- [Instructor] In the last several videos,
we've been exploring how
we can balance electrochemical reactions.
And we talked about how you can break down
any electrochemical
reaction into an oxidation
and a reduction half-reaction.
This is important for
understanding how we can learn
thermodynamic information for
any electrochemical reaction.
So the big premise of this
video is to figure out
how we can determine the
standard Gibbs free energy
of an electrochemical reaction, okay?
And we can do this using
standard data about
these electrochemical
half-reactions, okay?
So our goal is to determine Delta G nought
for a reaction.
And we are able to calculate
the standard Gibbs free energy
of an electrochemical
reaction using this equation.
Where in this case N is
the number of electrons
that get transferred
in the balanced electrochemical reaction.
That's important, the
electrochemical reaction
must be balanced and N is
the number of electrons
that get transferred in that reaction.
F is known as Faraday's constant
and it has a value of 96,485
joules per mole volt
and E nought is the
electrochemical potential.
And this potential always
has the unit of volt, okay?
So if we are able to figure
out the number of electrons
that are transferred,
which we can easily do
using our balancing approach,
and the electrochemical
potential of a reaction
then we can very easily calculate
the standard Gibbs free energy, okay?
And the way that we determine
this electrochemical potential
is using a table of electrochemical data.
Okay, so what we're looking
at here is that table
of electrochemical data that I referenced.
What I'll point out is that we're looking
at different chemical
reactions and we're given
this value of E nought.
The other thing that's
important to recognize here
is that these are all reduction reactions.
So this is known as a table
of standard reduction potentials, okay?
So we are able to figure out the potential
of each of our half reactions as long as
we recognize that this
table will only give
us a value for the reduction, okay?
So in this case zinc was being reduced.
So we should be able to find
this reaction exactly in our table.
And if we look closely
enough, we see down here
that zinc reacting with two electrons
is giving us elemental
zinc and this has a value
of negative 0.76 volts, okay?
So that's the potential
that we need to remember
to use in our calculation.
The other potential that
we need to find is that
for the oxidation of magnesium, okay?
And note that this is a table
of reduction potentials.
So what we're gonna do is to look
for the reverse of this reaction.
And we find that right here.
So the reduction of magnesium plus two
to give us elemental
magnesium has a potential
of negative 2.38.
But this is the reverse of that,
so the oxidation reaction has a potential
of 2.38 volts.
So it's the opposite of the
reduction reaction, okay?
So our two potentials that we need to use
are negative 0.76 volts
and plus 2,38 volts.
So I've written these two
values and associated them
with one of the two half-reactions, okay?
And remember according to Hess's law
we can add together two reactions
to give us a new reaction
and that's how we're
balancing these reactions.
We can do the same thing
for our potentials.
So if we add these two values together,
the sum is gonna give us the potential
of the overall balanced
electrochemical reaction.
And when we do this we get
an overall reaction potential
of 1.62 volts.
So this is the potential of
the reaction that we can use
in our Gibbs free energy
calculation, okay?
So that is our E nought value.
The last thing we need
for this calculation
is to know the number of
electrons that get transferred
in the balanced reaction.
And we can very easily spot this looking
at our balanced reaction here.
Both half reactions have
two electrons involved.
So in the balanced reaction
we are moving two electrons
from magnesium to zinc.
So to calculate our
standard Gibbs free energy,
we have negative two
'cause that's the number
of electrons times Faraday's constant,
which remember had the units
of joules per mole volts
times our electrochemical potential
which was 1,62 volts.
And when we do this,
we get a standard Gibbs free energy value
of negative
312,611
Joules per mole, okay?
So as long as we are able
to figure out the overall
potential of a reaction,
using the two half reactions,
then we can always calculate
the standard Gibbs free energy.
We'll go through this one more time
with one of the other
electrochemical reactions
that we've balanced.
So what we're looking at
here is the same reaction
that we balanced previously
which is the reaction
between silver and manganese.
Remember we break this
into two half reactions,
our reduction half-reaction
is silver gaining an electron
and our oxidation
half-reaction is water reacting
with manganese to give
us permanganate, okay?
Before we look at the
reduction potentials,
what I wanna remind you of
is that in this reaction
we actually needed to
multiply this reaction
by five so that the total
number of electrons is five.
So that's notable because
in our Delta G calculation,
N is equal to five, okay?
So let's go ahead and look
for these two reactions
in our table of standard
reduction potentials.
My reduction reaction was
silver gaining an electron
and I see here that that
reaction has a potential
of 0.8 volts.
And my oxidation reaction was
manganese reacting with water.
So remember I'm looking
for the reverse of that
because this is a table of reductions
and I see the reduction has
a potential of 1.49 volts,
so my oxidation has a potential
of negative 1.49 volts, okay?
We'll go ahead and apply these
values to our half reactions.
And when I add these two values together,
I get the potential for the overall
balanced electrochemical reaction,
which is negative 0.69.
And I'm now in a position
where I can go ahead
and calculate my standard
Gibbs free energy.
The number of electrons
transferred is five,
so we have negative five
times Faraday's constant
times our reaction potential
which is negative 0.69 volts.
So in this case my standard
Gibbs free energy is equal to
332,873
joules per mole, okay?
So two last things that I wanna point out.
First, note that I did
not take my potential
times this value of five, okay?
We do not multiply our reaction potentials
by that stoichiometric
coefficient ever, okay?
And the reason is that
this coefficient of five
actually gets built into our
Gibbs free energy calculation.
So we don't want to
multiply it by five twice.
The other thing I wanna point
out is that this reaction
had an overall negative
standard potential.
Which gives us a positive
or non spontaneous Delta G.
Whereas the previous example
we had an overall positive
reaction potential
which gives us a net negative
or spontaneous Gibbs free energy, okay?
And the reason for that is because
of this negative sign in our calculation.
So anytime we have a standard potential,
it represents a spontaneous reaction.
But if we have a negative potential
this represents a non
spontaneous reaction.
