EMF of a Cell: The maximum potential difference which is present between two electrodes of a cell is defined as the electromotive force of a cell or EMF of a cell. It’s also known as the net voltage between the half-reactions of oxidation and reduction. An electrochemical cell’s EMF is primarily used to identify whether it is galvanic or not. In this session, we’ll study more about this topic, including key formulas and how to compute the EMF of an electrochemical cell. Electrochemical cells, thermoelectric devices, solar cells, photodiodes, electrical generators, transformers, and even Van de Graaff generators can all produce EMF.

Electrochemical Cells

An electrochemical cell is a device that generates an electrical current from a chemical reaction (redox reaction).

Voltaic Cells

A voltaic cell, also known as a galvanic cell, is a device that generates electricity by a spontaneous redox reaction. The figure below depicts a simple voltaic cell. The spontaneous reaction of zinc metal with aqueous copper sulphate solution is used here.

\({\rm{Zn}} + {\rm{C}}{{\rm{u}}^{2 + }} \to {\rm{Z}}{{\rm{n}}^{2 + }} + {\rm{Cu}}\)

In the left container, a bar of zinc metal (anode) is immersed in a zinc sulphate solution. In the right container, a copper bar (cathode) is immersed in a copper sulphate solution. A copper cable connects the zinc and copper electrodes. The solutions in the anode and cathode compartments are connected by a salt bridge containing potassium sulphate solution.

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The anode compartment is where the oxidation half-reaction takes place.

\({\rm{Zn}} \to {\rm{Z}}{{\rm{n}}^{2 + }} + 2{{\rm{e}}^ – }\)

In the cathode compartment, the reduction of half-reaction occurs.

\({\rm{C}}{{\rm{u}}^{2 + }} + 2{{\rm{e}}^ – } \to {\rm{Cu}}\)

When the cell is set up, electrons move from the zinc electrode to the copper cathode via the wire. Zinc dissolves in the anode solution and forms \({\rm{Z}}{{\rm{n}}^{2 + }}\) ions as a consequence. \({\rm{C}}{{\rm{u}}^{2 + }}\) ions in the cathode half-cell pick up electrons on the cathode and are transformed to \(\text {Cu}\) atoms. \({\rm{SO}}_4^{2 – }\) ions from the cathode half-cell migrate to the anode half-cell across the salt bridge at the same time. \({\rm{Z}}{{\rm{n}}^{2 + }}\) ions from the anode half-cell migrate into the cathode half-cell in the same way. The electrical circuit is completed by the transfer of ions from one half-cell to the other, ensuring a constant supply of current. The cell will keep running until either the zinc metal or the copper ion is depleted.

Daniel Cell

It is a typical voltaic cell. It was named after John Daniel, a British scientist. It’s a simple zinc-copper cell, similar to the one described previously.

A permeable pot has been used to replace the salt bridge in this cell. The Daniel cell is identical to the voltaic cell described above in every way except that \({\rm{Z}}{{\rm{n}}^{2 + }}\) ions and \({\rm{SO}}_4^{2 – }\) ions travel to the cathode and anode, respectively, through the porous pot rather than the salt bridge. Regardless of this distinction, the cell diagram is the same.

Cell Reaction

The half-reactions in the anode and cathode compartments induce the flow of electrons from one electrode to the other in an electrochemical cell. The cell reaction is the net chemical change achieved by combining the two half-reactions. As a result, for the above-mentioned simple voltaic cell, we have

(a) Half-reactions:

\({\rm{Zn}}\left( {\rm{s}} \right) \to {\rm{Z}}{{\rm{n}}^{2 + }}\left( {{\rm{aq}}} \right) + 2{\rm{e}}\)

\({\rm{C}}{{\rm{u}}^{2 + }}\left( {{\rm{aq}}} \right) + 2{{\rm{e}}^ – } \to {\rm{Cu}}\left( {\rm{s}} \right)\)

(b) Cell reaction by adding up the half-reactions:

\({\rm{Zn}}\left( {\rm{s}} \right) + {\rm{C}}{{\rm{u}}^{2 + }}\left( {{\rm{aq}}} \right) \to {\rm{Z}}{{\rm{n}}^{2 + }}\left( {{\rm{aq}}} \right) + {\rm{Cu}}\left( {\rm{s}} \right)\)

Cell Potential or EMF

Electrons are liberated at the anode of a \(\text {Zn}-\text {Cu}\) voltaic cell, causing it to become negatively charged. By electrical repulsions, the negative electrode drives electrons across the external circuit. The discharge of \({\rm{C}}{{\rm{u}}^{2 + }}\) ions on the copper electrode gives it a positive charge. As a result, electrons from the outside circuit are drawn to this electrode. The ‘push’ of electrons at the anode and the ‘attraction’ of electrons at the cathode govern the current flow across the circuit. The ‘driving force’ or ‘electrical pressure’ that propels electrons across the circuit is made up of these two forces. The electromotive force (abbreviated emf) or cell potential is the driving force. The emf of a cell is also known as cell voltage and is measured in volts \((\text {V})\).

