Electrochemical Cells

Introduction

Every smartphone, laptop, and electric vehicle runs on electrochemical cells! These ingenious devices convert chemical energy directly into electrical energy through spontaneous redox reactions. Understanding how they work is essential not just for JEE, but for comprehending the technology powering our modern world.

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Electrochemical Cell Diagram

Visualize the complete galvanic cell with anode, cathode, salt bridge, and electron flow:

Interactive: Electrochemical Cell in Action

See how electrons flow through the external circuit while ions migrate through the salt bridge:

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What is an Electrochemical Cell?

An electrochemical cell is a device that converts chemical energy into electrical energy (or vice versa) through redox reactions.

Types of Electrochemical Cells

graph TD
    A[Electrochemical Cells] --> B[Galvanic/Voltaic Cells]
    A --> C[Electrolytic Cells]
    B --> B1[Spontaneous reactions]
    B --> B2[ΔG < 0, E°cell > 0]
    B --> B3[Chemical → Electrical]
    C --> C1[Non-spontaneous reactions]
    C --> C2[ΔG > 0, E°cell < 0]
    C --> C3[Electrical → Chemical]

    style B fill:#2ecc71
    style C fill:#e74c3c

Feature	Galvanic Cell	Electrolytic Cell
Energy conversion	Chemical → Electrical	Electrical → Chemical
Nature of reaction	Spontaneous	Non-spontaneous
ΔG	Negative	Positive
E°cell	Positive	Negative
Anode	Negative terminal	Positive terminal
Cathode	Positive terminal	Negative terminal
Example	Daniell cell, batteries	Electrolysis of water

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The Daniell Cell: A Classic Example

The Daniell cell was invented by John Frederic Daniell in 1836 and powered early telegraph systems!

Construction

Setup:

• Left half-cell: Zinc electrode in ZnSO₄ solution
• Right half-cell: Copper electrode in CuSO₄ solution
• Salt bridge: KCl or NH₄NO₃ solution in agar-agar gel

Reactions

At Anode (Zn electrode): Oxidation

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

At Cathode (Cu electrode): Reduction

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

Overall Cell Reaction:

$$\boxed{\text{Zn}_{(s)} + \text{Cu}^{2+}_{(aq)} \rightarrow \text{Zn}^{2+}_{(aq)} + \text{Cu}_{(s)}}$$

Cell Diagram (Cell Notation)

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

Convention:

• Anode (oxidation) on left
• Cathode (reduction) on right
• | = phase boundary
• || = salt bridge
• Concentration usually written: Zn | Zn²⁺(1M) || Cu²⁺(1M) | Cu

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Components of Electrochemical Cells

1. Electrodes

Anode:

• Electrode where oxidation occurs
• Electrons are released
• In galvanic cells: negative terminal
• Mass decreases if electrode participates in reaction

Cathode:

• Electrode where reduction occurs
• Electrons are consumed
• In galvanic cells: positive terminal
• Mass increases if metal ions deposit

2. Electrolyte

Ionic solution that allows ion flow between electrodes. Must contain ions of the electrode material or other species that can undergo redox reactions.

3. Salt Bridge

Function:

• Maintains electrical neutrality in half-cells
• Allows ion migration without mixing solutions
• Completes the internal circuit

Why needed? Without salt bridge:

• Zn²⁺ accumulates in anode compartment → positive charge builds up
• Cu²⁺ depletes in cathode compartment → negative charge builds up
• This charge separation stops electron flow!

Salt bridge action:

• Anions (Cl⁻) migrate toward anode
• Cations (K⁺) migrate toward cathode
• Neutralizes charge buildup

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Cell Notation (Cell Diagram)

Standard Representation

$$\text{Anode} | \text{Anode electrolyte} || \text{Cathode electrolyte} | \text{Cathode}$$

Notation Rules

1. Anode on left, cathode on right
2. | represents phase boundary (solid|liquid, gas|liquid)
3. || represents salt bridge
4. , separates species in same phase
5. Concentrations/pressures in parentheses
6. Inert electrodes (Pt, graphite) written explicitly

Examples

Example 1: Daniell cell

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

Example 2: Hydrogen-silver cell

$$\text{Pt}_{(s)} | \text{H}_2_{(1 \text{ atm})} | \text{H}^+_{(1M)} || \text{Ag}^+_{(1M)} | \text{Ag}_{(s)}$$

Example 3: Gas electrode with inert electrode

$$\text{Pt}_{(s)} | \text{Fe}^{2+}_{(aq)}, \text{Fe}^{3+}_{(aq)} || \text{Cl}_2_{(g)} | \text{Cl}^-_{(aq)} | \text{Pt}_{(s)}$$

Example 4: Concentration cell

$$\text{Pt}_{(s)} | \text{H}_2_{(1 \text{ atm})} | \text{H}^+_{(0.1M)} || \text{H}^+_{(1M)} | \text{H}_2_{(1 \text{ atm})} | \text{Pt}_{(s)}$$

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Electromotive Force (EMF)

Definition

EMF (E°cell) is the potential difference between two electrodes when no current is flowing (open circuit).

