Electrochemical Cells - Online Tutor, Practice Problems & Exam Prep

Galvanic (voltaic) cells generate electricity spontaneously through oxidation at the anode and reduction at the cathode, with half-reactions involving ions like Cu²⁺ and Cr. A salt bridge maintains charge balance. In contrast, electrolytic cells require external energy to drive non-spontaneous reactions, with similar oxidation and reduction processes. Line notation simplifies cell representation, indicating phase boundaries and the salt bridge. Key concepts include Gibbs free energy (ΔG), standard cell potential (E_cell), and reaction spontaneity, essential for understanding electrochemical systems.

Galvanic or Voltaic Cell

Hey everyone. So, galvanic or voltaic cells are spontaneous cells that produce or discharge electricity. Now remember, when they discharge all their electricity then they're classified as a dead battery. Now, here we have a basic model of a galvanic cell, voltaic cell. And we're going to say that in a galvanic or voltaic cell, the negative electrode is the anode, and the positive electrode is the cathode. Here we have 2 half reactions that are designated for the cathode and the anode. For the cathode, we have 3 moles of copper ion absorbing 6 moles of electrons to produce 3 moles of copper solid. So here that means we'd have Cu2+ particles floating around within this solution. The metal electrode itself is copper solid. For the anode half reaction, we have 2 moles of chromium solid, basically losing 6 electrons to produce 2 moles of chromium Cr3+ ions. So in this compartment here we have our chromium solid here and we have Cr3+ ions floating around. Now with a galvanic voltaic cell, we're going to say that these 2 jars are connected by this, which is called a salt bridge. Now, in a salt bridge, we have neutral ions, ions that are neither acidic nor basic in nature. Typically, we have chloride ions or nitrate ions. Those negative ions, they flow towards the anode side, and then we may have sodium ions and potassium ions which move this way towards the cathode side. We say that oxidation always occurs at the anode, reduction always occurs at the cathode. That's why the anode is losing electrons, electrons are moving away from the anode towards the cathode. As they move, we have the traveling of electrons from one side to another and in order to close this circuit, we need same charges moving in the opposite direction. So we have our anode here, we have our cathode here, we have electrons moving towards the cathode, and within the salt bridge, we have our negative ions moving towards the anode side. This completes the circuit and so through the movement of these 2 charges in opposite directions, we form a current. So this voltmeter here reads how much voltage is being produced. Now, we want our anodes to lose electrons easily, so we want their ionization energy, the energy required to move an electron, to be low. We want the cathode to attract the electrons, so we want its electron affinity to be high. What starts to happen is you're losing electrons over time, so these anode electrons weigh very little, but enough of them over time you start losing some mass. So we're going to say here your anode dissolves away. As the cathode gains more and more electrons its surface starts to become negatively charged. This attracts the submerged or dissolved copper ions within the solution, So you have positive ions adhering to a circuit that's slightly negative in charge. They're going to neutralize each other and so you're going to have an encrusting of copper on top of this electrode. So over time, the cathode is going to get bigger and we say the cathode plates out. Now to produce this electricity you want to make sure that the cathode side is attracting these negative electrons, so you want to make sure that this solution here has a good amount of positive charges in it that's going to attract the negative electrons toward that side. So you want to make sure the cathode solution concentration is high. At the same time you want to make sure that the anode concentration of positive ions is low because if this solution becomes too saturated with positive ions those negative electrons will not want to move towards the cathode. Because remember like charges repel each other. So this gives us the basic breakdown of our galvanic or voltaic cell. Remember with the anode we have oxidation and with the cathode we have reduction. We have 2 half reactions involved within this particular example, but we also have other examples of half reactions. All of them are written as reductions because for all of them the electrons are reactants. With each one, we have a standard cell potential associated with it. Remember that the higher your standard cell potential, then the more likely reduction will occur. And remember, if the more likely reduction occurs, that means you have a stronger oxidizing agent. Conversely, the lower your standard cell potential is and the more likely oxidation will occur. So more likely is oxidation, and the more likely oxidation happens, the stronger your reducing agent is. Okay, so just remember for this particular example we're looking at 2 specific half reactions, but we could easily come up with another galvanic voltaic cell example which incorporates some of these other half-reduction reactions.