Cell Diagram or Representation of a Cell

An electrochemical cell is represented by a cell diagram, which is a simplified symbolic representation of the cell. We’ll use the assumption that a cell is made up of two half-cells for this. Each half-cell is made up of a metal electrode that makes contact with metal ions in the solution once more. Thus, a zinc-copper cell has emf \(1.10 \,\text {V}\) and is represented as

\({\rm{Zn|ZnS}}{{\rm{O}}_4}||{\rm{CuS}}{{\rm{O}}_4}|{\rm{Cu}}\,\,\,\,\,\,\,\,\,\,\,\,\,{\rm{E =  + 1}}{\rm{.1}}\,{\rm{V}}\)

Calculating the EMF of a Cell

Using the formula below, the emf of a cell may be computed from the half-cell potentials of the two cells (anode and cathode).

\({{\rm{E}}_{{\rm{cell}}}} = {{\rm{E}}_{{\rm{cathode}}}} – {{\rm{E}}_{{\rm{anode}}}}\)
\( = {{\rm{E}}_{\rm{R}}} – {{\rm{E}}_{\rm{L}}}\)

Where \({{\rm{E}}_{\rm{R}}}\) and \({{\rm{E}}_{\rm{L}}}\) are the right-hand and left-hand electrode reduction potentials, respectively, it’s worth noting that the absolute values of these reduction potentials are unknown. These can be discovered by connecting the half-cell to a conventional hydrogen electrode with a reduction potential set to zero arbitrarily.

Single Electrode Potential

Two half-cells make up an electrochemical cell. The metal electrode in each half-cell transfers its ions into solution when the circuit is open. As a result, each electrode produces a potential in relation to the solution. The Single electrode potential is the potential of a single electrode in a half-cell. In a Daniel cell with no external connections, the anode \({\rm{Zn/Z}}{{\rm{n}}^{2 + }}\) develops a negative charge, while the cathode \({\rm{Cu/C}}{{\rm{u}}^{2 + }}\) develops a positive charge. The single electrode potential is determined by the amount of charge produced on each electrode. A half-single cell’s electrode potential is determined by the following factors: (a) concentration of ions in solution; (b) tendency to form ions; and (c) temperature.

Standard EMF of a Cell

The symbol E represents the emf generated by an electrochemical cell. With the help of a potentiometer, it may be measured. The value of emf is affected by the concentrations of reactants and products in the cell fluids, as well as the cell’s temperature. The standard emf is the emf of a cell that is determined under standard conditions. Standard conditions are (a) \(1 \,\text {M}\) reactants and products solutions and (b) a temperature of \(25^\circ {\rm{C}}\). The emf of a cell with \(1 \,\text {M}\) solutions of reactants and products in solution measured at \(25^\circ {\rm{C}}\) can thus be described as standard emf. The sign \({\rm{E}}^\circ \) represents the standard emf of a cell. Instead of concentration, \(1 \,\text {atm}\) pressure is a common condition for gases.

\({\rm{Zn}}|{\rm{Z}}{{\rm{n}}^{2 + }}\left( {{\rm{aq,}}\,{\rm{1}}\,{\rm{M}}} \right)||{\rm{C}}{{\rm{u}}^{2 + }}\left( {{\rm{aq}},\,1\,{\rm{M}}} \right)|{\rm{Cu\,\,\,\,\,\,\,\,\,\,\,E}}^\circ  =  + {\rm{1}}{\rm{.1}}\,{\rm{V}}\)

Determination of EMF of a Half-Cell

The emf of an isolated half-cell or its half-reaction is also referred to as a single electrode potential. By connecting two half-cells to a voltmeter, the emf of a cell made of two half-cells may be determined. However, it is impossible to directly measure the emf of a single half-cell. Combining the given half-cell with another standard half-cell is a convenient way to do so. A voltmeter is used to determine the emf of the newly built cell, \(\text {E}\). The expression can then be used to compute the emf of the unknown half-cell, \({\rm{E}}^\circ \)

\({{\rm{E}}_{{\rm{measured}}}} = {{\rm{E}}_{\rm{R}}} – {{\rm{E}}_{\rm{L}}}\)

If the standard half-cell acts as a cathode, the equation becomes.

