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9.10 Electrolysis and Faraday's Law

6 min readdecember 22, 2022

Jillian Holbrook

Jillian Holbrook

Jillian Holbrook

Jillian Holbrook

You made it to the last topic section of AP Chemistry. Before jumping in, congratulate yourself for making it this far! Over the AP Chem course, you have learned everything from acids and bases to equilibrium to thermodynamics.

For our final topic of Unit 9 and AP Chemistry, we will discuss and how we can use to make them happen. This builds on the foundations of how work, how we can differentiate galvanic (or voltaic) cells from , and how to use to make electrolysis calculations.

Review of Electrolytic Cells

As we learned in the introduction of galvanic and , an electrolytic cell is a cell in which power from an external source (usually a ) is used to spur by creating . require energy because they are thermodynamically unfavorable, and therefore nonspontaneous. This means that a chemical species in an electrolytic reaction that would normally be oxidized is instead reduced and vice versa.

Take a look at an example of an electrolytic cell with and :

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-SAeyCNWJKmO4.png?alt=media&token=6854a9ca-cfe5-447e-95ef-c9dd69b32e28

Image From Abigail Giordano

In this image, we see that electrons are being pumped out of Cu to form Cu2+ and transferred to Zn2+ to form metal. The arrows show the direction of the electron flow, meaning the redox reaction occurring is: Cu + Zn2+ → Cu2+ + Zn.

By using a table of , we can calculate the , Ecell:

First, we write out our half-reactions:

Cu → Cu2+ + 2e- (E = -0.34 V)

Zn2+ + 2e- → Zn (E = -0.76 V)

Adding our E values, we find that Ecell = -1.10 V. Therefore, because of the negative , we must introduce external power to cause the redox reaction to run.

Note on the in the cell diagram it must be a with a of over 1.10 V. This is because the must be enough to overcome the non-spontaneity of the redox reaction we want to occur (and also the spontaneousness of the reverse reaction which has an E value of +1.10 V). When we connect this , the pulls electrons in the direction of the nonspontaneous reaction. Therefore, the mass of the electrode will decrease, and the mass of the electrode will increase.

Comparing Electrolytic and Galvanic Cells

There are some important differences between a galvanic cell and an electrolytic cell that are necessary to know and recognize for the AP exam. Examine the following galvanic cell and electrolytic cell side by side:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-UDRtqX3EEknc.jpg?alt=media&token=52a04b1b-9b95-4350-ab41-486c894390b8

Image From LibreTexts

On the left, the galvanic cell has an where oxidation occurs and a where reduction occurs. The reaction occurring is with cadmium and . Electrons travel through a wire from the cadmium to the , causing the cadmium electrode to shrink and the electrode to grow. As the electrons travel, a measures the in volts that the reaction releases. Finally, a (with a neutral salt) connects the two half-cells to maintain neutrality.

We can take a closer look at a similar example of a galvanic cell with a and reaction below:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202022-12-20%20at%2010.17-Xu4erhyE0LjY.png?alt=media&token=15502889-f2e5-4c03-87c1-be0019c10e67

Image From LibreTexts

For this cell, the electrode will grow, and the electrode will shrink, which is typical of an and in .

On the right, we have an electrolytic cell. The first notable difference is the direction that the electrons travel. In the galvanic cell, electrons traveled from the cadmium to the electrode (and eventually to the Cu2+ to create Cu metal). The electrolytic cell has the opposite occurring. metal oxidizes into Cu2+, and Cd2+ reduces into Cd metal, the inverse reaction of the one in the galvanic cell.

Instead of a to measure , a (similar to a ) is used to produce an of at least 0.74 V. Because the reaction occurring in the electrolytic cell is nonspontaneous, it requires an external source of energy of this magnitude to run. The reaction also includes a because it is two separate half-cells. In this example, the electrode will shrink, and the cadmium electrode will grow. 

A major similarity between the two types of cells is that always, always, ALWAYS, oxidation occurs at the , and reduction occurs at the . No matter what type the cell is (galvanic or electrolytic), this is the standard method used to label electrodes.

The following comparison emphasizes additional differences between the cell types:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202022-12-20%20at%2010.07-wINWvBeGzoiP.png?alt=media&token=03cdd069-68dc-4345-a599-ed722450d4a0

Image From LibreTexts

Faraday’s Law and Electrolysis Problems

An essential type of problem regarding is calculating the mass of a metal that accumulates at an electrode. To do this, we want to complete a chain of conversions using the definition of an amp (1A = 1C/s) and Faraday’s constant (1 mol e- = 96485 coulombs), represented as I = q / t, where I is the current in amps, q is charge in coulombs, and t is time in seconds. Ultimately, using , we can calculate the amount of charge flow based on changes in the amounts of reactants and products in an electrochemical cell.

