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Lesson Video: Electrochemical Cell Potential Chemistry • 10th Grade

In this video, we will learn how to calculate the standard cell potential of galvanic cells using values from the electrochemical series.

15:49

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.

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