Cell EMF | Chemistry Optional Notes for UPSC PDF Download

Electromotive Force (EMF)

• The electromotive force (EMF) is the maximum potential difference between two electrodes of a galvanic or voltaic cell. This quantity is related to the tendency for an element, a compound or an ion to acquire (i.e. gain) or release (lose) electrons. For example, the maximum potential between  Zn and Cu of a well known cell
  Zn_(s)|Zn²⁺(1M)||Cu²⁺(1M)|Cu_(s)
• has been measured to be 1.100 V. A concentration of 1 M in an ideal solution is defined as the standard condition, and 1.100 V is thus the standard electromotive force, ΔE^o, or standard cell potential for the  Zn−Cu galvanic cell.

• The standard cell potential, ΔE^o, of a galvanic cell can be evaluated from the standard reduction potentials of the two half cells E^o. The reduction potentials are measured against the standard hydrogen electrode (SHE):
  Pt_(s)|H₂(g,1.0atm)|H⁺ (1.0M)
• Its reduction potential or oxidation potential is defined to be exactly zero.
• The reduction potentials of all other half-cells measured in volts against the SHE are the difference in electrical potential energy per coulomb of charge.
• Note that the unit for energy J = Coulomb volt, and the Gibbs free energy G is the product of charge q and potential difference E:
  G in J = q E in C V
  for electric energy calculations.

Evaluating Standard Cell Potential DE° of Galvanic Cells

• A galvanic cell consists of two half-cells. The convention in writing such a cell is to put the (reduction) cathode on the right-hand side, and the (oxidation) anode on the left-hand side. For example, the cell
  Pt|H₂|H + ||Zn²⁺ |Zn
  consists of the oxidation and reduction reactions:
  • H₂ → 2e⁻ + 2H⁺ anode (oxidation) reaction
  • Zn²⁺ + 2e⁻ → Zn cathode (reduction) reaction
• If the concentrations of  H⁺ and  Zn²⁺  ions are 1.0 M and the pressure of  H₂ is 1.0 atm, the voltage difference between the two electrodes would be -0.763 V(the  Zn  electrode being the negative electrode). The conditions specified above are called the standard conditions and the EMF so obtained is the standard reduction potential.
• Note that the above cell is in reverse order compared to that given in many textbooks, but this arrangement gives the standard reduction potentialsdirectly, because the  Zn half cell is a reduction half-cell. The negative voltage indicates that the reverse chemical reaction is spontaneous. This corresponds to the fact that  Zn metal reacts with an acid to produce  H₂ gas.
  As another example, the cell
  • Pt|H₂|H+||Cu+|Cu
• consists of an oxidation and a reduction reaction:
  • H₂ → 2e⁻ + 2H⁺ anode reaction
  • Cu²⁺ + 2^e− → Cucathode reaction
• and the standard cell potential is 0.337 V. The positive potential indicates a spontaneous reaction,
  Cu²⁺ + H₂ → Cu + 2H⁺
  but the potential is so small that the reaction is too slow to be observed.

Solved Example

Example 1: What is the potential for the following cell?
Zn|Zn²⁺ (1.0M)||Cu²⁺ (1.0M)| Cu
Ans: From a table of standard reduction potentials we have the following values
Cu²⁺ + 2e⁻ → CuE^∘ = 0.337 (1)
Zn → Zn²⁺ + 2e⁻E^∗ = 0.763 (2)
Add (1) and (2) to yield
Zn⁺ Cu²⁺ → Zn²⁺ + CuDE^∘ = E^∘ + E^∗ = 1.100 V
Note that E* is the oxidation standard potential, and E° is the reduction standard potential, E* = - E°. The standard cell potential is represented by dE°.

Discussion
The positive potential confirms your observation that zinc metal reacts with cupric ions in solution to produce copper metal.

Example 2: What is the potential for the following cell?
Ag|Ag⁺ (1.0M)||Li ⁺ (1.0M)|Li
Ans: From the table of standard reduction potentials, you find
Li⁺ + e⁻ → Li E^∘ = −3.045 (3)
Ag → Ag⁺ + e⁻ E^∗ = − 0.799 (4)
According to the convention of the cell, the reduction reaction is on the right. The cell on your left-hand side is an oxidation process. Thus, you add (4) and (3) to obtain
Li⁺ + Ag^→Ag⁺ + Li dE∘ = -3.844 V

Discussion

• The negative potential indicates that the reverse reaction should be spontaneous.
• Some calculators use a lithium battery. The atomic weight of  Li  is 6.94, much lighter than Zn (65.4).

Summary

• The electromotive force (EMF) is the maximum potential difference between two electrodes of a galvanic or voltaic cell.
• The standard reduction potential of  Mn⁺,1M | M couple is the standard cell potential of the galvanic cell:
  Pt|H₂,1atm|H⁺,1M||Mⁿ⁺, 1M|M
• The standard oxidation potential of  M|Mn⁺,  1M couple is the standard cell potential of the galvanic cell:
  M|Mn⁺,1M||H⁺,1M|H₂,1atm|Pt
• If the cell potential is negative, the reaction is reversed. In this case, the electrode of the galvanic cell should be written in a reversed order.