Take a look at this example problem:

Determine the mass of chromium that can be produced when a solution of Cr(NO3)2 is electrolyzed for 60 minutes with a current of 15 amps.

To begin with, we need to convert from amps to coulombs:

60 minutes * 60s/min * 15 C/s = 54000 coulombs

Next, we can use this value of charge to convert to moles of electrons:

54000 coulombs * 1 mol e-/96485C = 0.559 mol e-

Then, we can use stoichiometry to convert from mol e- to moles of chromium. After that, we use the (52.0 g/mol) to convert to grams:

0.559 mol e- * (1 mol Cr/2 mol e-) * (52g/mol Cr) = 14.55g Cr produced.

This sort of dimensional analysis can also be done in one long chain as follows:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-X8AzZL5308mE.png?alt=media&token=a8185d21-0351-4c40-a4bb-27e4c1fbd691

Prepare to solve for any of these unknowns: the number of electrons transferred, the mass of material deposited on or removed from an electrode, current, time elapsed, or the charge of ionic species. A problem could ask about finding the time necessary to produce a certain mass or the amperage required for a given time to produce a mass. To complete problems like these, you can simply manipulate the chain we completed previously.

For example, if a problem asked for a time but gave a mass, you could start with the mass, convert it to moles, then convert it to moles of electrons, then convert it to charge, and then to amperage. 

We just need to do proper unit cancellation. Look at the units here:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-1GNBm4hsMYTI.png?alt=media&token=905c50a7-c188-4c6a-af1d-a1b9b058c8bf

Now you know how to use Faraday's constant to solve electrolysis problems!

Key Terms to Review (22)

Ampere (Amps)

: An ampere, often shortened to "amp," is a unit of electric current representing one coulomb of charge moving past a point per second.

Anode

: The anode is the electrode where oxidation occurs in a chemical reaction. It's the site where electrons are lost.

Battery

: A battery is a device consisting of one or more electrochemical cells with external connections for powering electrical devices such as flashlights, smartphones, and electric cars.

Cathode

: The cathode is the electrode where reduction occurs in a chemical reaction. It's the site where electrons are gained.

Cell Potential

: Cell potential, also known as electromotive force (EMF), is the measure of the potential energy per unit charge available from the oxidation/reduction reactions to drive the reaction. It's measured in volts (V).

Copper

: Copper is a chemical element with the symbol Cu (from Latin: cuprum) and atomic number 29. It is a soft, malleable, and ductile metal with very high thermal and electrical conductivity.

Coulombs (Charge)

: A coulomb is the standard unit for electrical charge and represents approximately 6.242 x 10^18 elementary charges (like electrons or protons).

Current (I)

: In chemistry, current refers to the rate at which electric charge flows past a point in an electric circuit. It's measured in amperes (A).

Electrolytic Cells

: Electrolytic cells are devices that drive nonspontaneous redox reactions using an external source of voltage (electricity).

Electromotive Force

: Electromotive force (EMF) refers to the potential difference between two points in a circuit. It's essentially what drives electric current around a circuit.

Faraday's Law

: Faraday's Law of electromagnetic induction states that the voltage in a circuit is proportional to the rate of change in the magnetic field through the circuit.

Galvanic Cells

: Galvanic cells convert chemical energy into electrical energy through redox reactions.

Mass of Metal

: This term refers to how much matter is present within a given quantity or sample of metal. It's typically measured in grams (g) or kilograms (kg).

Molar Mass of Chromium

: The molar mass of chromium is the weight in grams of one mole (6.022 x 10^23 atoms) of chromium. It's approximately 52.00 grams per mole.

Nonspontaneous Redox Reactions

: Nonspontaneous redox reactions are chemical reactions that do not occur naturally without the input of energy. They involve the transfer of electrons from one species to another.

Power Supply

: A power supply is an electronic device that supplies electric energy to an electrical load.

Salt Bridge

: A salt bridge is a laboratory device used to connect the oxidation and reduction half-cells of a galvanic cell, allowing ion flow without mixing solutions.

Standard Reduction Potentials

: Standard reduction potentials refer to the tendency of a chemical species to acquire electrons and thereby be reduced. Each species has its own intrinsic reduction potential; more positive values are stronger oxidizing agents.

Time in Seconds (t)

: This is a unit of measurement for time. In the context of AP Chemistry, it often refers to the duration during which a chemical reaction or process takes place.

Voltage

: Voltage, also known as electric potential difference, is the force that pushes electric current through circuits. It's measured in volts (V).

Voltmeter

: A voltmeter is an instrument used for measuring electrical potential difference between two points in an electric circuit.

Zinc

: Zinc is a chemical element with the symbol Zn and atomic number 30. It is a transition metal, similar to iron and nickel, and it's essential for life.

