⚡ Galvanic Cells — Redox Review

Part 1 of 7 — Half-Reactions and Electron Transfer

Electrochemistry converts chemical energy into electrical energy (and vice versa). It is all built on redox reactions — reactions involving the transfer of electrons. Let's review the fundamentals before building galvanic cells.

Redox Review

Oxidation and Reduction

Together: OIL RIG

Oxidation Numbers

Oxidation numbers (states) help track electron transfer:

• Elements in standard state: 0
• Monatomic ions: charge = oxidation number
• O is usually −2 (except peroxides: −1)
• H is usually +1 (except metal hydrides: −1)
• Sum of oxidation numbers = charge of species

Identifying Redox

• The species that is oxidized is the reducing agent (it reduces something else)
• The species that is reduced is the oxidizing agent (it oxidizes something else)

Writing Half-Reactions

Every redox reaction can be split into two half-reactions:

Example: $\text{Zn}(s) + \text{Cu}^{2+}(aq) \rightarrow \text{Zn}^{2+}(aq) + \text{Cu}(s)$

Oxidation half-reaction: $\text{Zn}(s) \rightarrow \text{Zn}^{2+}(aq) + 2e^-$

Zinc loses 2 electrons (oxidation number: $0 \rightarrow +2$)

Reduction half-reaction: $\text{Cu}^{2+}(aq) + 2e^- \rightarrow \text{Cu}(s)$

Copper gains 2 electrons (oxidation number: $+2 \rightarrow 0$)

Key Points

• Electrons must balance — the number lost in oxidation = number gained in reduction
• The electrode where oxidation occurs = anode
• The electrode where reduction occurs = cathode

Memory trick: AN OX, RED CAT (Anode = Oxidation, Reduction = Cathode)

Redox Fundamentals Quiz 🎯

Oxidation State Practice 🧮

Determine the oxidation state of the underlined element:

1. The oxidation state of Mn in $\text{MnO}_4^-$ is:

2. The oxidation state of Cr in $\text{Cr}_2\text{O}_7^{2-}$ is:

3. The oxidation state of N in $\text{NO}_3^-$ is:

Redox Terminology 🔽

Exit Quiz — Redox Review ✅

🔋 Galvanic Cell Structure

Part 2 of 7 — Salt Bridges, Electron Flow, and Ion Flow

A galvanic (voltaic) cell converts the energy of a spontaneous redox reaction into electrical energy. By physically separating the two half-reactions, we force electrons to travel through an external circuit — generating an electric current.

Anatomy of a Galvanic Cell

The Two Half-Cells

A galvanic cell consists of two half-cells, each containing:

• An electrode (solid conductor, often a metal)
• An electrolyte solution (containing the relevant ions)

Key Components

The Zn-Cu Cell (Daniell Cell)

Anode (oxidation): $\text{Zn}(s) \rightarrow \text{Zn}^{2+}(aq) + 2e^-$

Cathode (reduction): $\text{Cu}^{2+}(aq) + 2e^- \rightarrow \text{Cu}(s)$

Overall: $\text{Zn}(s) + \text{Cu}^{2+}(aq) \rightarrow \text{Zn}^{2+}(aq) + \text{Cu}(s)$

Flow Directions

Electron Flow (through the wire)

$\text{Anode} \xrightarrow{e^-} \text{Cathode}$

Electrons flow from anode to cathode through the external circuit.

Ion Flow (through the salt bridge)

• Anions ($\text{NO}_3^-$, $\text{Cl}^-$, etc.) migrate toward the anode
• Cations ($\text{K}^+$, $\text{Na}^+$, etc.) migrate toward the cathode

Why Is the Salt Bridge Necessary?

Without a salt bridge:

1. The anode solution would become too positive (excess $\text{Zn}^{2+}$ produced)
2. The cathode solution would become too negative ($\text{Cu}^{2+}$ consumed)
3. Charge imbalance would stop the reaction immediately

The salt bridge maintains electrical neutrality by allowing ion migration.

Anode Sign Convention

In a galvanic cell:

• Anode = negative terminal (−)
• Cathode = positive terminal (+)

(This is opposite to electrolytic cells!)

Cell Structure Quiz 🎯

Cell Component Identification 🔽

Cell Analysis 🧮

For a galvanic cell with the overall reaction: $\text{Mg}(s) + \text{Fe}^{2+}(aq) \rightarrow \text{Mg}^{2+}(aq) + \text{Fe}(s)$

1. Which metal is the anode? (type the element symbol)

2. Which metal is the cathode? (type the element symbol)

3. How many electrons are transferred in the balanced reaction?

Exit Quiz — Cell Structure ✅

⚡ Standard Reduction Potentials

Part 3 of 7 — E° and Calculating Cell Voltage

Every half-reaction has a standard reduction potential ($E°$) that measures its tendency to gain electrons. By comparing two half-reactions, we can calculate the voltage (EMF) of a galvanic cell.