Standard EMF

Standard conditions:

• Temperature: 298 K (25°C)
• Pressure: 1 bar (≈ 1 atm)
• Concentration: 1 M for all solutions
• Pure solids and liquids

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

Calculating Cell EMF

For Daniell cell:

• $E°(\text{Cu}^{2+}/\text{Cu}) = +0.34 \text{ V}$ (cathode)
• $E°(\text{Zn}^{2+}/\text{Zn}) = -0.76 \text{ V}$ (anode)

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

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Standard Hydrogen Electrode (SHE)

The SHE is the universal reference electrode with assigned potential of 0.00 V.

Construction

• Electrode: Platinum foil coated with platinum black (high surface area)
• Gas: Pure H₂ at 1 bar pressure
• Electrolyte: 1 M H⁺ (usually HCl)
• Temperature: 298 K

Reaction

As anode (oxidation):

$$\text{H}_2 \rightarrow 2\text{H}^+ + 2e^-$$

(E° = 0.00 V)

As cathode (reduction):

$$2\text{H}^+ + 2e^- \rightarrow \text{H}_2$$

(E° = 0.00 V)

Cell Notation

$$\text{Pt}_{(s)} | \text{H}_2_{(1 \text{ bar})} | \text{H}^+_{(1M)} || \text{...}$$

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Common Electrode Systems

1. Metal-Metal Ion Electrode

Example: Zn/Zn²⁺, Cu/Cu²⁺

$$\text{M}^{n+} + ne^- \rightarrow \text{M}$$

Cell notation: $\text{M} | \text{M}^{n+}$

2. Gas Electrode

Example: Hydrogen electrode, Chlorine electrode

$$\text{Cl}_2 + 2e^- \rightarrow 2\text{Cl}^-$$

Cell notation: $\text{Pt} | \text{Cl}_2 | \text{Cl}^-$

Requires inert electrode (Pt) to transfer electrons

3. Redox Electrode

Example: Fe³⁺/Fe²⁺

$$\text{Fe}^{3+} + e^- \rightarrow \text{Fe}^{2+}$$

Cell notation: $\text{Pt} | \text{Fe}^{2+}, \text{Fe}^{3+}$

Both species in same solution, need inert electrode

4. Metal-Insoluble Salt Electrode

Example: Calomel electrode (Hg/Hg₂Cl₂)

$$\text{Hg}_2\text{Cl}_2 + 2e^- \rightarrow 2\text{Hg} + 2\text{Cl}^-$$

Example: Silver-silver chloride electrode

$$\text{AgCl} + e^- \rightarrow \text{Ag} + \text{Cl}^-$$

Cell notation: $\text{Ag} | \text{AgCl}_{(s)} | \text{Cl}^-$

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Measuring Standard Electrode Potential

Setup with SHE

To find $E°(\text{Zn}^{2+}/\text{Zn})$:

Cell:

$$\text{Zn}_{(s)} | \text{Zn}^{2+}_{(1M)} || \text{H}^+_{(1M)} | \text{H}_2_{(1 \text{ bar})} | \text{Pt}_{(s)}$$

Measured EMF: E°cell = +0.76 V

$$E°_{\text{cell}} = E°_{\text{cathode}} - E°_{\text{anode}}$$ $$0.76 = 0.00 - E°(\text{Zn}^{2+}/\text{Zn})$$ $$\boxed{E°(\text{Zn}^{2+}/\text{Zn}) = -0.76 \text{ V}}$$

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Spontaneity and Cell Potential

Relationship with Gibbs Free Energy

$$\boxed{\Delta G° = -nFE°_{\text{cell}}}$$

where:

• $n$ = number of electrons transferred
• $F$ = Faraday’s constant = 96,500 C/mol
• $E°_{\text{cell}}$ in volts
• $\Delta G°$ in joules

Spontaneity Criteria

E°cell	ΔG°	Reaction
Positive	Negative	Spontaneous
Zero	Zero	At equilibrium
Negative	Positive	Non-spontaneous

For Daniell cell:

$$\Delta G° = -2 \times 96500 \times 1.10 = -212,300 \text{ J} = -212.3 \text{ kJ}$$

The large negative ΔG° confirms highly spontaneous reaction!

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Practice Problems

Level 1: JEE Main

Q1. Write the cell notation for a cell with the following reaction:

$$\text{Mg}_{(s)} + 2\text{Ag}^+_{(aq)} \rightarrow \text{Mg}^{2+}_{(aq)} + 2\text{Ag}_{(s)}$$

Q2. In a galvanic cell, which electrode is the cathode?

