Standard Potentials - Online Tutor, Practice Problems & Exam Prep

Voltage (E_cell) in electrochemical cells indicates the work done as electrons move between electrodes. One volt equals joules per coulomb. Half-reactions are expressed as reductions, with higher potentials indicating a greater likelihood of reduction. The overall cell potential is calculated as E_cell = E₊ - E_- when concentrations are 1 M. If not, the Nernst equation is used. Understanding these concepts is crucial for determining oxidation and reduction tendencies in galvanic cells.

Standard Potential

So, voltage, which is represented by our variable \( e \), represents the amount of work done in an electrochemical cell as electrons travel from one electrode to another. Remember that one volt is equal to joules over coulombs. Now, here we have half reactions written as reductions. They're written as reductions because the electrons are all written as reactants. We have the oxidation number of our reactants decreasing as it becomes a product, and here we've highlighted this particular equation because this one here represents the SHE (Standard Hydrogen Electrode).

So, this is our reference electrode. When we talk about the potential or voltage of a particular half reaction, it's in reference when compared to the SHE electrode. So here, this is 1.507 volts, which means it has that much of a likelihood of undergoing a reduction compared to the SHE electrode. Realize here that the larger the potential of a half-reaction, the more it wants to be reduced. So, the more likely reduction will occur, and the smaller your \( e \) value, then the more likely oxidation will occur.

So what we can say here from this chart is that hydrogen, while the SHE electrode, when it's being compared to these bottom three, because it has a higher voltage or higher cell potential, wants to be reduced more so than the bottom three reactions. And then when comparing it to these top reactions because they have cell potentials that are larger than \( 0 \), they have a greater tendency to be reduced instead of the SHE electrode. So, by comparing the cell potentials between different half reactions, you can determine which one wants to be oxidized and which one wants to be reduced. This is important because this will help us determine the overall cell potential and overall voltage that can be generated from a galvanic or voltaic cell. So, we're going to say here when combining two half-reactions together, the cell potential for the total net reaction is given when the concentrations approach unity. So, it means that they're going to approach \( 1 \) molar.

So here, \( 1 \) molar. So as the concentrations approach \( 1 \) molar, we're going to say that our cell potential or \( e_{\text{cell}} \) equals \( E^+ - E^- \). We're going to say \( E^+ \) here represents the cathode electrode. \( E^- \) here represents the anode electrode. So, this is basically saying cathode minus anode will give us our overall cell potential. Realize that this equation is this simple, again, when the concentrations are equal to \( 1 \) molar.

If the concentrations are not equal to \( 1 \) molar, then this equation cannot be used to figure out our overall cell potential. In those cases, we'd have to rely on the Nernst equation in order to find our correct cell potential. So, for now, just realize that if you are not given the concentrations of the ions reacting within a given redox reaction, we assume that the concentrations have approached unity, therefore equal \( 1 \) and therefore our equation is just simply as stated here. Now that we've gotten down the basics in terms of cell potential and how the value of \( e \) can help us determine which one is being reduced versus oxidized, attempt to do the practice question here on the bottom. Here, we're given two half reactions.

We're given a half-reaction for lithium and a half-reaction for silver. Based on their given cell potential values, determine what my overall cell potential would be for this particular galvanic cell. Once you do that, come back and see if your answer matches up with mine.

Standard Potential

So in this example, it says determine the electrical or electric potential that results from a given galvanic cell. In the illustration, we show that this half reaction is transferring electrons. So this half reaction here is transferring electrons. They're moving away from this half reaction to the silver half reaction. The movement of electron tells us which one is the anode and which one is the cathode.

Remember at the anode, we always have oxidation but we have a loss of electrons. So this here represents my anode. Here, this represents my cathode. Now we don't necessarily need this illustration for the electrons moving from the anode to the cathode to tell them apart. There are a few things we can look at.

Here we have lithium in its neutral natural state, so its oxidation number is 0. And then here we have lithium plus 1. So its oxidation now is plus 1. We could have also said that the oxidation number goes from 0 to plus 1. It has increased because it has undergone oxidation which means that this has to be the anode.