Standard Reduction Potential Table

All half-reactions are written as reductions (gaining electrons):

Reading the Table

• More positive $E°$: stronger tendency to be reduced (stronger oxidizing agent)
• More negative $E°$: stronger tendency to be oxidized (stronger reducing agent)
• The Standard Hydrogen Electrode (SHE) is the reference: $E° = 0.00$ V

Calculating Standard Cell Potential

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

Important Rules

1. $E°$ values are NOT multiplied by stoichiometric coefficients (they are intensive properties)
2. The species with the higher (more positive) $E°$ is reduced (cathode)
3. The species with the lower (more negative) $E°$ is oxidized (anode)
4. A spontaneous galvanic cell always has $E°_{\text{cell}} > 0$

Worked Example: Zn-Cu Cell

• Cathode: $\text{Cu}^{2+} + 2e^- \rightarrow \text{Cu}$ ($E° = +0.34$ V)
• Anode: $\text{Zn}^{2+} + 2e^- \rightarrow \text{Zn}$ ($E° = -0.76$ V)

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

The positive $E°_{\text{cell}}$ confirms the reaction is spontaneous.

Reduction Potential Quiz 🎯

Cell Potential Calculations 🧮

Use: Ag⁺/Ag = +0.80 V, Fe²⁺/Fe = −0.44 V, Ni²⁺/Ni = −0.26 V, Cu²⁺/Cu = +0.34 V

1. $E°_{\text{cell}}$ for a cell with Ag cathode and Fe anode: (in V, to 3 significant figures)

2. $E°_{\text{cell}}$ for a cell with Cu cathode and Ni anode: (in V, to 3 significant figures)

3. $E°_{\text{cell}}$ for a cell with Ni cathode and Fe anode: (in V, to 3 significant figures)

Reduction Potential Concepts 🔽

Exit Quiz — Standard Reduction Potentials ✅

📝 Cell Notation (Line Notation)

Part 4 of 7 — Shorthand for Electrochemical Cells

Cell notation (also called line notation) is a compact way to describe a galvanic cell. It is frequently tested on the AP exam. Learning to read and write cell notation is essential.

Cell Notation Rules

The Format

$\text{Anode} \mid \text{Anode ion} \| \text{Cathode ion} \mid \text{Cathode}$

Conventions

Example: Daniell Cell

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

Read left to right:

1. Zn solid electrode (anode)
2. Phase boundary
3. Zn²⁺ ions in solution
4. Salt bridge
5. Cu²⁺ ions in solution
6. Phase boundary
7. Cu solid electrode (cathode)

Special Cases

Inert Electrodes

When a half-reaction involves only aqueous species (no solid metal), we use an inert electrode — typically Pt (platinum) or C (graphite):

$\text{Pt} \mid \text{Fe}^{2+}(aq), \text{Fe}^{3+}(aq) \| \text{Ag}^+(aq) \mid \text{Ag}(s)$

The comma separates species in the same phase.

Gas Electrodes

For reactions involving gases:

$\text{Pt} \mid \text{H}_2(g) \mid \text{H}^+(aq) \| \text{Ag}^+(aq) \mid \text{Ag}(s)$

The gas contacts the Pt electrode and is separated by a phase boundary.

Key Points for AP

• Anode is ALWAYS on the left
• Cathode is ALWAYS on the right
• Species are listed in the order they appear in the half-reaction
• The double line ($\|$) represents the salt bridge

Cell Notation Quiz 🎯

Reading Cell Notation 🧮

For the cell: $\text{Al}(s) \mid \text{Al}^{3+}(aq) \| \text{Ni}^{2+}(aq) \mid \text{Ni}(s)$

1. Which metal is the anode? (element symbol)

2. Which metal is the cathode? (element symbol)

3. How many electrons are transferred in the balanced reaction? (Al³⁺ needs 3e⁻, Ni²⁺ needs 2e⁻)

Cell Notation Elements 🔽

Exit Quiz — Cell Notation ✅

🔗 Connecting Free Energy and Cell Potential

Part 5 of 7 — ΔG° = −nFE°

One of the most important equations in AP Chemistry links Gibbs free energy directly to cell potential. This bridges thermodynamics and electrochemistry into a unified framework.

The Key Equation

$\Delta G° = -nFE°$

Why the Negative Sign?

• Spontaneous reactions have $\Delta G° < 0$
• Spontaneous galvanic cells have $E° > 0$
• The negative sign ensures: positive $E°$ → negative $\Delta G°$ ✓

Unit Check

$\Delta G° = -(\text{mol})(\text{C/mol})(\text{J/C}) = \text{J}$

The units work out to joules (convert to kJ by dividing by 1000).

