Batteries and Fuel Cells

Introduction

From the smartphone in your pocket to the electric car in your garage, batteries power our modern world! These portable electrochemical cells have revolutionized technology, enabling everything from pacemakers saving lives to Mars rovers exploring other planets. Understanding battery chemistry is essential not just for JEE, but for comprehending the energy revolution happening right now!

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Interactive: Battery Discharge Animation

Watch lithium ions migrate during battery discharge:

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What is a Battery?

A battery is a collection of one or more electrochemical cells that convert stored chemical energy into electrical energy through spontaneous redox reactions.

Key Terminology

• Cell: Single electrochemical unit
• Battery: One or more cells connected together
• Primary cell: Non-rechargeable (single use)
• Secondary cell: Rechargeable (reversible reactions)
• Fuel cell: Continuous supply of reactants from external source

Classification

graph TD
    A[Batteries] --> B[Primary Cells]
    A --> C[Secondary Cells]
    A --> D[Fuel Cells]
    B --> B1[Dry Cell]
    B --> B2[Alkaline Battery]
    B --> B3[Mercury Cell]
    C --> C1[Lead-Acid Battery]
    C --> C2[Nickel-Cadmium]
    C --> C3[Lithium-Ion]
    D --> D1[Hydrogen-Oxygen]
    D --> D2[Methanol Fuel Cell]

    style B fill:#e74c3c
    style C fill:#2ecc71
    style D fill:#3498db

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Primary Cells (Non-Rechargeable)

Primary cells cannot be recharged because the electrode reactions are irreversible. Once reactants are consumed, the cell is “dead.”

1. Dry Cell (Leclanché Cell)

The most common battery in flashlights, remote controls, and wall clocks!

Construction:

• Anode: Zinc container (Zn)
• Cathode: Carbon rod surrounded by MnO₂ + carbon powder
• Electrolyte: Paste of NH₄Cl + ZnCl₂
• Voltage: ~1.5 V

Reactions:

At Anode (Zn container):

$$\text{Zn} \rightarrow \text{Zn}^{2+} + 2e^-$$

At Cathode (Carbon rod):

$$2\text{MnO}_2 + 2\text{NH}_4^+ + 2e^- \rightarrow \text{Mn}_2\text{O}_3 + 2\text{NH}_3 + \text{H}_2\text{O}$$

Overall:

$$\boxed{\text{Zn} + 2\text{MnO}_2 + 2\text{NH}_4^+ \rightarrow \text{Zn}^{2+} + \text{Mn}_2\text{O}_3 + 2\text{NH}_3 + \text{H}_2\text{O}}$$

Characteristics:

• Voltage slowly decreases as reactants deplete
• NH₃ forms complexes: Zn²⁺ + 2NH₃ → [Zn(NH₃)₂]²⁺
• Not truly “dry” - contains moist paste
• Shelf life: ~2 years

Interactive Demo: See How Different Batteries Work

Explore the electrochemistry inside different types of batteries. Watch electron flow and ion migration during discharge and charging cycles.

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2. Alkaline Battery

Improved version of dry cell with better performance!

Construction:

• Anode: Powdered Zn in gel
• Cathode: MnO₂ powder
• Electrolyte: Concentrated KOH (alkaline)
• Voltage: ~1.5 V

Reactions:

At Anode:

$$\text{Zn} + 2\text{OH}^- \rightarrow \text{ZnO} + \text{H}_2\text{O} + 2e^-$$

At Cathode:

$$2\text{MnO}_2 + \text{H}_2\text{O} + 2e^- \rightarrow \text{Mn}_2\text{O}_3 + 2\text{OH}^-$$

Overall:

$$\boxed{\text{Zn} + 2\text{MnO}_2 \rightarrow \text{ZnO} + \text{Mn}_2\text{O}_3}$$

Advantages over dry cell:

• Longer shelf life (5-10 years)
• More stable voltage
• Better performance in high-drain devices (cameras, toys)
• Less likely to leak

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3. Mercury Cell (Button Cell)

Used in watches, hearing aids, and calculators.

