### Video Transcript

In this video, we will learn how to
calculate the standard cell potential of a galvanic cell using values from the
electrochemical series. Let’s start by briefly recapping
galvanic cells and their cell notation. We will use a zinc-copper cell as
an example.

A galvanic or voltaic cell is a
type of electrochemical cell. The diagram shows the setup. A spontaneous redox reaction
occurs, and this causes chemical energy to be converted to electrical energy and
current flows through the wire. Oxidation occurs in the zinc
half-cell. Zinc two plus ions are released
into solution from the anode. And the valence electrons from
these ions travel through the wire to the copper electrode, the cathode. Here, in this half-cell, reduction
occurs. Electrons entering the cathode
attract copper two plus ions in solution. Copper ions come out of solution
and are depleted or deposited onto this electrode. The circuit is completed by a salt
bridge or a porous membrane. The notation for this cell is Zn
solid; Zn2+ aqueous, one molar; Cu2+ aqueous, one molar; Cu solid.

The anode information is written on
the left-hand side and the cathode information on the right-hand side, with the
double line representing the salt bridge between the two half-cells. When the starting concentrations of
the electrolyte solutions are one mole per dm cubed or one molar and the air
pressure is one atmosphere and the temperature is 25 degrees Celsius, we call this a
standard cell. Spectator ions, in this case
sulfate ions, are not included in the cell notation because they do not take part in
the reaction.

Now, the reason why charge flows
spontaneously in a galvanic cell is because there is a potential difference between
the two electrodes. Specifically, we talk about the
potential of each electrode to be reduced. In this example, the copper
electrode is more easily reduced than the zinc electrode. We say copper has a greater
reduction potential than zinc, and that is why copper is reduced and zinc is
oxidized. The reduction potentials of various
metals and other substances have been determined. Their values are listed in a handy
table called the electrochemical series or the electromotive series. Let’s have a look.

The electrochemical series is a
fairly long list, and so I have only shown certain portions. The reduction of lithium is near
the top of the list, the reduction of fluorine near the bottom, and this section
somewhere in the middle. There are other equations which I
could not fit on screen. The series shows the electrode
potentials of the metals and other substances in volts. These potential values are for
standard conditions. Again, those conditions are
one-molar concentrations for the electrolyte solutions, one-atmosphere pressure, and
25 degrees Celsius.

The substances are listed in order
of increasing potential. Large negative values indicate
strong reducing agents, so lithium metal is a strong reducing agent. Large positive values indicate weak
reducing agents, so the fluoride ion is a weak reducing agent relative to lithium
and, in fact, relative to all the substances above it in the table. We have the converse happening at
the same time on the left-hand side of the table. Substances which are strong
oxidizing agents are at the bottom of the list and weak oxidizing agents at the
top. Occasionally, we find the
electrochemical series written upside down with a large negative standard reduction
potentials at the bottom and the positive values at the top. However, most of the time, we will
see it written as it appears here.

Do you notice some trends? Going up the series, the reducing
ability of the substances increases, and going down, their oxidizing abilities
increase. Notice that all the electrode
potentials are written as reduction potentials, and that is why all the
half-reactions are written as reductions with the electrons on the left-hand side of
the arrows. It is important to be consistent in
this way so that we can compare electrode potentials. We cannot compare the standard
reduction potential of an element with the standard oxidation potential of another
element. It just gets confusing.

So, by convention, in science, we
all use standard reduction potentials worldwide so that we understand each
other. Notice that the reference hydrogen
electrode has a 0.00-volt value. All other electrodes are measured
relative to this so that their values have meaning when we compare them. Notice also that all the
half-reactions are written with equilibrium arrows. The symbol for reduction potential
is capital 𝐸, and a standard reduction potential should have a plimsoll superscript
symbol. A plimsoll looks like a degree
symbol with a horizontal line drawn through it. However, occasionally in some
sources, we might find that the horizontal line has not been drawn through the
plimsoll.

How is the electrochemical series
useful to us? If we know the two half-cells used
in an electrochemical cell, the table will help us figure out which direction the
electrons flow in the wire and, therefore, which half-cell is the cathode and which
is the anode. Let’s look at an example.

Let’s use our example from earlier,
the zinc-copper cell. If the system is under standard
conditions, we can then use the electrochemical series to determine the direction of
electron flow in the wire and, therefore, which half-cell is the anode where
oxidation occurs and which is the cathode where reduction occurs. First, we need to find the two
elements of our system, in this case copper and zinc. Then, we need to go to the
electrochemical series and find the corresponding half-reactions for each, and here
they are.

On the electrochemical series,
these two reactions are separated by many other reactions and are in amongst other
half-reactions. Here, I have just written down the
two that we are looking at. In a galvanic cell, the electrode
with a larger or more positive potential is taken as the cathode. When we compare these two reduction
potentials, we can see that copper’s value is more positive and is larger. So copper is the cathode. We know that the more positive or
larger the reduction potential, the more easily that substance is reduced. Conversely, the electrode with the
smaller or more negative potential is taken as the anode. In other words, the smaller or more
negative the reduction potential is, the less likely is that electrode to be reduced
and the more likely it is to be oxidized.

Now, we can figure out the
direction of electron flow in the wire. Electrons will flow from the anode,
oxidizing it, to the cathode, reducing it. We have these three bits of
information just from looking at the electrochemical series. Zinc donates electrons to the wire,
while copper receives electrons from the wire. So, comparing the relative sizes of
two electrode potentials, we can figure out which is oxidation and which is
reduction.