Electrolytic Cells

Hey everyone. Before we talk about the other type of electrochemical cell, let's revisit certain variables. So here we're going to say in terms of spontaneity the following correlations between the variables can be made. Here we have Gibbs free energy under standard conditions, our equilibrium constant k, our standard cell potential, here we have our standard entropy and this is the entropy of our universe. We have the reaction quotient versus k, our equilibrium constant, and this will tell us the reaction classification as well as cell type. So here in the first row, when we have the configuration this way, these are all conditions that lead to a spontaneous reaction. And if we're talking about spontaneous reactions, then the electrochemical cell is a galvanic cell, or by its other name a voltaic cell. Now, if we were to reverse everything, reverse the sign, we'd expect the opposite result. So this would be a nonspontaneous reaction. And that'd be connected to the electrochemical cell we'll talk about right after this chart, which is your electrolytic cell. Then finally, if everything is equal to certain variables we're going to say that we are at equilibrium, and you'd represent a dead battery.

Now, here when we talk about the electrochemical cell it doesn't function spontaneously, so it requires an outside energy source, or a battery. Here we're going to say our electrochemical cell, or electrolytic, sorry, electrolytic cell is a nonspontaneous electrochemical cell and it consumes electricity, and so it requires a battery. Remember, a galvanic or voltaic cell is different. It is literally a battery. It produces and discharges electricity. Here, this one needs a power source, so it needs a battery. But here it doesn't matter if it's an electrolytic cell or galvanic cell, oxidation always occurs at the anode, reduction always occurs at the cathode. So here we see our electrons moving in this general direction, so they'd be moving towards a cathode that does not change. And the electrodes are leaving this electrode, so this would have to be our anode. What you should realize here though is that with an electrolytic cell things are not spontaneous so they don't happen naturally. The cathode here is negatively charged. Negative electrons don't want to go to something that's already negative. Remember, like charges repel. We need that outside energy source to force the electrons to go that way. Then, electrons don't want to leave something that's positive, here the anode is positive. But again we're using that battery to force the electrons away from our positive anode electrode. Now here, electron affinity would have to be low for the anode; we don't want the electrons to stay near the anode. Ionization here would have to be high for the cathode. We don't want those electrons once they go there to come off. So, basically, when it comes to an electrolytic cell it's nonspontaneous, a lot of the process or a lot of the way of labeling things are the opposite of a galvanic cell. Really the place that things hold true is in terms of reduction and oxidation. The cathode is still the site of reduction and the anode is still the site of oxidation.

Alright, so here, just remember these few key things about electrolytic cells. Remember the variables up above to help us determine if a reaction is spontaneous, nonspontaneous, or a dead battery.

