 25. degrees C. Well, temperature, temperature in here, this is the temperature in Kelvin, so we need to convert to Kelvin. So if you add 273.15, you get your temperature in Kelvin. So that would be 298.15.
So what we're gonna do is solve for RT over F to write a different form of the Nernst equation. And so the temperature is 298.15 Kelvin. so let's write that in, so 298.15 Kelvin. R is the gas constant, so remember the gas constant is 8.314, 8.314 joules over mole Kelvin. And F is Faraday's constant.
Remember Faraday's constant from an earlier video, that's 96,500 coulombs per mole, so Faraday's constant is the charge. of one mole of electrons. Alright, so let's solve for what all this is equal to.
So equal to, this is equal to.0257. And for units, Kelvin would cancel out, moles would cancel out, that gives us joules over coulombs, which is equal to volts. Alright, so this is equal to volts.
And we can write another form of the Nernst equation. So if your reaction at 25 degrees C, you can write the Nernst equation this way. You could say that the cell potential E is equal to the standard cell potential E zero minus, so all that RT over F is equal to this,.0257. So.0257 volts.
We still have N. Remember, N is the number of moles, let me use green for that, N is the number of moles of a... electrons that are transferred in your redox reaction. So we're gonna put n in here, and we still have the natural log of q, the reaction quotient.
So here is another form of the Nernst equation. So at 25 degrees, you can use this form. And then we can also write this into base 10 logarithm instead of natural log.
So we can do that conversion. So we also did that in an earlier video. but if you're trying to convert this 0.0257, you need to multiply by the natural log of 10. This is equal to 0.0592. So we can write the Nernst equation once again.
So E, or the cell potential, is equal to the standard cell potential, E zero, minus 0.0592 over N. And, And we essentially just change this from natural logarithm to base 10 logarithms. This would be log of Q, log of the reaction quotient.
So here is just another form of the Nernst equation. So why is the Nernst equation important? Why is it useful?
It's useful because it allows us to calculate a cell potential under non-standard state conditions. So think about this cell potential as being a single cell. as being the instantaneous cell potential.
And you can relate that to the progress of the reaction. So as you change concentrations, the reaction quotient Q changes. And that means that the instantaneous cell potential changes. So if you change the concentrations, if you change the concentrations, you're changing the cell potential.
And so we'll see more about that in the next video. So I think that the Nernst equation makes much more sense when you do some problems with it. and then you can understand better what it means.