On the other side, we have plus 10 for the oxidation numbers. We can see that the oxidation number decreases. Therefore, it has to represent reduction and therefore the cathode. In addition to this, we could've looked at the potentials given for each half reaction. Remember, up above we said that the larger your e value is, the more likely reduction will occur and the smaller your potential is, the more likely oxidation will occur.

So this one having the larger e value tells me that this has to be reduction. Because we don't we're not given any concentrations for the ions, we assume that the concentrations have approached unity, therefore equal one. And because of that, we can simply say that our overall cell potential equals cathode, which is e positive, minus anode, e minus. So that'd be 0.799 volts minus a minus 3.040 volts. And a minus of a minus really means plus.

3.839 V

So overall, this is 3.839 volts of electricity that have been generated from the movement of electrons from the anode compartment to the cathode compartment. Remember, earlier on we talked about the value of your cell potential could determine if this is a spontaneous process or not. Because our overall cell potential is greater than 0, we know that this is a spontaneous process which makes sense because a galvanic or voltaic cell represents a spontaneous electrochemical cell. So remember, this is just the fundamentals to help us determine what the overall cell potential is. Later on, when we talk about concentrations different from 1 molar, we'll have to utilize the use of the Nernst equation.

With the Nernst equation, we have to be very careful in terms of concentrations of ions as well as the moles of ions to determine the correct overall cell potential. For now, just assume that the concentrations equal unity because they're not given to us. And therefore, we simply use this version to help us determine the overall cell potential.

Standard Potential Calculations 1

So here it states, use the standard half-cell potentials listed below to calculate the standard cell potential for the following reaction occurring in an electrochemical cell at 25 degrees Celsius. Here it says, assume the concentrations have approached unity. So here we're given concentrations of our ions, so we have to assume that they have approached 1 molar. Therefore, we don't have to use a Nernst equation and can simply say that our potential equals our cathode minus anode. Now typically we would say that the smaller E value would represent oxidation and therefore my anode and that the larger cell potential would represent reduction and therefore my cathode.

But we cannot say that when we're given the overall equation. When we're given the overall equation, we actually have to look at the overall equation and determine what's being oxidized and what's being reduced. In that regard, then we see who's the cathode and who's the anode. Now if we look, we say that chlorine goes from its natural state which is an oxidation number of 0 to its charged form minus 1. So here, chlorine goes from being 0 to minus 1 so its oxidation number reduced itself.

Therefore, reduction has occurred and therefore that represents the cathode which happens to be the larger E value. But again, we can only say that the E value given, the larger one is the cathode only when they don't give us an overall equation. Because they give us an overall equation, we have to use the overall equation to determine who is truly the cathode and who is truly the anode. Now here, iron goes from being 0 in its oxidation number to plus 3. So, its oxidation number increased.

Therefore, it underwent oxidation and represents the anode. Now that we know who's the cathode and who's the anode based on the overall equation, we can say that our standard cell potential, E0, equals cathode minus anode. So that's 1.396V minus -0.040V. So minus of a minus really means that we're adding them together. So what we get at the end is 1.436V for this reaction and what that tells me is that this is a spontaneous process in which chlorine would naturally become reduced when in the presence of iron solid.

So just remember, we can say that the larger E value equals cathode, smaller E value equals the anode when we are not given the overall equation. When you're given the overall equation, you actually have to look at that instead to determine who's been reduced and therefore represents the cathode and who's been oxidized and therefore represents the anode. Now that we've seen this basic example, move on to example 2. Attempt it on your own. Once you do, come back and see if your answer matches up with mine.

Standard Potentials Calculations 1

So for the voltaic cell with the overall reaction, we have our standard cell potential as being equal to 1.10 volts. So our overall cell potential is this value. Here it says, given that the standard reduction potential of zinc ion to zinc solid is negative 0.762 volts, calculate the standard reduction potential for copper \(2^+\) plus two electrons giving us copper solid. Alright. So, in this question, we have our redox reaction.

