Cell Potential: Standard - Online Tutor, Practice Problems & Exam Prep

In an electrochemical cell, the standard cell potential (E^°_cell) is a crucial measure of the cell's ability to produce an electric current. It is defined by the difference in standard reduction potentials (E^°_red) of the cathode and anode, expressed in volts (V), which also equate to joules per coulomb (J/C). A positive E^°_cell indicates a spontaneous reaction, typical of galvanic or voltaic cells, where the cathode has a higher E^°_red than the anode. Conversely, in an electrolytic cell, the cathode has a lower E^°_red, resulting in a negative E^°_cell, signifying non-spontaneity. Understanding the relationship between cathode and anode potentials is key to determining the cell's standard potential and its type—galvanic/voltaic or electrolytic.

Standard Cell Potential Calculations

Here we're going to say that our standard subpotential is represented by the variable E0cell. Here it is the measure. Although reduction potential or standard reduction potential so E0red, involves between two half cells. So our Catholic compartment and our annual compartment here. Remember standard refers to the ions within the half cells having values of one molar, one atmosphere and pH equal to 7 volts is represented by capital V.

It represents the amount of work done at the electron travels from 1 electrode to another. Here volts is also units equal to units of joules per coulomb. Coulomb is a variable we've seen in earlier chaters. Coulombs uses the variable capital C and it's just the SI unit for electric charge.

Now here we're going to say that our standard cell potential of an electrochemical cell is calculated by the formula that it equals cathode minus anode. So remember, an Electro chemical cell is composed of two half cells, one being the cathode, one being the anode. If you can successfully determine which one is the capital and which one is the anode, simply use this formula here and you'll be able to find your standard cell potential.

Standard Cell Potential Example

Here it says what is the standard cell potential for a voltaic cell based on the following reduction reactions in which the copper electrode is the cathode and the zinc electrode is the anode. All right. So here we have two half reactions. In the first one we have zinc ion absorbing 2 electrons and becoming zinc solid. It has a standard reduction potential of -0.7621. Here the units will be in volts.

Then we have our copper reduction reaction where copper 2 plus ion accepts 2 electrons become copper solid. It has a standard reduction potential of 0.3394 volts. Now within the question, I tell us that the copper electrode is the cathode and the zinc electrode is the anode. From this point, we just remember that our standard cell potential, so Ecell, equals cathode minus anode.

So plug them in. So 0.3394 volts minus -0.7621 volts. Remember, a minus of a minus really means they're adding, so add them together. When we do that, we get our final answer as 1.1015 volts as the voltage of our standard cell potential for this particular question. So again, 1.1015 volts would be our final answer.

Galvanic Cell and Standard Cell Potential

Now recall that a standard subpotential value that's greater than 0 means the reaction is spontaneous. And when it comes to electrochemical cells, remember we have two types. We have our galvanic voltaic cell. Remember galvanic voltage? They're synonymous with each other. You can use them interchangeably. And then we have our electrolytic cell. These are our two typical types of electrochemical cells.

Now for galvanic voltaic cell, we're going to see that the cathode is the half cell compartment that has the higher standard reduction potential and then the anode is the one that has the lower standard reduction potential. This results in a standard cell potential that is greater than 0. So this makes sense here because the galvanic voltage cell is a spontaneous electrochemical cell, so we'd expect it to have a cell potential greater than 0.

The electrolytic cell, on the other hand, everything is kind of reversed here. Here the cathode is now the one with the lower standard reduction potential, and then the anode is the one with the higher standard reduction potential. But remember, your standard cell potential is still cathode minus anode. Because of this, the standard cell potential here will be less than 0.

So just remember, if we know the type of electrochemical cell that kind of guides us into what our standard cell potential should be at the end. And that's based on should the cathode have a higher or lower standard reduction potential or should it be the anode? Knowing this is key to getting the right answer at the end, so keep this in mind when looking at the two types of electrochemical cells.

Standard Cell Potential Example

Here it says given the follow redox reaction we have cerium solid plus aluminum ion reacting to produce aluminum solid plus cerium aqueous. Here it says find its standard sub potential when given the following half reactions. Here we're given the half reaction for the cerium 3 plus ion and the aluminum ion.

Now here the steps that we take is first refer to the redox reaction to determine which species is reduced and which is oxidized. This is incredibly important because remember that the cathode is a site of reduction, so the cathode equals reduction and the anode is a site of oxidation, so the anode equals oxidation. Once we know this, we can use the standard subpotential formula to find our final answer. And that's because standard subpotential, so E_cell, equals cathode minus anode.

If we take a look here, we see that cerium solid goes from zero for its oxidation state to +3. Its oxidation number increased, therefore it has been oxidized. So here, if it's the site of oxidation, that means it must be the anode. And then if we look at aluminum, aluminum goes from what? It goes from plus three in terms of its charge/oxidation state to neutral to its natural standard state, which is 0. So it goes from plus three to zero. Its oxidation number has been reduced or decreased, so reduction has occurred. Therefore it is the cathode.