The Thermodynamic Triangle

Three key relationships connect $\Delta G°$, $E°$, and $K$:

$\Delta G° = -nFE° = -RT\ln K$

From these, we can derive:

$E° = \frac{RT}{nF}\ln K$

At 25°C (298 K):

$E° = \frac{0.0257}{n}\ln K = \frac{0.0592}{n}\log K$

The Web of Connections

All Three Consistent

Worked Example

For the Daniell cell: $\text{Zn}(s) + \text{Cu}^{2+}(aq) \rightarrow \text{Zn}^{2+}(aq) + \text{Cu}(s)$

$E° = +1.10$ V, $n = 2$ mol $e^-$

Calculate ΔG°

$\Delta G° = -nFE° = -(2)(96{,}485)(1.10)$ $= -212{,}267 \text{ J} = -212.3 \text{ kJ}$

Calculate K at 298 K

$\ln K = \frac{nFE°}{RT} = \frac{(2)(96{,}485)(1.10)}{(8.314)(298)} = \frac{212{,}267}{2478} = 85.66$

$K = e^{85.66} = 1.6 \times 10^{37}$

This enormous $K$ confirms the reaction is virtually complete at equilibrium.

ΔG° and E° Quiz 🎯

Thermodynamic Triangle Calculations 🧮

1. $E° = +0.80$ V, $n = 1$. Calculate $\Delta G°$ in kJ. (to 1 decimal)

2. $\Delta G° = -579$ kJ, $n = 6$. Calculate $E°$ in V. (to 3 significant figures)

3. If $E° > 0$ for a cell, is $K$ greater than or less than 1? (type "greater" or "less")

Connecting the Three Quantities 🔽

Exit Quiz — ΔG° and E° ✅

🛠️ Problem-Solving Workshop — Galvanic Cells

Part 6 of 7 — Practice and Integration

This workshop brings together all galvanic cell concepts: half-reactions, cell notation, standard potentials, and the ΔG°-E° connection. Practice solving the types of problems you will see on the AP exam.

Problem-Solving Strategy

Step-by-Step Approach

1. Identify the two half-reactions
2. Determine which is oxidized (anode) and which is reduced (cathode) using $E°$ values
3. Calculate $E°_{\text{cell}} = E°_{\text{cathode}} - E°_{\text{anode}}$
4. Balance electrons (find $n$)
5. Calculate $\Delta G° = -nFE°$ if needed
6. Write cell notation if asked

Common Mistakes to Avoid

Mixed Galvanic Cell Problems 🎯

Use: $\text{Ag}^+/\text{Ag} = +0.80$ V, $\text{Zn}^{2+}/\text{Zn} = -0.76$ V, $\text{Fe}^{2+}/\text{Fe} = -0.44$ V, $\text{Cu}^{2+}/\text{Cu} = +0.34$ V

Calculation Workshop 🧮

Use: $\text{Cu}^{2+}/\text{Cu} = +0.34$ V, $\text{Fe}^{2+}/\text{Fe} = -0.44$ V

For the cell: Fe(s) | Fe²⁺(aq) || Cu²⁺(aq) | Cu(s)

1. $E°_{\text{cell}} = ?$ (in V, to 3 significant figures)

2. $n = ?$ (electrons transferred)

3. $\Delta G° = ?$ (in kJ, to nearest whole number)

Cell Analysis 🔽

For the cell: Al(s) | Al³⁺(aq) || Ag⁺(aq) | Ag(s)

Use: Al³⁺/Al = −1.66 V, Ag⁺/Ag = +0.80 V

Exit Quiz — Problem-Solving Workshop ✅

🎯 Synthesis & AP Review — Galvanic Cells

Part 7 of 7 — Mastery Check

This final review covers everything about galvanic cells: redox fundamentals, cell structure, standard potentials, cell notation, and the thermodynamic connections. Be ready for any AP question on this topic.

Master Summary

Essential Equations

Cell Components

Spontaneity Criteria

Comprehensive AP Review 🎯

Use: Zn²⁺/Zn = −0.76 V, Cu²⁺/Cu = +0.34 V, Ag⁺/Ag = +0.80 V, Fe²⁺/Fe = −0.44 V

Integration Problems 🧮

1. A cell has $E° = +2.00$ V and $n = 3$. What is $\Delta G°$ in kJ? (to nearest whole number)

2. A cell has $\Delta G° = -386$ kJ and $n = 4$. What is $E°$ in V? (to 3 significant figures)

3. If $E° = +0.50$ V and $n = 2$ at 298 K, is $K$ greater or less than 1? (type "greater" or "less")

Final Concept Review 🔽

Final Exit Quiz — Galvanic Cells Mastery ✅