Galvanic Cells | Chemistry Cheat Sheet

Overview

Galvanic (voltaic) cells convert chemical energy into electrical energy through spontaneous redox reactions. Each cell consists of two half-cells where oxidation and reduction occur separately.

Cell Components

Component	Function
Anode	Where oxidation occurs (negative terminal)
Cathode	Where reduction occurs (positive terminal)
Salt bridge	Allows ion flow; maintains electrical neutrality
External circuit	Allows electron flow from anode to cathode
Electrolyte	Ion solution in each half-cell

Memory Aid

AN OX and RED CAT

ANode = OXidation
REDuction = CAThode

Cell Diagram Notation

\text{Anode} \mid \text{Anode solution} \| \text{Cathode solution} \mid \text{Cathode}

Example: Zinc-Copper Cell

\text{Zn}(s) \mid \text{Zn}^{2+}(aq) \| \text{Cu}^{2+}(aq) \mid \text{Cu}(s)

Symbols

Symbol	Meaning
$\mid$	Phase boundary
$\\|\\|$	Salt bridge
,	Different species in same phase

Standard Electrode Potentials (E°)

Standard Conditions

All concentrations: 1 M
All gases: 1 atm
Temperature: 25°C (298 K)

Standard Hydrogen Electrode (SHE)

2\text{H}^+(aq, 1\text{M}) + 2e^- \rightleftharpoons \text{H}_2(g, 1\text{atm}) \quad E° = 0.00 \text{ V}

Reference point for all other electrode potentials.

Cell Potential (EMF)

Standard Cell Potential

E°_{\text{cell}} = E°_{\text{cathode}} - E°_{\text{anode}}

Or equivalently:

E°_{\text{cell}} = E°_{\text{reduction}} - E°_{\text{oxidation}}

Example: Zinc-Copper Cell

\text{Cu}^{2+} + 2e^- \rightarrow \text{Cu} \quad E° = +0.34 \text{ V (cathode)}

\text{Zn}^{2+} + 2e^- \rightarrow \text{Zn} \quad E° = -0.76 \text{ V (anode)}

E°_{\text{cell}} = +0.34 - (-0.76) = +1.10 \text{ V}

Spontaneity

$E°_{\text{cell}}$	Reaction	Cell Type
> 0	Spontaneous	Galvanic
< 0	Non-spontaneous	Electrolytic
= 0	At equilibrium	No net reaction

Relationship to Thermodynamics

Gibbs Free Energy

\Delta G° = -nFE°

Where:

$n$ = moles of electrons transferred
$F$ = Faraday constant (96,485 C/mol)
$E°$ = standard cell potential

Equilibrium Constant

E° = \frac{RT}{nF} \ln K = \frac{0.0592}{n} \log K \quad \text{(at 25°C)}

Or:

\log K = \frac{nE°}{0.0592}

The Nernst Equation

For non-standard conditions:

E = E° - \frac{RT}{nF} \ln Q

At 25°C:

E = E° - \frac{0.0592}{n} \log Q

Where Q = reaction quotient

Example

For Zn/Cu cell with [Zn²⁺] = 0.010 M and [Cu²⁺] = 2.0 M:

Q = \frac{[\text{Zn}^{2+}]}{[\text{Cu}^{2+}]} = \frac{0.010}{2.0} = 0.005

E = 1.10 - \frac{0.0592}{2} \log(0.005)

E = 1.10 - (0.0296)(-2.30) = 1.10 + 0.068 = 1.17 \text{ V}

Cell Diagram Examples

Daniell Cell

\text{Zn}(s) \mid \text{Zn}^{2+}(1\text{M}) \| \text{Cu}^{2+}(1\text{M}) \mid \text{Cu}(s)

Anode: $\text{Zn} \rightarrow \text{Zn}^{2+} + 2e^-$ Cathode: $\text{Cu}^{2+} + 2e^- \rightarrow \text{Cu}$ $E°_{\text{cell}} = 1.10$ V

Lead-Acid Battery (simplified)

\text{Pb}(s) \mid \text{PbSO}_4(s) \mid \text{H}_2\text{SO}_4(aq) \mid \text{PbO}_2(s) \mid \text{Pb}(s)

Overall: $\text{Pb} + \text{PbO}_2 + 2\text{H}_2\text{SO}_4 \rightarrow 2\text{PbSO}_4 + 2\text{H}_2\text{O}$ $E°_{\text{cell}} \approx 2.0$ V

Batteries

Primary Cells (non-rechargeable)

Battery	Voltage	Use
Zinc-carbon	1.5 V	Flashlights
Alkaline	1.5 V	Electronics
Lithium	3.0 V	Cameras

Secondary Cells (rechargeable)

Battery	Voltage	Use
Lead-acid	2.0 V/cell	Cars
NiCd	1.2 V	Tools
NiMH	1.2 V	Electronics
Li-ion	3.6 V	Phones, laptops

Fuel Cells

Continuous galvanic cells using external fuel supply.

Hydrogen Fuel Cell

Anode: $2\text{H}_2 \rightarrow 4\text{H}^+ + 4e^-$ Cathode: $\text{O}_2 + 4\text{H}^+ + 4e^- \rightarrow 2\text{H}_2\text{O}$ Overall: $2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}$

$E°_{\text{cell}} \approx 1.23$ V

Corrosion

Unwanted galvanic process.

Iron Rusting

Anode: $\text{Fe} \rightarrow \text{Fe}^{2+} + 2e^-$ (oxidation at scratch) Cathode: $\text{O}_2 + 2\text{H}_2\text{O} + 4e^- \rightarrow 4\text{OH}^-$ (at water droplet edge)

Prevention Methods

Coating (paint, plastic)
Galvanizing (zinc coating)
Cathodic protection (sacrificial anode)
Alloying (stainless steel)