Construction:

• Anode: Zinc-mercury amalgam (Zn-Hg)
• Cathode: Paste of HgO + carbon
• Electrolyte: Paste of KOH + ZnO
• Voltage: ~1.35 V (very stable)

Reactions:

At Anode:

$$\text{Zn}(\text{Hg}) + 2\text{OH}^- \rightarrow \text{ZnO} + \text{H}_2\text{O} + 2e^-$$

At Cathode:

$$\text{HgO} + \text{H}_2\text{O} + 2e^- \rightarrow \text{Hg} + 2\text{OH}^-$$

Overall:

$$\boxed{\text{Zn}(\text{Hg}) + \text{HgO} \rightarrow \text{ZnO} + \text{Hg}}$$

Characteristics:

• Very constant voltage (ideal for watches)
• Long shelf life
• Compact size (button shape)
• Environmental concern: Mercury is toxic (being phased out)

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Secondary Cells (Rechargeable)

Secondary cells have reversible electrode reactions. They can be recharged by passing current in the opposite direction (electrolysis).

1. Lead-Acid Battery (Lead Storage Battery)

The most common car battery since 1859!

Construction:

• Anode: Lead (Pb) grid
• Cathode: Lead dioxide (PbO₂) grid
• Electrolyte: 38% H₂SO₄ solution (≈6 M)
• Voltage per cell: ~2 V
• Car battery: 6 cells in series = 12 V

During Discharge (Galvanic mode):

At Anode (Pb):

$$\text{Pb} + \text{SO}_4^{2-} \rightarrow \text{PbSO}_4 + 2e^-$$

At Cathode (PbO₂):

$$\text{PbO}_2 + 4\text{H}^+ + \text{SO}_4^{2-} + 2e^- \rightarrow \text{PbSO}_4 + 2\text{H}_2\text{O}$$

Overall:

$$\boxed{\text{Pb} + \text{PbO}_2 + 2\text{H}_2\text{SO}_4 \xrightarrow{\text{discharge}} 2\text{PbSO}_4 + 2\text{H}_2\text{O}}$$

During Charging (Electrolytic mode):

Reverse the discharge reaction by applying external voltage (>2 V):

$$\boxed{2\text{PbSO}_4 + 2\text{H}_2\text{O} \xrightarrow{\text{charge}} \text{Pb} + \text{PbO}_2 + 2\text{H}_2\text{SO}_4}$$

Key Observations:

• H₂SO₄ is consumed during discharge → concentration decreases
• Density decreases during discharge (can measure state of charge!)
• Both electrodes convert to PbSO₄ when discharged
• Water is produced during discharge

Advantages:

• High current output (can start car engines!)
• Relatively cheap
• Well-established technology
• Reliable

Disadvantages:

• Heavy (lead is dense: 11.3 g/cm³)
• Contains toxic lead and sulfuric acid
• Lower energy density than modern batteries
• Susceptible to sulfation if left discharged

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2. Nickel-Cadmium (NiCd) Battery

Used in cordless tools, emergency lighting, and portable electronics.

Construction:

• Anode: Cadmium (Cd)
• Cathode: Nickel oxyhydroxide (NiO(OH))
• Electrolyte: Concentrated KOH
• Voltage: ~1.2 V

During Discharge:

At Anode:

$$\text{Cd} + 2\text{OH}^- \rightarrow \text{Cd(OH)}_2 + 2e^-$$

At Cathode:

$$2\text{NiO(OH)} + 2\text{H}_2\text{O} + 2e^- \rightarrow 2\text{Ni(OH)}_2 + 2\text{OH}^-$$

Overall:

$$\boxed{\text{Cd} + 2\text{NiO(OH)} + 2\text{H}_2\text{O} \xrightarrow{\text{discharge}} \text{Cd(OH)}_2 + 2\text{Ni(OH)}_2}$$

During Charging: Reverse the reaction

Characteristics:

• Can deliver high discharge currents
• Long cycle life (1000+ charges)
• Memory effect: Loses capacity if not fully discharged
• Toxic: Cadmium is harmful (being replaced by NiMH)

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3. Nickel-Metal Hydride (NiMH) Battery

Improved replacement for NiCd!