So we've determined the cathode and the anode, and now we can find the standard cell potential. So take the values and plug them in. So for this will be -1.677 - (-2.336). Remember, a minus of a minus just means that you're adding them together. So -1.677 + 2.336 gives me at the end 0.659 volts. This will represent the answer from my standard cell potential for the following example question.

Calculate the standard cell potential of an electrolytic cell when given the following half reactions. 

Standard Reduction Potentials

Fe³⁺ (aq) + e ^– →  Fe²⁺ (aq)        E°_red = + 0.769 V

Li⁺ (aq) + e ^– →  Li (s)                  E°_red = – 3.04 V

• A. –2.271 V
• B. –1.551 V
• C. –3.060 V
• D. –3.809 V

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°C.  

3 Cl_2­ (g) + 2 Fe (s)  →  6 Cl ^– (aq) + 2 Fe³⁺ (aq)

Standard Reduction Potentials

Cl₂ (g) + 2 e^– →  2 Cl ^– (aq)                      E°_red = + 1.396 V
Fe³⁺ (aq) + 3 e^– →  Fe (s)                         E°_red = – 0.040 V

• A. 1.024 V
• B. 1.436 V
• C. 1.356 V
• D. 0.999 V

Predict whether the following reaction will occur as written based on the calculated E^ºcell. 

Ag⁺ (aq) + Au (s)  →  Ag (s) + Au³⁺ (aq)

Standard Reduction Potentials

Ag⁺(aq) + e^– →  Ag (s)                         E°_red = + 0.80 V
Au³⁺ (aq) + 3 e^– →  Au (s)                    E°_red = + 1.50 V

• A. +0.70 V
• B. +2.30 V
• C. -0.70 V
• D. -2.30 V

Here’s what students ask on this topic:

How do you calculate standard cell potential?

To calculate the standard cell potential, you need to use the standard reduction potentials of the half-reactions occurring at the cathode and anode in an electrochemical cell. Here's how you do it:

1. Write down the half-reactions for the cathode and anode. Identify which substances are being reduced and which are being oxidized.
2. Look up the standard reduction potentials (E^°) for each half-reaction in a table of standard electrode potentials. These values are typically given in volts and are measured under standard conditions (1 M concentration, 1 atm pressure, and 25°C).
3. Assign the reduction potential to the cathode (since reduction occurs at the cathode) and the oxidation potential to the anode. Remember that the oxidation potential is the negative of the standard reduction potential for the anode reaction.
4. Calculate the standard cell potential (E^°_cell) by subtracting the anode potential from the cathode potential:

E^°_cell = E^°_cathode - E^°_anode

The result is the electromotive force (emf) of the cell under standard conditions, and it tells you the voltage that the cell can produce. If the value is positive, the cell can do work spontaneously. If it's negative, the cell reaction is non-spontaneous under standard conditions.

What is the standard cell potential?

The standard cell potential, also known as the standard electromotive force (emf), is a measure of the voltage or electrical potential difference between two half-cells in an electrochemical cell when operating under standard conditions. These standard conditions include all solutes at a concentration of 1 M, a pressure of 1 atmosphere for any gases involved, and a temperature of 25°C (298 K).

The standard cell potential is determined by the intrinsic properties of the materials involved in the half-reactions, and it gives an indication of the cell's ability to produce an electric current when no external current is present. It is calculated by taking the difference between the standard reduction potentials of the cathode and the anode:

$E^{°}{\mathrm{cell}}_{}=E^{°}{\mathrm{cathode}}_{}-E^{°}{\mathrm{anode}}_{}$

A positive standard cell potential indicates a spontaneous reaction, while a negative value suggests a non-spontaneous reaction under standard conditions. Standard cell potentials are tabulated for many reactions and can be used to predict the direction of electron flow and the feasibility of chemical processes.

What happens to the standard cell potential of a battery when the temperature increases?

The standard cell potential, also known as the electromotive force (EMF) of a battery, is influenced by temperature changes. As temperature increases, the standard cell potential can either increase or decrease depending on the nature of the chemical reactions within the battery.

For most batteries, the reactions are exothermic, meaning they release heat. According to the Nernst equation, which relates the cell potential to temperature, an increase in temperature will typically cause the cell potential to decrease for exothermic reactions. This is because the increased thermal energy tends to make the products of the chemical reaction more thermodynamically favored, thus reducing the voltage the battery can produce.

However, if the battery operates based on an endothermic reaction, which absorbs heat, an increase in temperature could lead to an increase in cell potential. This is less common in practical batteries but can occur in certain types of electrochemical cells.

It's important to note that extreme temperatures can damage the battery, reduce its lifespan, or affect its performance in other ways, regardless of the effect on cell potential.