There is another way to figure out
which is oxidation and which is reduction. This second method is a trick. The pink arrows look a bit like a
square letter C. It tells us that the top equation,
the zinc equation, should be read from right to left. In other words, zinc is being
oxidized from solid zinc to zinc two plus ions. And it tells us that the bottom
equation, the copper equation, should be read from left to right as is written. So, copper two plus ions are being
reduced to solid copper metal. Again, the top equation is flipped
from left to right, and the bottom is left as it is. Now, be careful! This method only works if the more
negative reduction potentials are written at the top of the list and the more
positive at the bottom.

Now that the two half-equations are
written in the correct orientation, we can work out the overall reaction. The two electrons on the left
cancel with the two electrons on the right. Then, we can add the two
half-reactions to get the overall equation. Now, let’s use the two electrode
potential values to work out the overall cell potential for the cell. We can calculate the standard cell
potential or the potential difference between the two standard electrodes using this
equation. Standard cell potential is equal to
the standard reduction potential of the cathode minus the standard reduction
potential of the anode.

𝐸 cell or emf is the electromotive
force. Electromotive force is the maximum
potential difference between the two electrodes, and this occurs at the beginning of
the reaction. Over time, as the redox reaction
proceeds, this value decreases. Now, let’s calculate this value for
our zinc-copper cell. Taking the copper value for the
cathode, we then subtract the zinc anode value, and we get an answer of 1.10 volts
for this electrochemical cell. A positive answer tells us that
this reaction is feasible, which means the reaction will occur spontaneously on its
own without us having to put energy into the system to drive a reaction.

What would happen if we swapped
these two values? We would get negative 1.10 volts
for the answer. This would tell us that the
reaction is not feasible when copper is made the anode and zinc the cathode. In other words, the spontaneous
reduction of zinc by copper will not occur.

Now, it’s time to practice.

Using the standard electrode
potentials in the table below, calculate the standard cell potential for a galvanic
cell consisting of Au3+/Au and Ni2+/Ni half-cells. The table gives two half-equations
with their standard electrode potentials. Au3+ aqueous plus three electrons
giving Au solid, and its standard electrode potential is 1.498 volts. The other half-equation is Ni2+
aqueous plus two electrons giving Ni solid with its standard electrode potential of
negative 0.257 volts. The answer options are (A) 1.241
volts, (B) 1.755 volts, (C) negative 1.241 volts, or (D) negative 1.755 volts.

We are told that we have a galvanic
cell with gold and nickel half-cells. The setup of the cell would look
like this. In a galvanic cell, a redox
reaction occurs spontaneously, generating a current in the wire connecting the
electrodes. We don’t know which direction the
electrical current is moving in this galvanic cell. We are asked to calculate the
standard cell potential or 𝐸 cell. Standard conditions are one molar
concentrations for the electrolytes, one-atmosphere air pressure, and 25 degrees
Celsius. 𝐸 cell is the potential difference
between the electrodes at the beginning of the reaction. It is the maximum potential
difference between these electrodes and 𝐸 cell is equal to 𝐸 cathode minus 𝐸
anode.

We are given the standard electrode
potentials for gold and nickel, but which is the cathode and which is the anode? These standard electrode potentials
are actually standard reduction potentials. That is why both half-equations are
written as reductions with the electrons on the left-hand side of the arrows. The larger or more positive
standard reduction potential, the more easily that electrode is reduced. Gold’s value of 1.498 volts is
bigger than and more positive than nickel’s value of negative 0.257 volts, telling
us gold is more easily reduced than nickel. Therefore, gold will be the cathode
and nickel the anode.

Now, let’s put our values into the
equation. 𝐸 cell is equal to 1.498 volts
minus negative 0.257 volts. Be aware of these two negative
signs. This gives an answer of positive
1.755 volts. The positive sign tells us that the
reaction with gold as the cathode and nickel as the anode is feasible and will occur
spontaneously. But what reaction is that? It is the overall reaction where
gold is reduced at the cathode and where nickel is oxidized at the anode. So, the direction of electron flow
would be from the nickel electrode to the gold electrode. We were asked to calculate the
standard cell potential for the gold-nickel galvanic cell, and the answer is 1.755
volts.

Let’s summarize what we’ve
learnt. We recapped the setup of a galvanic
cell and cell notation using the zinc-copper cell. As an example, we saw that anode
information is written on the left and cathode information on the right. We learnt that standard conditions
are one-atmosphere pressure, 25 degrees Celsius, and one-molar electrolyte
concentrations. Then, we had a look at the
electrochemical series, which is a list of standard reduction potentials and their
corresponding reduction half-reactions. We saw that this information is
listed usually in order of increasing potential, in other words, in order of
increasing potential to be reduced or ease of reduction.

Finally, we learnt how to calculate
the standard cell potential 𝐸 cell or electromotive force. The equation is 𝐸 cell is equal to
𝐸 cathode minus 𝐸 anode, where the plimsoll superscript indicates standard
conditions and values relative to the standard hydrogen electrode. We can determine which electrode in
a galvanic cell is the cathode and which is the anode. The cathode has the larger or more
positive reduction potential. Lastly, we learnt that the standard
cell potential can have a positive or negative value and that a positive value
indicates a feasible or spontaneous redox reaction.