Construction:

• Anode: Hydrogen-absorbing alloy (e.g., LaNi₅)
• Cathode: NiO(OH)
• Electrolyte: KOH
• Voltage: ~1.2 V

During Discharge:

At Anode:

$$\text{MH} + \text{OH}^- \rightarrow \text{M} + \text{H}_2\text{O} + e^-$$

(M = metal alloy)

At Cathode:

$$\text{NiO(OH)} + \text{H}_2\text{O} + e^- \rightarrow \text{Ni(OH)}_2 + \text{OH}^-$$

Advantages over NiCd:

• Higher capacity (30-40% more)
• Less memory effect
• Non-toxic (no cadmium)
• Better for environment

Used in: Hybrid cars (Toyota Prius used NiMH before switching to Li-ion), rechargeable AA/AAA batteries

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4. Lithium-Ion (Li-ion) Battery

The battery powering the modern world!

Construction:

• Anode: Graphite (carbon sheets)
• Cathode: Lithium cobalt oxide (LiCoO₂), or lithium iron phosphate (LiFePO₄)
• Electrolyte: Lithium salt (LiPF₆) in organic solvent
• Separator: Porous polymer membrane
• Voltage: ~3.7 V (higher than other batteries!)

During Discharge:

At Anode (graphite):

$$\text{Li}_x\text{C}_6 \rightarrow x\text{Li}^+ + 6\text{C} + xe^-$$

At Cathode (LiCoO₂):

$$\text{Li}_{1-x}\text{CoO}_2 + x\text{Li}^+ + xe^- \rightarrow \text{LiCoO}_2$$

Overall:

$$\boxed{\text{LiCoO}_2 + 6\text{C} \xrightarrow{\text{discharge}} \text{Li}_{1-x}\text{CoO}_2 + \text{Li}_x\text{C}_6}$$

Lithium ions shuttle back and forth between electrodes (called “rocking chair” mechanism)!

During Charging: Li⁺ ions move from cathode back to anode

Advantages:

• Highest energy density (150-250 Wh/kg)
• High voltage (3.7 V vs 1.2 V for NiMH)
• No memory effect
• Lightweight (lithium is lightest metal: 0.53 g/cm³)
• Low self-discharge

Disadvantages:

• Expensive (requires cobalt)
• Can overheat (requires battery management system)
• Degrades over time (even when not used)
• Safety concerns (can catch fire if damaged)

Applications: Smartphones, laptops, EVs, power tools, drones

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Comparison of Secondary Batteries

Feature	Lead-Acid	NiCd	NiMH	Li-ion
Voltage/cell	2.0 V	1.2 V	1.2 V	3.7 V
Energy density	30-50 Wh/kg	40-60 Wh/kg	60-120 Wh/kg	150-250 Wh/kg
Cycle life	200-300	1000+	500-1000	500-1500
Memory effect	No	Yes	Slight	No
Self-discharge	5%/month	20%/month	30%/month	2-5%/month
Cost	Low	Medium	Medium	High
Toxicity	High (Pb)	High (Cd)	Low	Medium
Applications	Cars	Tools	Hybrids	Electronics, EVs

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Fuel Cells

Fuel cells convert chemical energy directly to electrical energy with continuous supply of reactants from outside. Unlike batteries, they don’t run out as long as fuel is supplied!

Hydrogen-Oxygen Fuel Cell

The most important fuel cell - used in spacecraft and future cars!

