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

A galvanic cell is a type of electrochemical cell. Rather than an external power source driving a reaction (as occurs in electrolysis), reactions in galvanic cells are spontaneous.

### Definition: Galvanic Cell (Voltaic Cell)

It is a type of electrochemical cell where electrons are generated spontaneously through a redox reaction.

These electrons pass through an external circuit.

Galvanic cells often consist of two half-cells, connected by a salt bridge.

### Definition: Anode

It is the electrode of an electrochemical cell that provides electrons to the external circuit.

In a galvanic cell, the anode is the negative electrode.

### Definition: Cathode

It is the electrode of an electrochemical cell that accepts electrons from the external circuit.

In a galvanic cell, the cathode is the positive electrode.

An electrolytic cell typically involves reactions of the anions and cations in the electrolyte. In a galvanic cell, it is more common that cations in one half-cell are reduced, while the material the anode is made of is oxidized, producing cations in the other half-cell.

The difference in the energy (called the potential difference) of the electrons of the cathode and the anode is measured in volts. A potential difference of 1 volt is equivalent to a difference in energy of 1 joule per coulomb of charge.

Cell notation can be used to describe an electrochemical cell in a condensed easy-to-understand way. Each half-cell can be described separately, and then the notation for the two half-cells can be combined.

By convention, we place the oxidation half-cell (the half-cell with the anode) on the left and the reduction half-cell (the half-cell with the cathode) on the right. In between, we put two lines (called pipes) to indicate the presence of the salt bridge.

Electrodes, gases, and solutions are separated by a single line. For instance, this half-cell

would be written like this:The reverse process would be written the other way around:

Any state symbols or concentrations may be added in parentheses. For example, the notation below expresses that we have a zinc electrode in contact with a solution containing ions at 1 molar concentration:

The notation for a full cell might look like this:

Remember, the anode is where oxidation occurs, so the anode half-cell notation should describe an oxidation; meanwhile, the cathode is where reduction occurs, so the cathode half-cell notation should describe a reduction.

The tendency of a half-cell to give up electrons can be described by its standard reduction potential.

### Definition: Standard Reduction Potential

It is the potential difference between the standard hydrogen electrode and a half-cell, under set standard conditions (1 M solutions, gases at 1 atm, and typically a temperature of ).

A more-positive reduction potential reflects a greater tendency to accept electrons.

Standard reduction potentials are defined with electrons leaving the half-cell (anode) and entering the standard hydrogen electrode (cathode).

The apparatus used in the standard hydrogen electrode looks similar to the one shown below.

This electrode is immersed in a standard solution of 1 M acid, and hydrogen gas (at a pressure of 1 bar) is bubbled over the platinum electrode. Sulfuric and hydrochloric acids are often used; however, the important factor is the concentration, which must be 1.0 mol/L.

This is connected up to other half-cells, and the voltage is measured:

We can make a rough approximation at this point. If the electrode of the other half-cell is made of a more reactive metal, it will be the anode and electrons will flow from it to the hydrogen electrode. Ions of this more-reactive metal will then go into solution. At the hydrogen electrode, hydrogen ions will be reduced to form hydrogen gas.

Here is part of the reactivity series, showing some metals that are more or less reactive than hydrogen.

We can analyze lots of metals using the standard hydrogen electrode, measuring the direction of flow of the electrons and the difference in the energy of the electrodes. From this, we can produce the electromotive series (which is similar to the reactivity series).

Element | Reduction Reaction | Half-Cell in Cell Notation | Standard Reduction Potential (V) |
---|---|---|---|

Lithium | |||

Calcium | |||

Aluminum | |||

Zinc | |||

Iron | |||

Hydrogen | (By definition) 0.00 | ||

Copper | |||

Silver | |||

Gold |

These elements have other common half-cells, which include ions with other oxidation states (e.g., ).

### Definition: Electromotive Series

It is a sequence of elements (typically metals), arranged by their standard reduction potentials.

The electromotive series is a part of the more-general electrochemical series, which also includes more complicated electrochemical reactions.

As you can see, standard reduction potentials can be (and often are) negative.