9.10 Electrolysis and Faraday's Law

6 min readdecember 22, 2022

Jillian Holbrook

Jillian Holbrook

Jillian Holbrook

Jillian Holbrook

You made it to the last topic section of AP Chemistry. Before jumping in, congratulate yourself for making it this far! Over the AP Chem course, you have learned everything from acids and bases to equilibrium to thermodynamics.

For our final topic of Unit 9 and AP Chemistry, we will discuss and how we can use to make them happen. This builds on the foundations of how work, how we can differentiate galvanic (or voltaic) cells from , and how to use to make electrolysis calculations.

Review of Electrolytic Cells

As we learned in the introduction of galvanic and , an electrolytic cell is a cell in which power from an external source (usually a ) is used to spur by creating . require energy because they are thermodynamically unfavorable, and therefore nonspontaneous. This means that a chemical species in an electrolytic reaction that would normally be oxidized is instead reduced and vice versa.

Take a look at an example of an electrolytic cell with and :

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-SAeyCNWJKmO4.png?alt=media&token=6854a9ca-cfe5-447e-95ef-c9dd69b32e28

Image From Abigail Giordano

In this image, we see that electrons are being pumped out of Cu to form Cu2+ and transferred to Zn2+ to form metal. The arrows show the direction of the electron flow, meaning the redox reaction occurring is: Cu + Zn2+ → Cu2+ + Zn.

By using a table of , we can calculate the , Ecell:

First, we write out our half-reactions:

Cu → Cu2+ + 2e- (E = -0.34 V)

Zn2+ + 2e- → Zn (E = -0.76 V)

Adding our E values, we find that Ecell = -1.10 V. Therefore, because of the negative , we must introduce external power to cause the redox reaction to run.

Note on the in the cell diagram it must be a with a of over 1.10 V. This is because the must be enough to overcome the non-spontaneity of the redox reaction we want to occur (and also the spontaneousness of the reverse reaction which has an E value of +1.10 V). When we connect this , the pulls electrons in the direction of the nonspontaneous reaction. Therefore, the mass of the electrode will decrease, and the mass of the electrode will increase.

Comparing Electrolytic and Galvanic Cells

There are some important differences between a galvanic cell and an electrolytic cell that are necessary to know and recognize for the AP exam. Examine the following galvanic cell and electrolytic cell side by side:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-UDRtqX3EEknc.jpg?alt=media&token=52a04b1b-9b95-4350-ab41-486c894390b8

Image From LibreTexts

On the left, the galvanic cell has an where oxidation occurs and a where reduction occurs. The reaction occurring is with cadmium and . Electrons travel through a wire from the cadmium to the , causing the cadmium electrode to shrink and the electrode to grow. As the electrons travel, a measures the in volts that the reaction releases. Finally, a (with a neutral salt) connects the two half-cells to maintain neutrality.

We can take a closer look at a similar example of a galvanic cell with a and reaction below:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202022-12-20%20at%2010.17-Xu4erhyE0LjY.png?alt=media&token=15502889-f2e5-4c03-87c1-be0019c10e67

Image From LibreTexts

For this cell, the electrode will grow, and the electrode will shrink, which is typical of an and in .

On the right, we have an electrolytic cell. The first notable difference is the direction that the electrons travel. In the galvanic cell, electrons traveled from the cadmium to the electrode (and eventually to the Cu2+ to create Cu metal). The electrolytic cell has the opposite occurring. metal oxidizes into Cu2+, and Cd2+ reduces into Cd metal, the inverse reaction of the one in the galvanic cell.

Instead of a to measure , a (similar to a ) is used to produce an of at least 0.74 V. Because the reaction occurring in the electrolytic cell is nonspontaneous, it requires an external source of energy of this magnitude to run. The reaction also includes a because it is two separate half-cells. In this example, the electrode will shrink, and the cadmium electrode will grow. 

A major similarity between the two types of cells is that always, always, ALWAYS, oxidation occurs at the , and reduction occurs at the . No matter what type the cell is (galvanic or electrolytic), this is the standard method used to label electrodes.

The following comparison emphasizes additional differences between the cell types:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202022-12-20%20at%2010.07-wINWvBeGzoiP.png?alt=media&token=03cdd069-68dc-4345-a599-ed722450d4a0

Image From LibreTexts

Faraday’s Law and Electrolysis Problems

An essential type of problem regarding is calculating the mass of a metal that accumulates at an electrode. To do this, we want to complete a chain of conversions using the definition of an amp (1A = 1C/s) and Faraday’s constant (1 mol e- = 96485 coulombs), represented as I = q / t, where I is the current in amps, q is charge in coulombs, and t is time in seconds. Ultimately, using , we can calculate the amount of charge flow based on changes in the amounts of reactants and products in an electrochemical cell.