Construction:

• Anode: Porous carbon with Pt catalyst
• Cathode: Porous carbon with Pt catalyst
• Electrolyte: Concentrated KOH or acidic polymer membrane
• Fuel: H₂ gas (continuous supply)
• Oxidant: O₂ gas (continuous supply)
• Voltage: ~1.0 V per cell

Reactions (Alkaline electrolyte):

At Anode:

$$2\text{H}_2 + 4\text{OH}^- \rightarrow 4\text{H}_2\text{O} + 4e^-$$

At Cathode:

$$\text{O}_2 + 2\text{H}_2\text{O} + 4e^- \rightarrow 4\text{OH}^-$$

Overall:

$$\boxed{2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}}$$

Energy released: ΔG° = -237 kJ/mol H₂O

Only product: Pure water! (Can be used for drinking in spacecraft)

Reactions (Acidic electrolyte - PEM fuel cell):

At Anode:

$$2\text{H}_2 \rightarrow 4\text{H}^+ + 4e^-$$

At Cathode:

$$\text{O}_2 + 4\text{H}^+ + 4e^- \rightarrow 2\text{H}_2\text{O}$$

Overall: Same as above!

Advantages:

• High efficiency (60-70% vs 40% for combustion engines)
• Zero emissions (only water produced)
• Quiet operation (no moving parts)
• Continuous operation (as long as fuel supplied)
• Scalable (stack cells for more power)

Disadvantages:

• Hydrogen storage is difficult (high pressure tanks or cryogenic)
• Expensive (platinum catalysts)
• Hydrogen production requires energy (often from fossil fuels)
• Limited refueling infrastructure

Applications:

• Spacecraft (Apollo, Space Shuttle, ISS)
• Submarines (German Type 212)
• Cars (Toyota Mirai, Hyundai Nexo)
• Backup power systems

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Other Fuel Cells

Methanol Fuel Cell (DMFC):

• Fuel: Methanol (CH₃OH)
• Anode: CH₃OH + H₂O → CO₂ + 6H⁺ + 6e⁻
• More convenient than H₂ (liquid fuel)
• Lower efficiency

Solid Oxide Fuel Cell (SOFC):

• High temperature (800-1000°C)
• Can use natural gas
• High efficiency (60%+)
• Stationary power generation

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Practice Problems

Level 1: JEE Main

Q1. Which of the following is a primary cell?

• (a) Lead-acid battery
• (b) Dry cell
• (c) Nickel-cadmium battery
• (d) Lithium-ion battery

Q2. What is the voltage of a typical lead-acid car battery?

• (a) 1.5 V (b) 6 V (c) 12 V (d) 24 V

Q3. Write the cathode reaction in a dry cell.

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Level 2: JEE Main/Advanced

Q4. In a lead-acid battery during discharge:

• (a) H₂SO₄ concentration increases
• (b) H₂SO₄ concentration decreases
• (c) Density of electrolyte increases
• (d) Water is consumed

Q5. Why does a mercury cell maintain constant voltage during discharge?

Q6. Calculate the mass of PbO₂ required at the cathode to deliver 0.2 F of charge in a lead-acid battery. Given: M(PbO₂) = 239

Q7. In a hydrogen-oxygen fuel cell, what volume of H₂ (at STP) is needed to produce 1.5 kWh of energy? Given: ΔG° = -237 kJ/mol for H₂O formation, 1 kWh = 3600 kJ

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Level 3: JEE Advanced

Q8. A lead-acid battery has 500 g of H₂SO₄ in 1 L of solution (density = 1.28 g/mL). After discharge, 100 g of H₂SO₄ remains. Calculate:

• (a) Initial concentration of H₂SO₄
• (b) Final concentration of H₂SO₄
• (c) Total charge delivered (assume complete reaction)

Q9. In a lithium-ion battery, the cathode reaction is:

$$\text{LiCoO}_2 \rightleftharpoons \text{Li}_{1-x}\text{CoO}_2 + x\text{Li}^+ + xe^-$$

If a battery with 10 g of LiCoO₂ can extract 0.5 moles of Li⁺, calculate:

• (a) Value of x
• (b) Theoretical capacity in mAh Given: M(LiCoO₂) = 98

Q10. Why can’t we use aqueous electrolytes in lithium-ion batteries? What would happen?

