Our modern lives are totally dependent on electricity. In this lesson, we learn about electricity spontaneously produced by electrochemical cells or batteries. We make the link between the potential energy they produce and Gibbs free energy.
The Galvanic Cell
Our lives would be unimaginable without electricity or batteries. Our lives literally depend on them. A battery is an electrochemical cell, which converts chemical energy into electrical energy. Here, we will focus on the galvanic cell, where a spontaneous chemical reaction produces electrical energy. This energy powers our cell phones, our laptops, our cars, pretty much everything!
A galvanic cell, also called a voltaic cell, makes use of reduction-oxidation chemical reactions. A redox reaction is divided into two half-reactions. One half-reaction involves the loss of electrons, and we say this is oxidized. The other half-reaction involves the gain of electrons, and we say this is reduced. I like to use the word OILRIG to help me remember which way this goes: oxidation is loss, reduction is gain. The number of electrons lost must be the same as the number of electrons gained. We must make sure we are balanced.
Here is an example of two half-reactions:
We have copper two plus gaining two electrons forming solid copper. From OILRIG, you know this is the reduction half-reaction. The second half-reaction is solid zinc losing two electrons forming zinc two plus. Again, OILRIG tells you this is the oxidation half-reaction. This is a balanced equation, as the number of electrons gained and lost is the same.
In a galvanic cell, the two half-reactions occur at two different electrodes, often metal or wire in a solution. Let us now look at a typical galvanic cell:
On the left, we are at the anode, and we have a zinc electrode dipped in zinc two plus solution. An Ox lives here because electrons are produced at the anode during oxidation. These two electrons move through the wire to where the Red Cat lives. Here a reduction takes place at the copper cathode.
A salt bridge completes the circuit, and we have a voltage being produced. Different half cells produce different voltages. This voltage is known as the cell potential energy, or E cell, and is a measure of the spontaneity of the reaction.
Measuring the Cell Potential Energy
The driving force behind a galvanic cell is the cell potential energy. The larger the cell potential, the more work we can get out of the cell. So how do we know how much energy we are going to get out? In each different cell you put together you will have two half-reactions. One is the oxidation, An Ox, and one is the reduction, Red Cat.
Each will have a standard voltage associated with it. These are Eox (or E oxidation) and Ered (or E reduction). The value depends on the reaction taking place there. We can simply look up our reaction in a standard potential table and calculate the overall cell potential, Ecell. Before we go ahead and do that, let us take a closer look at the standard potential table.
Standard Potential Table
The first thing to notice is that standard potentials are all shown as reduction reactions. This is just convention. In reality, you will have one reduction and one oxidation reaction. Please do not change the reaction around or the sign of the number. You just find your reaction in the reduction form and use the number as it is written. You don't even need to worry about the number of electrons transferred. Just use the number given to you. For our cell, we will use the zinc two plus and the copper two plus reactions.
So, say you are putting together a cell and you are not sure which half-reaction belongs to Red Cat (is being reduced) and which half-reaction belongs to An Ox (is being oxidized). There is a super easy way to figure this out. The most negative value always goes with An Ox. The more positive value always goes with Red Cat. So for our cell, the table shows us the zinc value is more negative and is with the Ox and the copper value is more positive and goes with Red Cat. Zinc is being oxidized, and the copper is being reduced.
Okay, now we understand the table, let us calculate the cell potential energy for our cell by using the following equation: E(cell) = E(red) - E(ox). We simply subtract E(ox) from E(red) to find the overall value. So, looking up the numbers in the table, we have 0.34 - -0.762 = +1.10V. The bigger this positive number is, the more spontaneous the reaction, and the more work we can get out of the cell.
The Link Between Free Energy and Cell Potential Energy
Both the cell potential energy (E) and Gibbs Free Energy (G) measure the spontaneity of a reaction. So, how are they linked? It turns out that these two quantities can be linked by the following equation: delta G = -n * F * E. Delta G is the standard free energy change for the reaction. The little degree sign just tells you this cell is at standard conditions. Standard conditions here are one atmosphere pressure and one molar concentration.
- E is the standard voltage, or cell potential energy, for the reaction.
- N is the number of moles of electrons transferred in the cell.
- F is the Faraday constant, which is roughly 96,500 J/mol V.
It is very important you notice that delta G and E have opposite signs. A spontaneous reaction has a negative Gibbs Free Energy value and a positive cell potential energy. So, let us calculate the free energy for our cell.
We can see that 2 electrons are transferred, so n = 2. We have already calculated the cell potential energy, so E = 1.10V. So, putting in the numbers: Delta G = - 2 mol electrons x 96,500 J/mol V x 1.10V = - 212,300 J or - 212.3 kJ. We have a positive cell potential and a negative Gibbs Free Energy, so we have a spontaneous reaction.
In this lesson, you have learned that energy can be converted from chemical to electrical energy in an electrochemical cell. A galvanic cell uses spontaneous redox reactions to harness energy. Redox reactions are divided into two half-reactions. Oxidation takes place at the anode and reduction takes place at the cathode. The cell potential energy is a measure of the spontaneity of the reaction. A positive cell potential energy is required for the reaction to be spontaneous. Finally, the link between free energy and the cell potential energy is delta G = -n * F * E.
You should have the ability to do the following after watching this video lesson:
- Describe the two half-reactions that make up redox reactions
- Recall how a galvanic cell works
- Explain what cell potential energy is and how to use a standard potential table
- Identify the link between free energy and cell potential energy