• (a) Where oxidation occurs
• (b) Where reduction occurs
• (c) The negative terminal
• (d) Where electrons are produced

Q3. Calculate E°cell for:

$$\text{Zn}_{(s)} + 2\text{Ag}^+_{(aq)} \rightarrow \text{Zn}^{2+}_{(aq)} + 2\text{Ag}_{(s)}$$

Given: E°(Ag⁺/Ag) = +0.80 V, E°(Zn²⁺/Zn) = -0.76 V

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Level 2: JEE Main/Advanced

Q4. For the cell:

$$\text{Pt} | \text{H}_2(1 \text{ atm}) | \text{H}^+(1M) || \text{Ni}^{2+}(1M) | \text{Ni}$$

If E°cell = -0.25 V, find E°(Ni²⁺/Ni).

Q5. A galvanic cell is set up with aluminum and silver electrodes. Write:

• (a) Half-reactions at each electrode
• (b) Overall cell reaction
• (c) Cell notation Given: E°(Al³⁺/Al) = -1.66 V, E°(Ag⁺/Ag) = +0.80 V

Q6. Why is a salt bridge necessary in a galvanic cell? What happens if it’s removed?

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Level 3: JEE Advanced

Q7. For the cell:

$$\text{Pt} | \text{Fe}^{2+}(0.1M), \text{Fe}^{3+}(0.01M) || \text{Ag}^+(1M) | \text{Ag}$$

Write the cell reaction and calculate E°cell. Given: E°(Fe³⁺/Fe²⁺) = +0.77 V, E°(Ag⁺/Ag) = +0.80 V

Q8. Calculate ΔG° for the reaction:

$$3\text{Cu}_{(s)} + 2\text{Au}^{3+}_{(aq)} \rightarrow 3\text{Cu}^{2+}_{(aq)} + 2\text{Au}_{(s)}$$

Given: E°(Au³⁺/Au) = +1.50 V, E°(Cu²⁺/Cu) = +0.34 V

Q9. Design a galvanic cell that uses the reaction:

$$2\text{Al}_{(s)} + 3\text{Cd}^{2+}_{(aq)} \rightarrow 2\text{Al}^{3+}_{(aq)} + 3\text{Cd}_{(s)}$$

Write cell notation and calculate E°cell. Given: E°(Al³⁺/Al) = -1.66 V, E°(Cd²⁺/Cd) = -0.40 V

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Solutions to Practice Problems

A1. $\text{Mg}_{(s)} | \text{Mg}^{2+}_{(aq)} || \text{Ag}^+_{(aq)} | \text{Ag}_{(s)}$

A2. (b) Where reduction occurs

A3. E°cell = 0.80 - (-0.76) = 1.56 V

A4. E°(Ni²⁺/Ni) = E°cathode = E°cell + E°anode = -0.25 + 0 = -0.25 V

A7. Cell reaction: Fe²⁺ + Ag⁺ → Fe³⁺ + Ag; E°cell = 0.80 - 0.77 = 0.03 V

A8. n = 6, E°cell = 1.50 - 0.34 = 1.16 V ΔG° = -6 × 96500 × 1.16 = -671.88 kJ

A9. $\text{Al}_{(s)} | \text{Al}^{3+}_{(aq)} || \text{Cd}^{2+}_{(aq)} | \text{Cd}_{(s)}$; E°cell = -0.40 - (-1.66) = 1.26 V

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Common Mistakes to Avoid

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Key Points for JEE

Must Remember

1. AN OX, RED CAT - Anode oxidation, Reduction cathode
2. E°cell = E°cathode - E°anode (ALWAYS!)
3. Positive E°cell → Spontaneous → Galvanic cell
4. Standard conditions: 298 K, 1 bar, 1 M
5. Salt bridge maintains electrical neutrality

Quick Formulas

$$\boxed{E°_{\text{cell}} = E°_{\text{cathode}} - E°_{\text{anode}}}$$ $$\boxed{\Delta G° = -nFE°_{\text{cell}}}$$ $$\boxed{E°_{\text{cell}} > 0 \implies \text{Spontaneous}}$$

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Real-Life Applications

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Related Topics

Within Electrochemistry

• Oxidation-Reduction - Understanding redox fundamentals
• Electrode Potentials - Electrochemical series and predictions
• Nernst Equation - EMF at non-standard conditions
• Electrolysis - Non-spontaneous electrochemical reactions
• Batteries - Practical galvanic cells (primary and secondary)
• Corrosion - Electrochemical degradation of metals

Cross-Chapter Connections

• Thermodynamics - Gibbs Energy - ΔG° = -nFE° relationship
• Thermodynamics - Enthalpy - Heat effects in cells
• Chemical Equilibrium - Relationship between K and E°
• Chemical Kinetics - Reaction rates at electrodes
• Ionic Equilibrium - Ion concentrations in cells
• Solutions - Concentration Methods - Molarity in cell calculations

Foundation Topics

• Stoichiometry - Mole calculations in electrolysis
• Mole Concept - Faraday’s laws calculations

Physics Connections

• Current Electricity - Ohm’s law, resistance in circuits
• Electrostatics - Electric potential concepts
• Drift Velocity - Electron movement

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