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Solutions to Practice Problems

A1. (b) Dry cell - Non-rechargeable

A2. (c) 12 V - Six 2V cells in series

A3. $2\text{MnO}_2 + 2\text{NH}_4^+ + 2e^- \rightarrow \text{Mn}_2\text{O}_3 + 2\text{NH}_3 + \text{H}_2\text{O}$

A4. (b) H₂SO₄ concentration decreases - It’s consumed in the reaction

A5. Because the electrolyte composition (KOH concentration) remains constant. ZnO and H₂O formed don’t affect [OH⁻].

A6. PbO₂ + 4H⁺ + SO₄²⁻ + 2e⁻ → PbSO₄ + 2H₂O (n = 2) Moles = 0.2/2 = 0.1 mol Mass = 0.1 × 239 = 23.9 g

A7. Energy needed = 1.5 × 3600 = 5400 kJ Moles of H₂O = 5400/237 = 22.78 mol Moles of H₂ = 22.78 mol Volume = 22.78 × 22.4 = 510.3 L

A8. (a) Initial M = 500/98 ÷ 1 = 5.1 M (b) Final M = 100/98 ÷ 1 = 1.02 M (c) H₂SO₄ consumed = 400 g = 4.08 mol From reaction: 2 mol H₂SO₄ → 2 mol e⁻ Charge = 4.08 × 96500 = 393,720 C = 109.4 Ah

A9. (a) Moles of LiCoO₂ = 10/98 = 0.102 mol x = 0.5/0.102 = 4.9 (This is theoretical maximum, impractical!)

A10. Lithium reacts violently with water!

$$2\text{Li} + 2\text{H}_2\text{O} \rightarrow 2\text{LiOH} + \text{H}_2$$

The battery would fail immediately and potentially explode. That’s why Li-ion batteries use organic solvents like ethylene carbonate.

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Common Mistakes to Avoid

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Key Takeaways for JEE

Must Remember

1. Primary cells: Irreversible, non-rechargeable (dry, alkaline, mercury)
2. Secondary cells: Reversible, rechargeable (lead-acid, NiCd, NiMH, Li-ion)
3. Fuel cells: Continuous fuel supply, high efficiency, only water byproduct
4. Lead-acid discharge: Both electrodes → PbSO₄, H₂SO₄ consumed
5. Li-ion: Highest energy density, no memory effect, 3.7 V

Voltage Summary

Battery Type	Voltage per Cell
Dry cell / Alkaline	1.5 V
Mercury cell	1.35 V
Lead-acid	2.0 V
NiCd / NiMH	1.2 V
Li-ion	3.7 V
H₂-O₂ fuel cell	~1.0 V

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Future Battery Technologies (2025+)

Emerging Technologies

• Sodium-ion batteries: Cheaper than Li-ion (sodium abundant)
• Aluminum-air batteries: 1300 Wh/kg theoretical energy density!
• Lithium-sulfur: 2-5× energy density of Li-ion
• Flow batteries: Large-scale grid storage

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Real-Life Applications

Electric Vehicles (2025)

Model	Battery Type	Capacity	Range
Tesla Model Y	Li-ion (NCA)	75 kWh	330 miles
BYD Seagull	LiFePO₄	30 kWh	190 miles
Toyota Mirai	H₂ fuel cell	5.6 kg H₂	400 miles
Nissan Leaf	Li-ion (NMC)	62 kWh	226 miles

Energy Storage

• Grid storage: Tesla Megapack (3 MWh Li-ion)
• Home backup: Tesla Powerwall (13.5 kWh)
• Portable: Power banks (10,000-30,000 mAh Li-ion)

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Related Topics

Within Electrochemistry

• Electrochemical Cells — Fundamental cell principles
• Electrode Potentials — Predicting cell voltages
• Nernst Equation — Voltage vs concentration
• Electrolysis — Charging secondary batteries

Cross-Chapter Connections

• Thermodynamics — Energy efficiency, ΔG calculations
• Chemical Kinetics — Rate of discharge/charge
• Coordination Compounds — Battery electrolytes

Physics Connections

• Current Electricity — Power, energy, resistance
• Electromagnetism — Magnetic effects in batteries

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