Line Notation

Hey everyone, so here we're going to say line notation is a quick simple method to describe an electrochemical cell without having to draw it out in detail. Now, here this represents the lines of a standard line notation and we're going to say that these single lines represent phase boundaries. And these phase boundaries separate the lower oxidation state of an ion or compound from the higher oxidation state. The double line, and also these higher and this lower, they're both separated by a phase boundary here. What about a double line? Well, this double line is indicative of our salt bridge, which itself represents a physical separation or physical boundary that separates our 2 containers of solution within a typical electrochemical cell. Now, here if we take a look, we have an example of a galvanic or voltaic cell, and we have here our cathode and our anode. So here we see electrons moving from this side to this side. Remember, with the anode we always have oxidation, and with the cathode we always have reduction. So, since the electrons are moving towards the right, that must mean the cathode is over here. And remember, with the galvanic or voltaic cell, which is spontaneous in nature, the cathode is your positive electrode. Your anode where electrons are leaving is your negative electrode. Looking at these two half reactions we can see that for the cathode we have copper 2 ion absorbing 6 electrons to become copper solid. So this would be our copper solid electrode and dissolved within it, we'd have our copper 2+ ions. And then we'd say here for the anode we have chromium solid as our electrode and we have our chromium 3+ ion dissolved within the solution. The salt bridge is the tube that connects the 2 solutions together. Remember in this salt bridge we typically have neutral ions in the form of chloride ions or nitrate ions, which move towards the anode side. And we could have sodium ions or potassium ions, which move over here to this side. Now, here if we were to write out the overall equation from these two half reactions, remember, the electrons always cancel out, so what will come down is we have 3 copper ions, copper 2 ions, plus 2 chromium solids give us 3 copper solids plus 2 chromium 3 ions. Here we write out what's going on in terms of this galvanic or voltaic cell with this line notation. And remember to write the line notation it's as easy as a, b, c. A represents our anode side. B is the break, the physical boundary or physical distance between the two solutions, and C is our cathode. Remember from up here, we said that the higher oxidation states are in the center and the lower ones are on the ends. So for the anode, let's see we have copper solid and we have copper 3+. Copper 3+ has an oxidation number of +3 based on its charge, copper solid is neutral so its oxidation number is 0. So copper solid would be here and copper 3+ would be here. Then in the cathode compartment, we have copper 2+ and copper solid. The higher oxidation state will be copper 2+ ion, and the lower oxidation state will be copper solid. So this will represent the standard line notation based on the two half reactions given to us. Now if we were to take into account activities, we could say that as our activity reaches unity, then our activity would equal 1. So again, activity equals 1 as we approach unity. So what would that mean in terms of my line notation? It would just mean we'd add a little bit more information, so we just add our activity of chromium solid equals 1, our activity of chromium 3+ equals 1, our activity of copper 2+ equals 1, and our activity of copper equals 1. Again, you'd only include this if you were asked to include the activities of all forms within this line notation. If you're not asked that information, you don't have to worry about it. But just remember line notation is just a convenient and fast way for us to write out what's going on within a given electrochemical cell without having to go into too much detail. Alright. So keep that in mind when you construct your own different types of line notations.

Line Notation

So here we have to write the half reactions as well as the overall net ionic equation for the following line notation. Remember, with line notation we have an anode, a break, and a cathode. For the anode portion, we're going to say we have copper solid. And here it gives us copper (II) ion aqueous. We're going to say here that this is an oxidation because at the anode we have oxidation. On this side the overall charge is 0. Over here, the overall charge is plus 2. We need to make sure that both sides of the equation have the same overall charge. So we're going to have to put electrons on the more positive side. So this side is plus 2 and this side here is 0. In order to make this side here also equal to 0, we have to add 2 electrons. So this here represents our reaction at the anode where we have copper solid being oxidized to copper (II) ion with the release of 2 electrons.

Now, at the cathode, we have the silver ion being reduced to give us silver solid. So the overall charge here is plus 1. The overall charge here is 0. We add electrons to the more positive side, so we have to add 1 electron here. So that one electron gives us an overall charge of 0, just like the product side. Now the number of electrons must be the same in terms of both half reactions because they're going to cancel one another out. Here we'd have to multiply this entire equation by 2 to have the same number of electrons. So what we're going to have now are our 2 equations. And we have 2 electrons plus 2 Ag⁺ gives me 2 Ag solid. So electrons cancel out. So at the end, we have copper solid plus 2 Ag⁺, aqueous, produces copper (II) ion plus 2 silver solids. So that represents our equation, our overall net ionic equation as well as the two half reactions. So your two half reactions would be this one here. And then this one after we've multiplied by 2. And then we have our overall equation at the end. So remember, line notation or cell notation is just a convenient way for us to quickly describe what's going on in terms of our electrolytic cell, which substances are being oxidized versus which ones are being reduced, and the number of electrons that are transferred between the 2 cells within our electrochemical cell.

Line Notation Calculations

So here we need to sketch the galvanic cell and determine the cell notation for the following redox reaction. Alright. So what we have here is we have our hydrogen ion becoming H₂ gas. Here, its oxidation state for each H⁺ ion is just plus 1 because it's equal to the charge of the ion. Here, it's in its natural neutral form so its oxidation number is 0. So we're going to say that hydrogen, H⁺ goes from being plus 1 to being 0. We're going to say its oxidation number decreased, therefore it was reduced. Because it was reduced, that means it must represent the cathode. Then here we have iron in its natural neutral form. So when it's in its natural or standard state, its oxidation number is equal to 0. Here, it's in its ion form with a plus 2 charge. The charge of an ion is equal to its oxidation number. So, now it's plus 2. Its oxidation number increased by going from 0 to plus 2. Therefore, it was oxidized and because it was oxidized, it represents the anode.