\({{\rm{E}}_{\rm{R}}} = {{\rm{E}}_{{\rm{measured}}}}\)

On the other hand, if a standard half-cell is an anode, the equation takes the form

\({{\rm{E}}_{\rm{L}}} =  – {{\rm{E}}_{{\rm{measured}}}}\)

For coupling with the unknown half-cell, the standard hydrogen half-cell, also known as the Standard Hydrogen Electrode (SHE), is chosen. A platinum electrode is immersed in a \(1 \,\text {M}\) solution of \({{\rm{H}}^ + }\) ions at a temperature of \(25^\circ {\rm{C}}\). One atmosphere of hydrogen gas enters the glass hood and bubbles over the platinum electrode. At the platinum electrode, hydrogen gas goes into the solution, generating \({{\rm{H}}^ + }\) ions and electrons.

\({{\rm{H}}_2} \to 2{{\rm{H}}^{2 + }} + 2{{\rm{e}}^ – }\)

The standard hydrogen electrode’s emf has been arbitrarily assigned the value of zero volts. As a result, SHE can serve as a benchmark for other electrodes.

The appropriate half-cell is united with the hydrogen electrode, and the whole cell’s emf is determined with a voltmeter. The emf of the cell is the emf of the half-cell.

\({\rm{E}}{^\circ _{{\rm{cell}}}} = {\rm{E}}{^\circ _{\rm{R}}} – {\rm{E}}{^\circ _{\rm{L}}}\)

Summary

1. The maximum potential difference which is present between two electrodes of a cell is defined as the electromotive force of a cell or EMF of a cell.
2. A voltaic cell, also known as a galvanic cell, is a device that generates electricity by a spontaneous redox reaction
3. The cell reaction is the net chemical change achieved by combining the two half-reactions.
4. The emf of a cell may be computed from the half-cell potentials of the two cells (anode and cathode).
5. The emf of an isolated half-cell or its half-reaction is also referred to as a single electrode potential. By connecting two half-cells to a voltmeter, the emf of a cell made of two half-cells may be determined.

FAQs on EMF of a Cell

Q.1. What is an electrochemical cell?
Ans: An electrochemical cell is a device that generates an electrical current from a chemical reaction (redox reaction).

Q.2. What is the EMF of a cell?
Ans: The ‘push’ of electrons at the anode and the ‘attraction’ of electrons at the cathode govern the current flow across the circuit. The ‘driving force’ or ‘electrical pressure’ that propels electrons across the circuit is made up of these two forces. The electromotive force (abbreviated emf) or cell potential is the driving force. The emf or cell potential is also known as cell voltage and is measured in volts \((\text {V})\).

Q.3. How can we calculate the EMF of a cell?
Ans: Using the formula below, the emf of a cell may be computed from the half-cell potentials of the two cells (anode and cathode).
\({{\rm{E}}_{{\rm{cell}}}} = {{\rm{E}}_{{\rm{cathode}}}} – {{\rm{E}}_{{\rm{anode}}}}\)
\( = {{\rm{E}}_{\rm{R}}} – {{\rm{E}}_{\rm{L}}}\)

Where \({{\rm{E}}_{\rm{R}}}\) and \({{\rm{E}}_{\rm{L}}}\) are the right-hand and left-hand electrode reduction potentials, respectively, it’s worth noting that the absolute values of these reduction potentials are unknown. These can be discovered by connecting the half-cell to a conventional hydrogen electrode with a reduction potential set to zero arbitrarily.

Q.4. What is a Daniel cell?
Ans: It is a typical voltaic cell. It was named after John Daniel, a British scientist. It’s a simple zinc-copper cell.
A permeable pot has been used to replace the salt bridge in this cell. The Daniel cell is identical to the voltaic cell in every way except that \({\rm{Z}}{{\rm{n}}^{2 + }}\) ions and \({\rm{SO}}_4^{2 – }\) ions travel to the cathode and anode, respectively, through the porous pot rather than the salt bridge. Regardless of this distinction, the cell diagram is the same as the voltaic cell.

Q.5. Which electrode can be used to calculate the EMF of a half-cell?
Ans: Standard Hydrogen electrode is used to calculate the EMF of a half-cell.

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