If we were to connect a half-cell with a negative reduction potential to a standard hydrogen electrode, electrons would actually flow from the half-cell to the standard hydrogen electrode, rather than the other way around.

The more positive a standard reduction potential, the greater the tendency to accept electrons and be reduced. This means that a more-positive standard reduction potential indicates that a half-cell is more strongly oxidizing:

Or, to put it another way, the more negative a standard reduction potential is, the more strongly reducing the half-cell is. Remember, reduction potentials refer to the reduction of the half-cell, not the standard hydrogen electrode.

Standard reduction potentials are complementary to standard oxidation potentials:

standard reduction potential: V standard oxidation potential: V

### Equation: Relationship between Reduction Potential and Oxidation Potential for the Same Electrochemical System

is the reduction potential, and is the oxidation potential. The relationship is

For standard reduction potentials, we write the corresponding equation with the reduced species (e.g., the metal) on the right and the oxidized species (e.g., the metal ion) on the left. Electrons are always on the left-hand side.

If we reverse this, we have the equivalent oxidation process. The standard oxidation potential is exactly the opposite of the standard reduction potential, so we tend to only talk about one type, the standard reduction potential.

### Example 1: Identifying the Significance of the Value of Standard Electrode Potential in terms of the Reducing or Oxidizing Strength of a Component

The standard electrode potential of the half-cell equation is measured to be V.

What does this tell you about the oxidizing or reducing ability of the chemical species on the left-hand side of the equation?

- It is a strong reducing agent.
- It is a strong oxidizing agent.

### Answer

The standard electrode potential is the difference in electrical potential between a half-cell and the standard hydrogen electrode. Standard electrode potentials are reduction potentials (so, the electrons appear on the left of the equation).

V is a very high value for a reduction potential. This indicates that against the standard hydrogen electrode, this half-cell will produce a potential difference of V. A positive potential difference shows that the reaction will be spontaneous.

is the chemical on the left of the equation. It generates a lot of energy when it absorbs electrons, so we consider it to be a strong oxidizing agent (it will cause other species to be oxidized).

If we know the standard reduction potential of a half-cell, we can combine it with others and predict what the cell potential would be if we connected two different half-cells.

Let’s say we are combining half-cells of copper and zinc.

The corresponding standard reduction potentials are shown.

Standard Reduction Potential (V) | Reduction Equation | Half-Cell in Cell Notation | |
---|---|---|---|

Copper | |||

Zinc |

The standard reduction potential of copper is positive (copper has a greater tendency to be reduced than hydrogen).

The standard reduction potential of zinc is negative (zinc has a lower tendency to be reduced than hydrogen).

It should be clear what happens when we combine these half-cells. If copper has a higher reduction potential than hydrogen and hydrogen has a greater reduction potential than zinc, then copper has a higher reduction potential than zinc.

Therefore, electrons will flow from the zinc half-cell (anode) to the copper half-cell (cathode) when we connect them.

Since electrons flow to the copper half-cell, we consider it to be “more positive,” and it is given the symbol. It does not have to have an actual net positive charge; it is only a way of labeling it so that we can remember which way electrons flow.

Now we have to reverse one of the equations: reduction will be taking place in the copper half-cell; therefore, oxidation must be taking place in the zinc half-cell.

Reaction at the Cathode | Reaction at the Anode |
---|---|

To calculate the standard cell potential, , we can use the standard electrode potentials.

You can think of this calculation in two different ways:

The cell potential is the difference in the reduction potential of the reduction half-cell and the oxidation half-cell.

### Equation: Standard Cell Potential from the Reduction Potential of the Anode Half-Cell and the Reduction Potential of the Cathode Half-Cell

The cell potential is the sum of the reduction potential of the reduction half-cell (the cathode side) and the oxidation potential of the oxidation half-cell (the anode side).

### Equation: Standard Cell Potential from the Reduction Potential of the Anode Half-Cell and the Oxidation Potential of the Cathode Half-Cell

Just be careful; different sources use different notation, and may refer to an oxidation potential or the reduction potential of the half-cell where oxidation is taking place (the anode side). This is the notation used here.

