Electrochemistry: Cell Potentials, Redox Reactions, and Equilibrium (Chapter 19 Study Notes)

Electrochemistry Fundamentals

Oxidation States and Redox Reactions

Electrochemistry studies chemical processes that cause electrons to move, generating electric current. Redox (reduction-oxidation) reactions involve the transfer of electrons between species, changing their oxidation states.

• Oxidation: Loss of electrons; increase in oxidation state.

• Reduction: Gain of electrons; decrease in oxidation state.

• Identifying Oxidation States: Assign oxidation numbers to each atom to determine which species are oxidized or reduced.

• Balancing Redox Reactions: Use the half-reaction method to balance electrons and charges.

• Example: $\text{Au}^{3+} + 3e^- \rightarrow \text{Au} (s)$ (Reduction) $\text{Ag}^+ + e^- \rightarrow \text{Ag} (s)$ (Reduction)

Standard Reduction Potentials

Each half-reaction has a standard reduction potential ($E^\circ$), measured in volts (V), indicating its tendency to gain electrons.

• Standard Hydrogen Electrode (SHE): Reference electrode with $E^\circ = 0.00$ V.

• Table of Standard Reduction Potentials: Used to predict cell voltage and spontaneity.

• Example Table:

Half-Reaction	$E^\circ$ (V)
Ni2+ + 2e- → Ni(s)	-0.23
Al3+ + 3e- → Al(s)	-1.66
Ag+ + e- → Ag(s)	+0.80
Au3+ + 3e- → Au(s)	+1.50

Electrochemical Cells

Galvanic (Voltaic) Cells

Galvanic cells convert chemical energy into electrical energy via spontaneous redox reactions.

• Anode: Electrode where oxidation occurs (loss of electrons).

• Cathode: Electrode where reduction occurs (gain of electrons).

• Salt Bridge: Maintains electrical neutrality by allowing ion flow.

• Cell Notation: $\text{Anode} | \text{Anode solution} || \text{Cathode solution} | \text{Cathode}$

• Example: $\text{Ag}(s) | \text{Ag}^+(aq, 1.0M) || \text{Au}^{3+}(aq, 1.0M) | \text{Au}(s)$

Cell Potential ($E_{cell}$)

The cell potential is the voltage produced by the cell, calculated from the reduction potentials of the half-reactions.

• Formula: $E_{cell}^\circ = E_{cathode}^\circ - E_{anode}^\circ$

• Example: $E_{cell}^\circ = (+1.50\,V) - (+0.80\,V) = +0.70\,V$

• Direction of Electron Flow: Electrons flow from anode to cathode.

Thermodynamics of Electrochemical Cells

Relationship Between $E_{cell}^\circ$, $\Delta G^\circ$, and $K$

Cell potential, free energy change, and equilibrium constant are interrelated and determine the spontaneity of a reaction.

• Spontaneous Reaction: $\Delta G^\circ < 0$ (negative) $E_{cell}^\circ > 0$ (positive) $K > 1$

• Key Equations:

Relationship	Equation (LaTeX)
Free Energy and Cell Potential	$\Delta G^\circ = -n F E_{cell}^\circ$
Free Energy and Equilibrium Constant	$\Delta G^\circ = -RT \ln K$
Cell Potential and Equilibrium Constant	$E_{cell}^\circ = \frac{0.0592\,V}{n} \log K$

• Constants: $F = 96,485$ coulombs/mole $e^-$ (Faraday's constant) $R = 8.314$ J/(mol·K) (Gas constant)

Calculating Work and Free Energy

The maximum electrical work obtainable from a cell is equal to the change in free energy.

• Formula: $\Delta G^\circ = -n F E_{cell}^\circ$

• Example Calculation: For $n = 6$ electrons, $E_{cell}^\circ = 1.43$ V: $\Delta G^\circ = -6 \times 96,485 \times 1.43 = -830$ kJ

Calculating Equilibrium Constant ($K$) from $E_{cell}^\circ$

The equilibrium constant for a redox reaction can be calculated using the cell potential.

• Formula: $E_{cell}^\circ = \frac{0.0592}{n} \log K$

• Example: $E_{cell}^\circ = 1.43$ V, $n = 6$ $1.43 = \frac{0.0592}{6} \log K$ $K = 9 \times 10^{14}$

Nernst Equation and Non-Standard Conditions

Nernst Equation

The Nernst equation calculates cell potential under non-standard conditions (concentrations ≠ 1 M, pressures ≠ 1 atm).

• General Form: $E_{cell} = E_{cell}^\circ - \frac{RT}{nF} \ln Q$

• Simplified at 25°C: $E_{cell} = E_{cell}^\circ - \frac{0.0592}{n} \log Q$

• $Q$: Reaction quotient (ratio of product concentrations to reactant concentrations).

• Example: For $\text{Cu}^{2+}(2.0\,M)$ and $\text{Zn}^{2+}(0.010\,M)$: $E_{cell} = 1.10 - \frac{0.0592}{2} \log \left( \frac{0.010}{2.0} \right ) = 1.10 + 0.0592/2 \times 2.30 = 1.10 + 0.068 = 1.17$ V

Concentration Cells

Concentration cells generate voltage due to differences in ion concentrations between two half-cells.

• Cell Notation: $\text{Cu}(s) | \text{Cu}^{2+}(aq, 0.10\,M) || \text{Cu}^{2+}(aq, 1.0\,M) | \text{Cu}(s)$

• Voltage Calculation: Use the Nernst equation with differing concentrations.

Applications and Biological Context

Neuronal Membrane Potential

Electrical signals in neurons are generated by changes in ion concentrations across membranes, calculated using the Nernst equation.

• Formula: $E_{cell} = E_{cell}^\circ - \frac{RT}{nF} \ln \left( \frac{[K^+]_{inside}}{[K^+]_{outside}} \right )$

• Application: Explains how nerve impulses are generated and propagated.

Summary Table: Key Equations and Relationships

Quantity	Equation (LaTeX)	Meaning
Cell Potential	$E_{cell}^\circ = E_{cathode}^\circ - E_{anode}^\circ$	Standard cell voltage
Free Energy Change	$\Delta G^\circ = -n F E_{cell}^\circ$	Maximum work from cell
Equilibrium Constant	$\Delta G^\circ = -RT \ln K$	Relates free energy to equilibrium
Nernst Equation	$E_{cell} = E_{cell}^\circ - \frac{0.0592}{n} \log Q$	Cell potential under non-standard conditions

Practice and Conceptual Questions

• Predicting Spontaneity: If $E_{cell}^\circ$ is positive, the reaction is spontaneous; if negative, non-spontaneous.

• Calculating $K$: Use $E_{cell}^\circ$ and $n$ to find $K$ for a redox reaction.

• Cell Potential and Concentration: Apply the Nernst equation to determine how changes in ion concentrations affect cell voltage.

• Electrochemical Cell Analysis: Given $Q$ and $K$, deduce the signs of $E_{cell}$ and $E_{cell}^\circ$.

Additional info: These notes expand on the provided slides by including definitions, formulas, and context for each concept, ensuring a self-contained study guide for Chapter 19 (Electrochemistry) in General Chemistry.