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ChemistryEdu Logo Electrochemistry | EMF of a Cell#

EMF of a Cell#

  • EMF stands for Electromotive Force.

  • EMF is the potential difference between the electrodes when the cell is not in use.

  • When the switch is OFF in the circuit:

\[EMF = V_{cathode} - V_{anode}\]

  • It is also defined as the maximum voltage which a cell can supply.

  • EMF is the voltage which is responsible for the motion of electrons in the external circuit.

Calculation of EMF of a cell (Ecell)#

  • EMF of a cell is given by:
\[E_{cell} = E_{cathode} - E_{anode}\]

Use Reduction Potential values in this formula.

  • We can also calculate Ecell as:
\[E_{cell} = E_{ox} + E_{red}\]
  • Standard EMF of a cell is given by:
\[E^0_{cell} = E^0_{cathode} - E^0_{anode}\]

Use Standard Reduction Potential values in this formula.

  • We can also calculate E0cell as:
\[E^0_{cell} = E^0_{ox} + E^0_{red}\]

Relation between Gibbs Free Energy and Ecell#

  • The relation between Gibbs Free Energy and Ecell can be expressed using the below expression:
\[ΔG = -nFE_{cell}\]

Case 1. If the cell reaction is spontaneous

\[ΔG < 0\]
\[-nFE_{cell} < 0\]
\[E_{cell} > 0\]

Thus, for a cell reaction to be spontaneous, Ecell should be positive.

Case 2. If the cell reaction is non-spontaneous

\[ΔG > 0\]
\[-nFE_{cell} > 0\]
\[E_{cell} < 0\]

Thus, for a cell reaction to be non-spontaneous, Ecell should be negative.

Case 3. If the cell reaction is in equilibrium

\[ΔG = 0\]
\[-nFE_{cell} = 0\]
\[E_{cell} = 0\]

Representation of a Galvanic Cell#

Rules to represent a galvanic cell#

  • Left half of the cell should represent anode, where oxidation takes place.
  • Right half of the cell should represent cathode, where reduction takes place.
  • Left half and right half should be separated by the symbol of salt bridge (||).
  • If an inert electrode is used, it should be written in left side before anode separated by comma.

Represent a Daniell Cell with the following half cell reactions and Pt is used as an inert electrode

\[ Anode:\ Zn_{(s)} → Zn^{(2+)}_{(aq)} + 2e^- \]
\[ Cathode:\ Cu^{(2+)}_{(aq)} + 2e^- → Cu_{(s)} \]

This cell can be represented by applying the above rules:

\[Pt_{(s)},\ Zn_{(s)}/{Zn^{2+}_{(C_1 M)}}\ || Cu^{2+}_{(C_2 M)}/Cu_{(s)}\]

Pt is the inert electrode, left part represent anode and right part represent cathode. "||" represents salt bridge which separates anode and cathode.