9.S: Electrochemistry (Study Guide)

9.1 Balancing Oxidation – Reduction reactions

Redox reactions are defined by changes in reactant oxidation numbers, and those most relevant to electrochemistry involve actual transfer of electrons. Aqueous phase redox processes often involve water or its characteristic ions, H⁺ and OH⁻, as reactants in addition to the oxidant and reductant, and equations representing these reactions can be challenging to balance. The half-reaction method is a systematic approach to balancing such equations that involves separate treatment of the oxidation and reduction half-reactions.

• Oxidation-Reduction (redox) processes - net movement of electrons from one reactant to another
• Oxidizing agent – accepts electrons and is reduced
• Reducing agent – loses electrons and is oxidized
• To balance a redox reaction
  • split into half reactions
  • balance mass
  • balance electrons

9.2 Galvanic Cells

Galvanic cells are devices in which a spontaneous redox reaction occurs indirectly, with the oxidant and reductant redox couples contained in separate half-cells. Electrons are transferred from the reductant (in the anode half-cell) to the oxidant (in the cathode half-cell) through an external circuit, and inert solution phase ions are transferred between half-cells, through a salt bridge, to maintain charge neutrality. The construction and composition of a galvanic cell may be succinctly represented using chemical formulas and others symbols in the form of a cell schematic (cell notation).

• redox reaction does electrical work, pushing electrons through an external circuit connecting the physically separated half-cells
• Oxidation at negative anode
• Reduction at positive cathode
• Conventions:
  • oxidation half-reaction at the -ve anode
  • reduction half-reaction at the +ve cathode
  • electron flow from anode (-ve) to cathode (+ve)
  • solid electrodes may be active (Zn, Cu) or inactive (graphite, platinum)
  • porous disc or salt bridge required
• Shorthand notation can be used to describe cells. A vertical line, │, denotes a phase boundary and a double line, ‖, the salt bridge. Information about the anode is written to the left, followed by the anode solution, then the salt bridge (when present), then the cathode solution, and, finally, information about the cathode to the right.

9.3 Standard Reduction Potentials

The property of potential, E, is the energy associated with the separation/transfer of charge. In electrochemistry, the potentials of cells and half-cells are thermodynamic quantities that reflect the driving force or the spontaneity of their redox processes. The cell potential of an electrochemical cell is the difference in between its cathode and anode. To permit easy sharing of half-cell potential data, the standard hydrogen electrode (SHE) is assigned a potential of exactly 0 V and used to define a single electrode potential for any given half-cell. The electrode potential of a half-cell, E_X, is the cell potential of said half-cell acting as a cathode when connected to a SHE acting as an anode. When the half-cell is operating under standard state conditions, its potential is the standard electrode potential, E°_X. Standard electrode potentials reflect the relative oxidizing strength of the half-reaction’s reactant, with stronger oxidants exhibiting larger (more positive) E°_X values. Tabulations of standard electrode potentials may be used to compute standard cell potentials, E°_cell, for many redox reactions. The arithmetic sign of a cell potential indicates the spontaneity of the cell reaction, with positive values for spontaneous reactions and negative values for nonspontaneous reactions (spontaneous in the reverse direction).

• The standard hydrogen electrode (SHE) is chosen as the zero and all other half-cells are compared to it
• The standard reduction potential can be determined by subtracting the standard reduction potential for the reaction occurring at the anode from the standard reduction potential for the reaction occurring at the cathode. The minus sign is needed because oxidation is the reverse of reduction.

E^o_cell =E^o_cathode - E^o_anode

• E_cell measured in SI unit: volts (V)
• for a spontaneous reaction E_cell is +ve

9.4 Nernst Equation

Potential is a thermodynamic quantity reflecting the intrinsic driving force of a redox process, and it is directly related to the free energy change and equilibrium constant for the process. For redox processes taking place in electrochemical cells, the maximum (electrical) work done by the system is easily computed from the cell potential and the reaction stoichiometry and is equal to the free energy change for the process. The equilibrium constant for a redox reaction is logarithmically related to the reaction’s cell potential, with larger (more positive) potentials indicating reactions with greater driving force that equilibrate when the reaction has proceeded far towards completion (large value of K). Finally, the potential of a redox process varies with the composition of the reaction mixture, being related to the reactions standard potential and the value of its reaction quotient, Q, as described by the Nernst equation.

• spontaneous reactions, which have ΔG<0, must have Ecell>0

\[ΔG°=−nFE^\circ_\ce{cell} \nonumber \]

\[ΔG°=−RT\ln K \nonumber \]

So

\[ E^\circ_\ce{cell}=\dfrac{RT}{nF}\ln K \nonumber \]

at standard temperature (298.15 K)

\[\begin{align*} E^\circ_\ce{cell}&=\dfrac{RT}{nF}\:\ln K \\[4pt] &=\dfrac{\mathrm{0.0257\: V}}{n}\:\ln K \end{align*} \nonumber \]

or

\[E^\circ_\ce{cell}=\dfrac{\mathrm{0.0592\: V}}{n}\:\log K \nonumber \]

The common form we use is

\[E_\ce{cell}=E^\circ_\ce{cell}−\dfrac{RT}{nF}\:\ln Q\]

which for reactions occuring at 25 °C (298.15 K) becomes

\[E_\ce{cell}=E^\circ_\ce{cell}−\dfrac{\mathrm{0.0257\: V}}{n}\:\ln Q\]

or

\[ E_\ce{cell}=E^\circ_\ce{cell}−\dfrac{\mathrm{0.0592\: V}}{n}\log_{10} Q \]