Take a look at this example problem:

Determine the mass of chromium that can be produced when a solution of Cr(NO3)2 is electrolyzed for 60 minutes with a current of 15 amps.

To begin with, we need to convert from amps to coulombs:

60 minutes * 60s/min * 15 C/s = 54000 coulombs

Next, we can use this value of charge to convert to moles of electrons:

54000 coulombs * 1 mol e-/96485C = 0.559 mol e-

Then, we can use stoichiometry to convert from mol e- to moles of chromium. After that, we use the (52.0 g/mol) to convert to grams:

0.559 mol e- * (1 mol Cr/2 mol e-) * (52g/mol Cr) = 14.55g Cr produced.

This sort of dimensional analysis can also be done in one long chain as follows:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-X8AzZL5308mE.png?alt=media&token=a8185d21-0351-4c40-a4bb-27e4c1fbd691

Prepare to solve for any of these unknowns: the number of electrons transferred, the mass of material deposited on or removed from an electrode, current, time elapsed, or the charge of ionic species. A problem could ask about finding the time necessary to produce a certain mass or the amperage required for a given time to produce a mass. To complete problems like these, you can simply manipulate the chain we completed previously.

For example, if a problem asked for a time but gave a mass, you could start with the mass, convert it to moles, then convert it to moles of electrons, then convert it to charge, and then to amperage. 

We just need to do proper unit cancellation. Look at the units here:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-1GNBm4hsMYTI.png?alt=media&token=905c50a7-c188-4c6a-af1d-a1b9b058c8bf

Now you know how to use Faraday's constant to solve electrolysis problems!

Key Terms to Review (22)

Ampere (Amps)

: An ampere, often shortened to "amp," is a unit of electric current representing one coulomb of charge moving past a point per second.

Anode

: The anode is the electrode where oxidation occurs in a chemical reaction. It's the site where electrons are lost.

Battery

: A battery is a device consisting of one or more electrochemical cells with external connections for powering electrical devices such as flashlights, smartphones, and electric cars.

Cathode

: The cathode is the electrode where reduction occurs in a chemical reaction. It's the site where electrons are gained.

Cell Potential

: Cell potential, also known as electromotive force (EMF), is the measure of the potential energy per unit charge available from the oxidation/reduction reactions to drive the reaction. It's measured in volts (V).

Copper

: Copper is a chemical element with the symbol Cu (from Latin: cuprum) and atomic number 29. It is a soft, malleable, and ductile metal with very high thermal and electrical conductivity.

Coulombs (Charge)

: A coulomb is the standard unit for electrical charge and represents approximately 6.242 x 10^18 elementary charges (like electrons or protons).

Current (I)

: In chemistry, current refers to the rate at which electric charge flows past a point in an electric circuit. It's measured in amperes (A).

Electrolytic Cells

: Electrolytic cells are devices that drive nonspontaneous redox reactions using an external source of voltage (electricity).

Electromotive Force

: Electromotive force (EMF) refers to the potential difference between two points in a circuit. It's essentially what drives electric current around a circuit.

Faraday's Law

: Faraday's Law of electromagnetic induction states that the voltage in a circuit is proportional to the rate of change in the magnetic field through the circuit.

Galvanic Cells

: Galvanic cells convert chemical energy into electrical energy through redox reactions.

Mass of Metal

: This term refers to how much matter is present within a given quantity or sample of metal. It's typically measured in grams (g) or kilograms (kg).

Molar Mass of Chromium

: The molar mass of chromium is the weight in grams of one mole (6.022 x 10^23 atoms) of chromium. It's approximately 52.00 grams per mole.

Nonspontaneous Redox Reactions

: Nonspontaneous redox reactions are chemical reactions that do not occur naturally without the input of energy. They involve the transfer of electrons from one species to another.

Power Supply

: A power supply is an electronic device that supplies electric energy to an electrical load.

Salt Bridge

: A salt bridge is a laboratory device used to connect the oxidation and reduction half-cells of a galvanic cell, allowing ion flow without mixing solutions.

Standard Reduction Potentials

: Standard reduction potentials refer to the tendency of a chemical species to acquire electrons and thereby be reduced. Each species has its own intrinsic reduction potential; more positive values are stronger oxidizing agents.

Time in Seconds (t)

: This is a unit of measurement for time. In the context of AP Chemistry, it often refers to the duration during which a chemical reaction or process takes place.

Voltage

: Voltage, also known as electric potential difference, is the force that pushes electric current through circuits. It's measured in volts (V).

Voltmeter

: A voltmeter is an instrument used for measuring electrical potential difference between two points in an electric circuit.

Zinc

: Zinc is a chemical element with the symbol Zn and atomic number 30. It is a transition metal, similar to iron and nickel, and it's essential for life.


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AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.


© 2024 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.