Electrochemistry Notes

Redox Reactions

• Oxidation: Loss of electrons.
• Reduction: Gain of electrons.
• Examples:
  • $Na(s) \rightarrow Na^+(aq) + e^-$
  • $Fe^{3+}(aq) + 3e^- \rightarrow Fe(s)$
  • $Zn(s) + Cu^{2+}(aq) \rightarrow Cu(s) + Zn^{2+}(aq)$
    • Zinc loses 2 electrons, so it is oxidized.
    • Copper gains 2 electrons, so it is reduced.
• Mnemonic:
  • OIL RIG: Oxidation Is Loss, Reduction Is Gain.
  • LEO the lion goes GER: Loss of Electrons is Oxidation, Gain of Electrons is Reduction.

Oxidation Number Rules

• Single element species: 0
• Alkali & alkaline earth metals: +1, +2
• Fluorine: -1
• Hydrogen: +1 (except in metal hydrides, where it's -1)
• Oxygen: -2 (except in peroxides, where it's -1)
• Everything else (e.g., halogens, transition metals…): It depends!
• The overall charge of a compound is 0.
• The overall charge of an ion will be shown.

Voltaic Cells (Batteries)

• Apparatus that produces electrical energy directly from a spontaneous redox reaction.
• Two half-cells (reduction and oxidation) are separated.
• Electron transfer happens through an external circuit (electricity).
• Cells are linked by an external circuit (wire) and a salt bridge.
• Cathode: Reduction occurs here.
• Anode: Oxidation occurs here.
  • Mnemonic: AN OX chases a RED CAT.
• Electrons flow from the anode (higher reduction potential) to the cathode (lower reduction potential).
  • Alphabetical order: A (Anode) comes before C (Cathode).
• The potential difference between the two electrodes is the driving force for the reaction to occur.
• Salt Bridge: U-shaped tube containing a salt solution that maintains charge balance because once one electron flows, the charges in each beaker would not be balanced, and the flow would stop.
  • Cations move towards the cathode.
  • Anions move towards the anode.

Writing Cell Diagrams

• Symbols that show how the components of an electrochemical cell are connected.
  1. Write the symbol of the anode on the left, cathode on the right, and a double vertical line to represent the salt bridge.
  2. Use vertical lines to indicate phase changes and symbols of ions or compounds to represent electrolytes that are changed by the cell reaction.
  3. Indicate concentrations of dissolved species and partial pressures of any gases (if known).
• Example:
  • $Zn(s) | Zn^{2+}(aq) || Cu^{2+}(aq) | Cu(s)$
  • $Zn(s) | Zn^{2+}(1.00 M) || Cu^{2+}(1.00 M) | Cu(s)$
• Process:
  • As electrons leave the anode (zinc), a zinc atom is converted to a zinc cation (oxidized), which dissolves, reducing the mass of the zinc electrode: $Zn(s) \rightarrow Zn^{2+}(aq) + 2e^-$
  • As electrons arrive at the cathode (copper), they combine with copper cations in solution (reduced), forming neutral copper atoms, which deposit on the cathode, increasing the mass of the copper cathode: $Cu^{2+}(aq) + 2e^- \rightarrow Cu(s)$
• Cathode gains mass, and the anode loses mass.

Electrical Potential

• Electromotive force: Electrical driving force between the anode and cathode (Potential between the anode and cathode).
• Cell potential ($E_{cell}$): Potential energy per unit charge characteristic of a half-cell reaction.
  • Measured in Volts (V).
  • 1 Volt = 1 Joule/Coulomb (energy/unit charge).
  • 1 electron has a charge of $1.60 \times 10^{-19}$ Coulombs (C).
• Positive (+) $E_{cell}$ indicates a spontaneous reaction.
• Negative (-) $E_{cell}$ indicates a nonspontaneous reaction.
• Each electrochemical cell is made up of 2 half cells, so the Ecell is based on both of those cells.
• Standard Reduction Potentials: Energy in volts for a half-reaction.

Standard Reduction Potentials

• All half-reactions are shown as reductions. If the half-reaction is reversed, it shows the oxidation, and the sign is reversed.
  • Example:
    • $Ag(s) \rightarrow Ag^{1+}(aq) + e^-$ $E° = -0.800 V$
    • $Ag^{1+}(aq) + e^- \rightarrow Ag(s)$ $E° = +0.800 V$
• Positive potential indicates spontaneity.
  • Top of the table is easily reduced.
  • Bottom of the table is easily oxidized.
• Potential relative to the Standard Hydrogen Electrode (SHE).

Standard Cell Potentials

• $E_{cell}$ under standard conditions (1 M, 25°C).
  • $E<em>{cell}° = E</em>{red}°(cathode) - E_{red}°(anode)$
  • $E<em>{cell}° = E</em>{red}°(cathode) + E_{ox}°(anode)$
• Can change the sign for the anode half-reaction since oxidation occurs there.
• Intensive Property: Does not change with quantity.
  • Example:
    • $Ag^{1+}(aq) + e^- \rightarrow Ag(s)$ $E° = +0.800 V$
    • $2Ag^{1+}(aq) + 2e^- \rightarrow 2Ag(s)$ $E° = +0.800 V$

Spontaneity in Reactions

• ΔG˚: negative means spontaneous.
• K: greater than one means spontaneous in the forward reaction.
• E˚cell: positive means spontaneous.

$E_{cell}$ and ΔG

• $ΔG = -nFE_{cell}$
  • ΔG: Gibb’s Free Energy
  • n: number of electrons transferred
  • F: Faraday Constant (96,485 J/V ∙ mol e-)
  • $E_{cell}$: Cell potential
• Spontaneous reactions have a NEGATIVE ΔG, so they have a POSITIVE $E_{cell}$

$E<em>{cell}$ and $K</em>{eq}$

• At STP (298 K):
  • $ΔG = -RTlnK$
  • $ΔG = -nFE°$
  • E° =
    \frac{RT}{nF}lnK
  • E° =
    \frac{0.0591}{n}logK

Nernst Equation

• Used to calculate cell potentials under NON-STANDARD conditions.
• Most common non-standard conditions are differing concentrations.
• Q is used when the system is not at equilibrium (non-standard concentrations).
• E{cell} = E{cell}° -
  \frac{RT}{nF}lnQ