For this example, we are left with the following:

Remember,

If the cell potential is positive, the reaction is spontaneous.

If we get a negative cell potential, this indicates we may have written the reactions the wrong way round: if we reverse the direction, the cell potential should be positive.

Let’s summarize the whole process:

- Identify the reactions occurring in the half-cells:
- Identify the half-cell with the most-positive reduction potential.

If using an electromotive series where the reduction potentials increase top-to-bottom, the element with the greatest reduction potential will be lower down.Element Reduction Reaction Standard Reduction Potential (V) Zinc Copper - The half-cell with the most-positive reduction potential will be the cathode side; the other half-cell will be the anode side. The reduction reaction for the anode side will have to be reversed:
- The cell potential is the reduction potential of the cathode side minus the reduction potential of the anode side:

### Example 2: Calculating a Standard Cell Potential from Standard Electrode Potentials

Find, to 3 decimal places, the standard electrode potential for the galvanic cell with the following overall reaction:

Half-Equation | ||
---|---|---|

Standard Electrode Potential, (V) |

### Answer

The standard electrode potential of a galvanic cell is the potential difference between the anode and the cathode. In the reaction, we can see silver ions () being reduced to silver metal; this would occur at the cathode. We can also see iron atoms () being oxidized to iron(II) ions (); this would occur at the anode.

The standard cell potential will be the standard reduction potential of the reaction at the cathode minus the standard reduction potential of the reaction of the anode (since the equivalent oxidation will be taking place instead):

So, the standard cell potential for this galvanic cell is V.

Next, we will look at some quick ways of doing it.

If we look back at the electromotive series, we can see copper has a more-positive standard reduction potential than zinc. So, we know if we pair the zinc and copper half-cells, the copper half-cell will be the reduction half-cell ( ions will be reduced to form copper on the copper cathode).

If we write out the cell notation, it is easier to write out the copper half-cell on the right:

Then, we reverse the direction of the zinc half-cell (so that it produces electrons rather than absorbs them):

This way, electrons are always flowing left to right, which matches how we write chemical equations:

We can then combine these half-equations to produce the overall reaction equation:

So, remember, reduction is on the right!

### Example 3: Calculating a Cell Potential from Standard Electrode Potentials of Cadmium and Nickel

Using the standard electrode potentials shown in the table, calculate, to 3 decimal places, the cell potential for the following electrochemical cell:

Half-Equation | ||
---|---|---|

Standard Electrode Potential, (V) |

- V
- V
- V
- V
- V

### Answer

The cell notation given describes the following cell:

- On one side, a cadmium electrode, , is in contact with a 1 molar solution of cadmium(II) ions, .
- On the other side, a 1 molar solution of nickel(II) ions, , is in contact with a nickel electrode, .
- The half-cells are connected by a salt bridge, .

Also, a wire connects the cadmium and nickel electrodes.

The reaction at the nickel electrode is This has a standard electrode potential of V.

Meanwhile, at the cadmium electrode, This has a standard electrode potential of V.

The most positive of the two electrode potentials is that of cadmium, so we expect the reduction to take place on the cadmium side (the cathode side). This means that the cell notation is not written out the way we might expect, with the cathode side on the right. In this case, it is on the left. Remember, it is the electrode potentials that determine which side is the cathode side, not the way it is written.

From here, we can calculate the answer:

The cell potential for the given electrochemical cell is V. The correct answer is A.

Let’s summarize what we have learned about calculating the standard cell potential of galvanic cells.

### Key Points

- A galvanic cell consists of two half-cells, connected by a salt bridge.
- In a galvanic cell, electrons flow spontaneously from the anode to the cathode.
- Standard electrode potentials (which are reduction potentials) are measured against the standard hydrogen electrode, with solutions at 1 M, gases at 1 atm, and typically a temperature of .
- Standard electrode potentials of half-cells can be combined to calculate cell potentials:
- The half-cell with the most-positive electrode potential will be the cathode side (the reduction reaction will take place).
- The half-cell with the least-positive electrode potential will be the anode side (the oxidation reaction will take place).
- The equation is as follows: