Electrochemistry

Redox Principles and Half-Reaction Balancing

• Redox reactions involve electron transfer between species, resulting in oxidation state changes.
• Oxidation consists of an increase in oxidation number; reduction consists of a decrease.
• The half-reaction method balances complex equations by separating the reaction into two parts.
• Steps include balancing non-O/H atoms, adding $H_{2}O$ for oxygen, $H^{+}$ for hydrogen, and adding $e^{-}$ to balance charge.
• In basic solutions, add $OH^{-}$ to neutralize $H^{+}$ and form water, canceling excess water as needed.

Galvanic Cells and Notation

• Galvanic cells use spontaneous redox reactions to produce electricity.
• Half-cells contain electrodes: the anode (site of oxidation) and the cathode (site of reduction).
• A salt bridge allows cations and anions to move, completing the circuit.
• Cell potential ($E_{cell}$), also called cell voltage or electromotive force (emf), is measured in volts ($V$).
• Cell diagram notation: $\text{Anode}(s) | \text{Anode Ion}(aq) || \text{Cathode Ion}(aq) | \text{Cathode}(s)$.

Standard Reduction Potentials

• The Standard Hydrogen Electrode (SHE) is the global reference: $2H^{+}(aq) + 2e^{-} \rightarrow H_{2}(g)$, where $E^{o} = 0.0\,V$.
• Standard cell potential calculation: $E^{o}<em>{cell} = E^{o}</em>{cathode} - E^{o}_{anode}$.
• Potential oxidizing agents are on the left side of reduction half-reactions; the best agents have the highest $E^{o}$.
• Potential reducing agents are on the right side; the best agents have the lowest (most negative) $E^{o}$.

Thermodynamics of Electrochemical Cells

• Relation between free energy ($\Delta G^{o}$) and potential: $\Delta G^{o} = -nFE^{o}_{cell}$.
• Faraday's constant ($F$): $96485\,C/mol\,e^{-}$.
• Relation between potential and the equilibrium constant ($K$): $E^{o}_{cell} = \frac{0.0592\,V}{n} \log(K)$ at $25^{\circ}C$.
• Spontaneous reactions occur when E^{o}_{cell} > 0 and \Delta G^{o} < 0.

Nernst Equation and Concentration Effects

• The Nernst Equation calculates cell potential under non-standard conditions: $E_{cell} = E^{o}_{cell} - \frac{0.0592\,V}{n} \log(Q)$.
• Increasing reactant concentration or decreasing product concentration increases $E_{cell}$.
• Batteries die because as reactants are depleted, $Q$ approaches $K$, and $E_{cell}$ tends toward zero.

Electrolysis and Corrosion

• Electrolysis: An external voltage is applied to drive a non-spontaneous reaction in an electrolytic cell.
• Stoichiometry of electrolysis relates current ($A = C/s$) and time to the mass of material plated: $\text{Charge}(C) = \text{current}(A) \times \text{time}(s)$.
• Corrosion: Spontaneous oxidation of metals (e.g., rusting of iron requiring oxygen and water).
• Prevention: Galvanized iron uses Zinc ($Zn$) as a sacrificial electrode because it oxidizes more easily than Iron ($Fe$).

Questions & Discussion

• Question: Which species is the strongest oxidizing agent among $Br_{2}$, $I_{2}$, $Cl_{2}$, and $F_{2}$?
• Response: $F_{2}$ is the strongest because it has the highest standard reduction potential ($E^{o} = +2.87\,V$).
• Question: Which species is the strongest reducing agent among $Fe^{3+}$, $Ni^{2+}$, and $Na^{+}$?
• Response: $Na$ (from the reduction of $Na^{+}$) is the strongest because it has the lowest reduction potential ($E^{o} = -2.71\,V$).
• Question: How do you ensure the result for $E^{o}_{cell}$ is positive for a galvanic cell?
• Response: Arrange the equation $E^{o}<em>{cell} = E^{o}</em>{cathode} - E^{o}_{anode}$ such that the larger reduction potential is the cathode value.