Galvanic cells

  • galvanic cells are a form of energy storage
  • a basic galvanic cell is composed of two main parts:
    • Two electrodes
      • a negative anode, which consists of a more electronegative metal, immersed in a salt solution containing the same metal
      • a positive cathode, which consists of a less electronegative metal, immersed in a salt solution containing the same metal
      • the two electrodes are connected via a conductive wire
      • the more electronegative metal provides electrons for the less electronegative metal
        • the anode is slowly dissolved into solution
        • the cathode slowly grows as the dissolved metal slowly percipitates out
        • a redox reaction occurs
    • Salt bridge
      • as one solution gets more and more positive and the other more and more negative, a salt bridge transfers the anions and cations from the salts dissolved in the anode and cathode solutions
      • it is an essential part, because it ensures charge neutrality of the two solutions

Standard electrode potential $E^0$

The potential of the redox half-reacion measured against a standard hydrogen electrode under stadnard conditions is determined by the standard electrode potential.

  • the elements with the standard electrode potential higher than zero will grab electrons more easily
  • the elements with the standard electrode potential lower than zero will release electrons more easily
  • entire cell reaction is a combination of the two redox half-reaction and its electrode potential is the sum of the standard electrode potentials of these two reactions
Ion Half-reaction $E^0$ (V)
$Au^+$ $Au^+ + e^- \longrightarrow Au$ 1.692
$Ag^+$ $Ag^+ + e^- \longrightarrow Ag$ 0.7996
$Cu^{2+}$ $Cu^{2+} + 2\ e^- \longrightarrow Cu$ 0.342
$H^+$ $2\ H^+ + 2\ e^- \longrightarrow H_2$ 0
$Fe^{3+}$ $Fe^{3+} + 3\ e^- \longrightarrow Fe$ -0.037
$Pb^{2+}$ $Pb^{2+} + 2\ e^- \longrightarrow Pb$ -0.126
$Ni^{2+}$ $Ni^{2+} + 2\ e^- \longrightarrow Ni$ -0.257
$Cd^{2+}$ $Cd^{2+} + 2\ e^- \longrightarrow Cd$ -0.403
$Fe^{2+}$ $Fe^{2+} + 2\ e^- \longrightarrow Fe$ -0.447
$Zn^{2+}$ $Zn^{2+} + 2\ e^- \longrightarrow Zn$ -0.762
$Al^{3+}$ $Al^{3+} + 3\ e^- \longrightarrow Al$ -1.662
Table of standard electron potentials of some elements

Relating electrode potential to $\Delta{G}$

$$\Delta{G} = -nFE$$

  • where:
    • $n$ is the ammount of electrons trasfered (mol)
    • $F$ is the Faraday’s constant
    • $E$ is the cell electrode potential
  • a cell with a positive cell electrode potential involves a thermodynamically favored and vice versa

Faraday constant $F$

Faraday constant is the magnitude of charge that is carried by one mole of electrons. $$F = e \cdot N_A = 96,485\ C \cdot mol^{-1}$$

  • $e$ is the elementary charge of an electron ($\approx 1.602 \cdot 10^{-19}$)

$E^0$ calculation based on $K$

$$-nFE^0 = -RT\ln{K}$$ $$E^0 = \cfrac{RT}{nF}\ln{K}$$

  • $R$ and $F$ are constants and $T$ is also constant under standard conditions (298.15 K)
    • $\cfrac{RT}{F} = 0.0257\ J \cdot C^{-1}$

$$E^0 = \cfrac{0.0257}{n}\ln{K}$$

Nernst equation

  • Nernst equation calculates the electrode potential even under nonstandard conditions $$E = E^0 - \cfrac{RT}{nF}\ln{Q}$$

Concentration cell

  • concentration cell is a galvanic cell made up of same electrodes immersed in solutions of different concentration
  • the electrode immersed in the less concentrated solution will dissolve into solution, whereas the electrode immersed in the more concentrated solution will grow as the zinc precipitates out

Electrolytic cell

  • electrolytic cell is the opposite of a galvanic cell
    • a galvanic cell uses a spontaneous redox reaction to generate an electric current
    • an electrolytic cell uses electic current to initiate a non-spontaneous reaction
  • the standard electrode potential of a electrolysis reaction is opposite to the standard electrode potential of the reaction in a galvanic cell
  • the notion of electrodes (cathode and anode) is also opposite
  • electric current $I$ is defined as the amount of charge trasfered over time

$$I = \cfrac{Q}{t}$$

Faraday’s first law of electrolysis

The amount of chemical change produced by a current at an electrode-electrolyte boundary is proportional to the quantity of electricity used. $$m = A \cdot Q$$

  • where:
    • $A$ is the electro-chemical equivalent
      • it is different for every substance
    • $m$ is the mass of elements deposited on an electrode

Faraday’s second law of electrolysis

The amounts of chemical changes produced by the same quantity of electricity in different substances are proportional to their equivalent weights. $$A = \cfrac{M}{nF}$$

Combination of both Faraday’s laws

$$m = \cfrac{MQ}{nF}$$