So here, we're going to draw our quick sketch of our galvanic cell. So here we have our iron electrode, and we're going to have our salt bridge here. We have our wire connected to our voltmeter which measures the amount of voltage that's being generated from the electrons moving from the anode side to the cathode side. Now here, this is interesting because we're dealing with H⁺ to H₂. These two species together, means we're talking about the SHE (Standard Hydrogen Electrode). And when we're talking about SHE, we have to realize that we don't have a hydrogen electrode because hydrogen exists in a gaseous state. So it's not solid like we have iron here. So to show the SHE electrode, what we have is we have a platinum wire and that platinum wire is connected to a platinum surface. We're going to have this little beaker here and it's going to have a porous opening here to allow H⁺ ions to flow through. So we have H⁺ ions dissolved within this solution here. We have iron(II) ions dissolved here. Electrons are traveling from the anode side to the cathode side, and they're traveling down this wire. At the same time, we have another tube that's connected to the outside, and from this tube, we have H₂ gas coming in. So we have electrons that are traveling down this platinum wire here and at the same time, we also have hydrogen traveling down as well. They will meet here near this opening here. And at the same time, we have hydrogen coming in through these openings in the small little jar, the H⁺ will come into contact with electrons and create H₂ gas. So you have the generation of H₂ gas here within this container and the H₂ gas will bubble out of the solution. You have hydrogen gas, H₂ gas also getting pumped in as well. So that also comes out of the solution too over time. That's the basic setup of the SHE or Standard Hydrogen Electrode.

Now how would we write the cell notation for this? Well, we have our iron, solid. Remember, we're going to put the lower oxidation numbers on the outside. Here, we're going to say that the activities of these approach unity so that means they're equal to 1. So we have the activity for iron equals 1. We have our phase boundary. We have Fe²⁺ aqueous. Its activity is equal to 1. So here we have our actual physical breakdown. Next, we're going to have H⁺ aqueous with its activity. We have our phase boundary. We have H₂ gas, its activity. And then we have just platinum solid over here. So remember, we need physical solid electrodes involved. That's why the platinum solid is being used. And because the platinum solid is in itself not being involved in the redox reaction, we call it an inert electrode. This compartment here of my line notation or cell notation, represents SHE. And realize here that SHE is also referred to as our reference electrode. Because it has a potential equal to 0. So when we're saying that a metal or an element has a potential that's positive, it's positive relative to the SHE electrode. When we say that it's a negative potential for an ion or a metal, it's negative in reference to the SHE electrode. So the SHE electrode just represents our reference electrode where we compare all the other half reactions that we deal with with when it comes to redox reactions. So realize here that the cell notation or line notation that we wrote is a much quicker way of illustrating what's going on in terms of our galvanic cell instead of having to draw out the whole thing. And remember here, this would be our anode. Over here would be our cathode. Remember that oxidation always occurs at the anode, so electrons leave the anode and go to the cathode where reduction will occur. So just remember, the little intricate parts of this idea of the SHE electrode and how it relates to line notation in this particular example. Now that we've seen this, move on to the next question or practice question. This one, the same basic understanding. We have to determine which one is being oxidized and therefore represents the anode and which one's being reduced, therefore representing the cathode. Figure that out in order to sketch the galvanic cell and also write the line or cell notation from the information given. Once you do that, come back and see if your answer matches up with mine.

