- [Voiceover] 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,
all right, by the same equation.
This equation down here comes from thermodynamics
and we're going to plug in for delta G and delta G zero,
so we're going to plug this in for delta G
and we're going to plug this in for delta G zero,
so that gives us negative nFe
is equal to negative nFE zero
plus RT natural log of Q,
where Q is the reaction quotient.
Let's divide everything by negative nF,
so we're going to 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, E zero, minus RT
over nF
times the natural log of Q,
where Q is the reaction quotient,
so this is the Nernst equation.
All right, 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.
I should say the form when you're talking about
a certain temperature,
so at 25 degrees C.
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 going to 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.
So let's solve for what all this is equal to,
This is 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,
so this is equal to volts,
and we can write another form of the Nernst equation.
So, if your reaction's 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, right?
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 electrons that are transferred
in your redox reaction,
so we're going to 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,
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 .0257
you need to multiply by the natural log of 10.
This is equal to .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 .0592
over n, and we essentially just changed
this from natural logarithm to base 10 logarithm
so 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 beause it allows us to calculate a cell
potential under non-standard state conditions,
so think about this cell potential as being the
instantaneous cell potential,
and you can relate that to the progress of the reaction,
right?
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.