Galvanic Cells, Standard Reduction Potentials, and Electrochemical Cells

Galvanic Cells and Standard Reduction Potentials

Introduction to Electrochemical Cells

Electrochemical cells are devices that convert chemical energy into electrical energy through redox reactions. They are also known as voltaic cells, galvanic cells, or batteries. In these cells, a spontaneous redox reaction generates a flow of electrons, producing electricity.

• Chemical energy is converted to electrical energy in a battery.

• Cell potential (Eo) is the difference in potential energy between two electrodes.

• For a battery to work, the redox reaction must be spontaneous (Eo must be positive).

Spontaneous Reactions and Free Energy

A spontaneous reaction in an electrochemical cell is characterized by a negative free energy change (ΔGo < 0). The relationship between free energy and cell potential is given by:

• $oxed{ riangle G^{ ext{o}} = -n F E^{ ext{o}}_{ ext{cell}} }$

• Where n is the number of moles of electrons transferred, F is Faraday's constant (96,485 C/mol e-), and Eocell is the standard cell potential.

Balancing Redox Reactions

Balancing in Acidic and Basic Solutions

Redox reactions must be balanced for both mass and charge. The process differs slightly depending on whether the reaction occurs in acidic or basic solution.

• In acidic solution, use H+ and H2O to balance hydrogen and oxygen.

• In basic solution, use OH- and H2O.

• Example: NO3- (aq) + Cu(s) → NO(g) + Cu2+ (aq) Balance in acidic and basic conditions.

Standard Reduction Potentials

Definition and Use

Standard reduction potentials (Eo) measure the tendency of a chemical species to be reduced. They are tabulated for half-reactions under standard conditions (1 M, 1 atm, 25°C).

• A more positive Eo means a greater tendency to be reduced (stronger oxidizing agent).

• A more negative Eo means a greater tendency to be oxidized (stronger reducing agent).

Calculating Standard Cell Potential

The standard cell potential is calculated using the standard reduction potentials of the two half-reactions:

• $E^{ ext{o}}_{ ext{cell}} = E^{ ext{o}}_{ ext{cathode}} - E^{ ext{o}}_{ ext{anode}}$

• Example: Cu(s) + 2 Ag+(aq) → Cu2+(aq) + 2 Ag(s) Ag+ + e- → Ag(s)    Eo = +0.800 V Cu2+ + 2e- → Cu(s)    Eo = +0.337 V $E^{ ext{o}}_{ ext{cell}} = 0.800 - 0.337 = 0.463 ext{ V}$

Identifying Spontaneous Reactions

Using Standard Reduction Potentials

To determine if a reaction is spontaneous, calculate Eocell. If Eocell > 0, the reaction is spontaneous.

• Example: Cu2+(aq) + Zn(s) → Cu(s) + Zn2+(aq) Cu2+ + 2e- → Cu(s)    Eo = +0.337 V Zn2+ + 2e- → Zn(s)    Eo = -0.763 V $E^{ ext{o}}_{ ext{cell}} = 0.337 - (-0.763) = 1.10 ext{ V}$ (spontaneous)

Oxidizing and Reducing Agents

Strength of Agents

The strongest oxidizing agent is the species with the most positive reduction potential; the strongest reducing agent is the species with the most negative reduction potential.

• Oxidizing agent: Most easily reduced (most positive Eo).

• Reducing agent: Most easily oxidized (least positive Eo).

Species	Standard Reduction Potential (V)
Cu2+ + 2e- → Cu(s)	+0.337
Zn2+ + 2e- → Zn(s)	-0.763

• Cu2+ is the strongest oxidizing agent.

• Zn(s) is the strongest reducing agent.

Galvanic Cell Construction and Notation

Cell Diagram and Line Notation

A galvanic cell consists of two half-cells connected by a salt bridge. The anode is where oxidation occurs (left side in line notation), and the cathode is where reduction occurs (right side).

• Line notation: Anode | Anode solution || Cathode solution | Cathode

• Example: Zn(s) | Zn2+(aq, 1.0 M) || Cu2+(aq, 1.0 M) | Cu(s)

• Anode: Zn(s) → Zn2+ + 2e- (oxidation, negative charge)

• Cathode: Cu2+ + 2e- → Cu(s) (reduction, positive charge)

Cell Operation and Electron Flow

• Electrons flow from anode to cathode through the external circuit.

• Ions flow through the salt bridge to maintain charge balance.

• The mass of the anode decreases (oxidation), while the mass of the cathode increases (reduction).

Building a Battery from Half-Reactions

Combining Half-Reactions

To build a battery, combine two half-reactions with different reduction potentials. The cell potential is the difference between the cathode and anode potentials.

• Example: Au3+(aq) + 3e- → Au(s)    Eo = +1.50 V Ag+(aq) + e- → Ag(s)    Eo = +0.80 V Ag(s) → Ag+(aq) + e-    Eo = -0.80 V $E^{ ext{o}}_{ ext{cell}} = 1.50 - 0.80 = 0.70 ext{ V}$

• Line notation: Ag(s) | Ag+(aq, 1.0 M) || Au3+(aq, 1.0 M) | Au(s)

Relationship Between Eocell, ΔGo, and K

Thermodynamic Connections

For a spontaneous reaction:

• $riangle G^{ ext{o}} < 0$ (negative)

• $E^{ ext{o}}_{ ext{cell}} > 0$ (positive)

• $K > 1$ (equilibrium constant favors products)

Key equations:

• $riangle G^{ ext{o}} = -n F E^{ ext{o}}_{ ext{cell}}$

• $riangle G^{ ext{o}} = -RT ext{ln} K$

• $E^{ ext{o}}_{ ext{cell}} = rac{0.0592}{n} ext{log} K$

Summary Table: Key Concepts in Electrochemistry

Concept	Definition/Equation
Cell Potential (Eocell)	$E^{ ext{o}}_{ ext{cell}} = E^{ ext{o}}_{ ext{cathode}} - E^{ ext{o}}_{ ext{anode}}$
Free Energy Change (ΔGo)	$riangle G^{ ext{o}} = -n F E^{ ext{o}}_{ ext{cell}}$
Equilibrium Constant (K)	$riangle G^{ ext{o}} = -RT ext{ln} K$
Relationship between Eocell and K	$E^{ ext{o}}_{ ext{cell}} = rac{0.0592}{n} ext{log} K$
Oxidizing Agent	Species with most positive Eo
Reducing Agent	Species with least positive Eo

Additional info: These notes expand on the original slides by providing full definitions, equations, and context for each concept, as well as examples and tables for clarity.