Coulometry - Online Tutor, Practice Problems & Exam Prep

Electrochemical cells can be classified based on spontaneity, determined by Gibbs free energy (ΔG), equilibrium constant (K), cell potential (E_cell), and entropy (ΔS). A spontaneous reaction (ΔG < 0) indicates a galvanic cell, while a non-spontaneous reaction (ΔG > 0) indicates an electrolytic cell, which requires an external energy source. At equilibrium (ΔG = 0), the cell behaves like a dead battery. In both cell types, the anode undergoes oxidation and the cathode reduction, but their charge roles differ in electrolytic cells, necessitating a battery to drive the reaction.

Coulometry

Different types of electrochemical cells that exist can be connected to the idea of spontaneity. Whether an electrochemical cell is spontaneous or not helps us to categorize them and split them into 2 different camps. Here we're going to say, in terms of spontaneity, the following correlations between the following variables can be made. Here we have Gibbs free energy under standard conditions. That's what this little circle here means.

Standard conditions being 25 degrees Celsius where your pH is equal to 7, where your concentration is equal to 1 molarity. We also have K, which is our equilibrium constant. We have our cell potential. We have ΔS, which is our entropy, and then we have Q versus K. Q is our reaction quotient.

It's used as a way to determine if we are at equilibrium or not. From these variables, we can determine the type of reaction classification we have, meaning is it spontaneous, non-spontaneous, or at equilibrium and from that, we can determine what type of electrochemical cell we have. So if we take a look at the first row when ΔG is less than 0, that means that K will be greater than 1, your cell potential will be greater than 0, ΔStotal or ΔSuniverse based on the second law of thermodynamics, our Q will be less than K.

Now, this part helps us determine direction. If you set up a number line and K is here in the middle and Q is less than it, then Q is always going to shift in the direction to get to K, our equilibrium constant. So our reaction would shift in the forward direction. All of these variables are telling me one thing, that my reaction is spontaneous. When we have a spontaneous reaction, that means our electrochemical cell is a galvanic or voltaic cell.

Next, if we reverse the order of all the signs where ΔG is greater than 0, K is less than 1, your cell potential is less than 0 as well as your entropy of your universe is less than 0. Here, Q would be greater than K. So here, we'd move in the reverse direction in terms of our chemical reaction. So here, this would mean that our reaction is non-spontaneous. When you have a non-spontaneous reaction, that means your electrochemical cell is an electrolytic cell.

We'll talk a bit more about electrolytic cells down below, but just realize here electrolytic cells represent non-spontaneous electrochemical cells. Then finally when everything is equal to their given value, this means that we are at equilibrium. When an electrical cell is at equilibrium, that means it represents a dead battery. It has discharged all its electricity or it's consumed all the electricity, therefore, it is at a state of equilibrium. Here because it's non-spontaneous, it requires an outside energy source to work. So here it requires a battery and so because it requires a battery, it consumes electricity. Remember, a galvanic/voltaic cell produces or discharges electricity. An electrolytic one consumes electricity.

Here we have an example of a basic electrolytic cell. Here we have the implementation of a battery in order to drive electrons from one side to the other side. Now, here our positive electrode will actually be the anode. Remember for a galvanic or voltaic cell, the anode was negative. Now, because we're dealing with an electrolytic cell, it's positive. And now, the cathode is negative.

If we think about it, it doesn't make too much sense for negative electrons to want to travel to a negative electrode. Like charges repel each other. That's why we require a battery. The battery is there to force the reaction to occur because it's not a natural process. Here, the electron affinity, if we're talking in terms of this, image here, we'd say that the electron affinity for the cathode would be low.

Electrons do not want to go to the negative cathode and then the ionization energy for the anode would be high. It would take a lot of energy to remove the negative electrons from the anode. They just don't want to leave the anode to go to a negative electrode. So basically things are reversed in terms of a galvanic cell versus an electrolytic cell. The only common thing, the thing that's always consistent, is that the anode still undergoes oxidation and the cathode still undergoes reduction.

The problem here, though, is it's not a natural process because negative electrons again don't want to go to something with the same charge that it has. That's why a battery is required to force this reaction to happen. So this is the common feature of both types of electrochemical cells, whether they're spontaneous or non-spontaneous. The anode always undergoes oxidation whereas the cathode always undergoes reduction. So just remember the differences between an electrolytic cell versus a galvanic/voltaic cell.

And remember the different variables, when you look at them in conjunction with one another, help to determine if a chemical reaction is spontaneous, non-spontaneous, or at equilibrium.

Here’s what students ask on this topic:

What is the difference between galvanic and electrolytic cells?

Galvanic (or voltaic) cells and electrolytic cells are both types of electrochemical cells, but they operate under different principles. A galvanic cell generates electrical energy from a spontaneous redox reaction, where ΔG < 0, K > 1, and E_cell > 0. In this cell, the anode is negative, and the cathode is positive. Conversely, an electrolytic cell requires an external energy source to drive a non-spontaneous reaction, where ΔG > 0, K < 1, and E_cell < 0. Here, the anode is positive, and the cathode is negative. Despite these differences, both types of cells involve oxidation at the anode and reduction at the cathode.

How does Gibbs free energy relate to the spontaneity of electrochemical cells?

Gibbs free energy (ΔG) is a key indicator of the spontaneity of a reaction in electrochemical cells. For a spontaneous reaction, ΔG is less than 0 (ΔG < 0), indicating that the reaction can proceed without external energy. This is typical of galvanic cells. For a non-spontaneous reaction, ΔG is greater than 0 (ΔG > 0), meaning the reaction requires an external energy source to proceed, as seen in electrolytic cells. At equilibrium, ΔG equals 0 (ΔG = 0), indicating no net reaction occurs, similar to a dead battery.

What role does the equilibrium constant (K) play in electrochemical cells?

The equilibrium constant (K) helps determine the direction and extent of a reaction in electrochemical cells. For a spontaneous reaction, K is greater than 1 (K > 1), indicating that the products are favored. This is typical in galvanic cells. For a non-spontaneous reaction, K is less than 1 (K < 1), meaning the reactants are favored, as seen in electrolytic cells. When K equals 1 (K = 1), the system is at equilibrium, and no net reaction occurs.

Why do electrolytic cells require an external energy source?

Electrolytic cells require an external energy source, such as a battery, because they drive non-spontaneous reactions where ΔG > 0. In these cells, the anode is positive, and the cathode is negative, which is opposite to galvanic cells. The external energy source forces electrons to move against their natural tendency, enabling the oxidation at the anode and reduction at the cathode. This process consumes electrical energy to make the reaction occur.

What happens at the anode and cathode in electrochemical cells?

In all electrochemical cells, the anode is where oxidation occurs, and the cathode is where reduction takes place. In a galvanic cell, the anode is negative, and the cathode is positive. In an electrolytic cell, the anode is positive, and the cathode is negative. Despite the difference in charge roles, the fundamental processes of oxidation at the anode and reduction at the cathode remain consistent across both types of cells.