Sketch the galvanic cell and determine the line notation for the following redox reaction:

Ni²⁺ (aq) + Mg (s) ⇌ Ni (s) + Mg ²⁺ (aq)

 

So here we again, we have to sketch the galvanic cell and determine the line notation for the following redox reaction. Here, we have nickel 2+ ion with an oxidation number of +2. It then goes to its natural or neutral form which gives us the oxidation number of 0. So, it goes from being plus 2 to 0. So, its oxidation number was reduced. Therefore, it represents the cathode. Then we have magnesium solid in its natural state so its oxidation number is 0. It goes to being a plus 2 charge. So now, its oxidation number has increased. Therefore, it represents the anode where oxidation has occurred. If we draw our galvanic cell here, we have our salt bridge. We have our electrode. Here, the solid electrode from my anode will represent the magnesium solid. We have our wire here which connects to our other solid electrode, which in this case is the nickel electrode. We have our voltmeter here which reads the amount of voltage that's produced in terms of this galvanic or voltaic cell. The electrons are leaving my anode going towards the cathode. Through this process, we have the generation of magnesium ions Mg2+. We have our negative ions traveling this way. We have some positive ions this way. Here we have the generation of nickel 2+ ions Ni2+ in this solution as well. Now if we're gonna talk about the line or cell notation, we'd first talk about our anode. So the lower oxidation state would be magnesium solid. Activity here approaches, unity which is 1. We have our phase boundary. Now we have our magnesium 2 ion. Here we have our actual break. Then we have our nickel 2+ ion. Our phase boundary, And that represents our line or cell notation in terms of this galvanic cell. This one is a bit more simple. We didn't have to worry about the introduction of any outside gas being formed. But realize when we have gases involved, we typically would use some type of inert solid to react and act as our electrode within the redox reaction. And this one, because both we have both the magnesium solid and the nickel solid, there is no need to introduce any type of inert solid like platinum. So this would be a simple basic question to approach when it comes to line notation and the drawing of any galvanic or voltaic cell.

Here’s what students ask on this topic:

What is the difference between a galvanic cell and an electrolytic cell?

A galvanic (or voltaic) cell generates electricity spontaneously through redox reactions, with oxidation occurring at the anode and reduction at the cathode. It functions as a battery, producing and discharging electricity. In contrast, an electrolytic cell requires an external energy source, such as a battery, to drive non-spontaneous reactions. Despite this difference, both types of cells have oxidation at the anode and reduction at the cathode. The key distinction lies in the spontaneity of the reactions and the need for an external power source in electrolytic cells.

How does a salt bridge function in a galvanic cell?

A salt bridge in a galvanic cell maintains electrical neutrality by allowing the flow of ions between the two half-cells. It typically contains a salt solution with neutral ions, such as chloride (Cl^-) or nitrate (NO₃^-). These ions migrate to balance the charge as electrons move through the external circuit. Negative ions move towards the anode, where oxidation occurs, and positive ions move towards the cathode, where reduction occurs. This movement of ions completes the circuit and allows the cell to generate a continuous flow of electricity.

What is line notation in electrochemical cells?

Line notation is a shorthand method to describe an electrochemical cell without detailed diagrams. It uses single lines to represent phase boundaries between different oxidation states and a double line to indicate the salt bridge. For example, in a galvanic cell with copper and chromium half-reactions, the line notation might be: Cr(s) | Cr³⁺(aq) || Cu²⁺(aq) | Cu(s). This notation quickly conveys the components and reactions occurring at the anode and cathode, as well as the presence of the salt bridge.

What is the relationship between Gibbs free energy and cell potential in electrochemical cells?

The relationship between Gibbs free energy (ΔG) and cell potential (E_cell) in electrochemical cells is given by the equation: ΔG = -nFE_cell, where n is the number of moles of electrons transferred, and F is the Faraday constant (approximately 96485 C/mol). A negative ΔG indicates a spontaneous reaction, corresponding to a positive E_cell in a galvanic cell. Conversely, a positive ΔG indicates a non-spontaneous reaction, requiring an external energy source, as seen in electrolytic cells.

How do you determine the spontaneity of a reaction in an electrochemical cell?

The spontaneity of a reaction in an electrochemical cell can be determined by the standard cell potential (E_cell) and Gibbs free energy (ΔG). If E_cell is positive, the reaction is spontaneous, and ΔG is negative, indicating a galvanic cell. If E_cell is negative, the reaction is non-spontaneous, and ΔG is positive, indicating an electrolytic cell. The relationship is given by ΔG = -nFE_cell, where n is the number of moles of electrons transferred, and F is the Faraday constant.