Zinc is going from its neutral natural state where its oxidation number is equal to 0 to its charged state. Remember, for an ion, its charge equals its oxidation number. So here it's plus 2. It goes from an oxidation number of 0 to an oxidation number of plus 2. Since its oxidation number has increased, it's undergone oxidation.

And because it represents oxidation, it's going to be the anode. Then we're going to say within this equation we have copper \(2^+\) , so oxidation number is plus 2 and it goes to 0. Right? So it's being reduced therefore it represents the cathode where reduction occurs. Here, we assume our concentrations have gone to unity so they're equal to 1 molar.

Therefore, my standard cell potential equals cathode minus anode. So my standard cell potential is 1.10 volts. We don't know what the potential of our cathode is, that's what we're looking for. Minus a minus 0.762 volts. So, remember minus a minus really means positive.

So, subtract 0.762 volts from both sides. So the potential here for my cathode would be equal to 0.338 volts. So that would be our final answer. So just remember, for questions like this, it's important to be able to look at the redox reaction and determine from that what's been oxidized and therefore represents the anode and what's been reduced and therefore represents the cathode. Once you've figured that out, just remember to fall back on the equation, fill in the given values and solve for the missing variable, which in this case was just the potential of my cathode.

Here’s what students ask on this topic:

What is the standard electrode potential and how is it measured?

The standard electrode potential (E°) is the measure of the individual potential of a reversible electrode at standard state, which is 1 M concentration for solutions, 1 atm pressure for gases, and pure solids or liquids for other phases, all at 25°C. It is measured using a standard hydrogen electrode (SHE) as the reference, which is assigned a potential of 0.00 V. The potential of the electrode in question is measured by connecting it to the SHE in an electrochemical cell and measuring the voltage difference.

How do you calculate the overall cell potential in a galvanic cell?

The overall cell potential (E_cell) in a galvanic cell is calculated using the equation:

$E_{\mathrm{cell}}=E_{\mathrm{cathode}}-E_{\mathrm{anode}}$

Here, E_cathode is the standard reduction potential of the cathode, and E_anode is the standard reduction potential of the anode. This equation assumes that the concentrations of all reacting species are 1 M. If the concentrations are not 1 M, the Nernst equation must be used to account for the effect of concentration on the cell potential.

What is the Nernst equation and when is it used?

The Nernst equation is used to calculate the cell potential under non-standard conditions. It is given by:

$E_{\mathrm{cell}}=E_{\mathrm{cell}}°-\frac{\mathrm{RT}}{\mathrm{nF}}\cdot \ln \left(Q\right)$

where E_cell is the cell potential, E_cell° is the standard cell potential, R is the gas constant (8.314 J/mol·K), T is the temperature in Kelvin, n is the number of moles of electrons transferred, F is the Faraday constant (96485 C/mol), and Q is the reaction quotient. The Nernst equation adjusts the standard cell potential to account for the actual concentrations of the reactants and products.

Why are standard electrode potentials written as reduction reactions?

Standard electrode potentials are written as reduction reactions because it provides a consistent way to compare the tendencies of different species to gain electrons. In these half-reactions, electrons are written as reactants, and the potential indicates how easily the species can be reduced. A higher (more positive) standard reduction potential means the species is more likely to gain electrons and be reduced. This convention simplifies the comparison of different half-reactions and the calculation of overall cell potentials.

How does the standard hydrogen electrode (SHE) function as a reference electrode?

The standard hydrogen electrode (SHE) functions as a reference electrode by providing a stable and reproducible potential of 0.00 V under standard conditions. It consists of a platinum electrode in contact with 1 M H₊ ions and hydrogen gas at 1 atm pressure. The SHE is used to measure the electrode potentials of other half-cells by connecting them in an electrochemical cell and measuring the voltage difference. This allows for the determination of standard electrode potentials relative to the SHE.