Batteries — Concepts, Formulas & Examples

Batteries are devices that convert chemical energy to electrical energy through redox reactions. CBSE Class 12 and NEET cover batteries in the electrochemistry chapter. Expect one question a year on cell types or emf.

Core Concepts

Primary vs secondary cells

Primary cells cannot be recharged — reaction is not easily reversible. Dry cell (Leclanche) is an example. Secondary cells can be recharged — reactions are reversible. Lead-acid and lithium-ion are examples.

The fundamental difference is thermodynamic reversibility. In a primary cell, the products form structures that cannot be easily converted back to reactants by passing reverse current. In a secondary cell, the electrode materials change phase or oxidation state in a way that can be reversed electrically.

Dry cell (Leclanche)

Zinc anode, carbon rod cathode, NH4Cl paste as electrolyte, MnO2 as depolariser. EMF about 1.5 V. Used in torches, clocks, remotes. Cheap but short-lived.

Half-reactions:

Anode: $\text{Zn} \to \text{Zn}^{2+} + 2e^-$

Cathode: $\text{MnO}_2 + \text{NH}_4^+ + e^- \to \text{MnO(OH)} + \text{NH}_3$

The MnO2 acts as a depolariser — it prevents accumulation of H2 gas at the cathode, which would reduce the cell’s voltage. The carbon rod is just a current collector, not a reactant.

Lead-acid battery

Lead anode, lead dioxide cathode, dilute H2SO4 electrolyte. EMF 2 V per cell, six cells give 12 V. Used in cars. Reversible — can be recharged by passing current backward.

Discharge (producing electricity):

Anode: $\text{Pb} + \text{SO}_4^{2-} \to \text{PbSO}_4 + 2e^-$

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

Overall: $\text{Pb} + \text{PbO}_2 + 2\text{H}_2\text{SO}_4 \to 2\text{PbSO}_4 + 2\text{H}_2\text{O}$

During discharge, both electrodes convert to PbSO4 and H2SO4 concentration decreases (specific gravity drops). During charging, the reverse happens.

The specific gravity of the electrolyte tells you the battery’s charge state. A fully charged lead-acid battery has specific gravity about 1.28; a discharged one drops to about 1.10. This is how mechanics check car batteries with a hydrometer.

Lithium-ion battery

Graphite anode, lithium cobalt oxide cathode, lithium salt in organic solvent. High energy density, light weight. Used in laptops, phones, EVs. Rechargeable many times.

During discharge, Li+ ions move from the graphite anode to the LiCoO2 cathode through the electrolyte. During charging, the reverse happens. The lithium ions intercalate (insert between layers) in both electrode materials — this is why Li-ion batteries are also called “rocking chair batteries.”

Why Li-ion dominates modern electronics:

Highest energy density of any commercial rechargeable battery (~250 Wh/kg vs ~40 Wh/kg for lead-acid)
No memory effect (unlike older NiCd batteries)
Low self-discharge rate
Long cycle life (500-1000+ charge cycles)

Fuel cell

Continuous supply of fuel (e.g. H2) and oxidant (O2). Converts chemical energy to electrical directly without combustion. High efficiency, used in spacecraft.

Anode: $\text{H}_2 \to 2\text{H}^+ + 2e^-$

Cathode: $\frac{1}{2}\text{O}_2 + 2\text{H}^+ + 2e^- \to \text{H}_2\text{O}$

Overall: $\text{H}_2 + \frac{1}{2}\text{O}_2 \to \text{H}_2\text{O}$

The only byproduct is water — making this the cleanest energy conversion possible. Efficiency is about 60-80%, compared to 25-30% for combustion engines.

Nernst Equation and EMF

E_{cell} = E°_{cell} - \frac{RT}{nF} \ln Q

At 25°C (298 K):

E_{cell} = E°_{cell} - \frac{0.0592}{n} \log Q

where $E°_{cell}$ = standard EMF, $n$ = number of electrons transferred, $Q$ = reaction quotient, $F$ = Faraday constant (96485 C/mol).

E°_{cell} = E°_{cathode} - E°_{anode}

For a spontaneous reaction, $E°_{cell}$ must be positive. If negative, the reaction goes in the reverse direction.

Worked Examples

$E_{cell} = E_{cathode} - E_{anode}$ . For a Daniell cell with Cu at +0.34 V and Zn at -0.76 V, EMF = 0.34 - (-0.76) = 1.10 V.

Over time water is lost as hydrogen and oxygen during recharging. Topping up with distilled water keeps the electrolyte at the right level and concentration.

For the Daniell cell ( $\text{Zn} | \text{Zn}^{2+}(0.1\text{M}) || \text{Cu}^{2+}(1\text{M}) | \text{Cu}$ ):

$E°_{cell} = 1.10$ V, $n = 2$

$Q = \frac{[\text{Zn}^{2+}]}{[\text{Cu}^{2+}]} = \frac{0.1}{1} = 0.1$

$E_{cell} = 1.10 - \frac{0.0592}{2} \log(0.1) = 1.10 - \frac{0.0592}{2}(-1) = 1.10 + 0.0296 = 1.13$ V

Lower Zn2+ concentration at the anode increases the cell’s EMF (Le Chatelier — the forward reaction is favoured).

In primary cells, the reactants are consumed and cannot be regenerated. The zinc casing dissolves, MnO2 is reduced, and eventually there is not enough reactant to sustain the current. In secondary cells, repeated cycling causes physical degradation of electrodes (cracking, dendrite formation), eventually reducing capacity.

Comparison of Battery Types

Feature	Dry Cell	Lead-Acid	Li-Ion	Fuel Cell
Type	Primary	Secondary	Secondary	Continuous
EMF	1.5 V	2 V/cell	3.6 V/cell	~1 V
Rechargeable	No	Yes	Yes	N/A (continuous fuel)
Energy density	Low	Low	High	Very high
Weight	Light	Heavy	Light	Light (system heavy)
Main use	Torches, remotes	Cars, UPS	Phones, laptops, EVs	Spacecraft, buses
Lifespan	Months	3-5 years	2-5 years	Depends on fuel supply

Common Mistakes

Saying all batteries can be recharged. Primary cells cannot.

Confusing anode and cathode. In a battery, the anode is where oxidation happens; cathode is where reduction happens.

Writing that lithium-ion is a primary cell. It is secondary.

Forgetting the sign convention. $E°_{cell} = E°_{cathode} - E°_{anode}$ . Students often subtract in the wrong order and get a negative value for a spontaneous cell.

Saying fuel cells store energy. They do not — they convert fuel to electricity continuously. Batteries store energy; fuel cells convert it on demand.

Exam Weightage and Revision

Electrochemistry (including batteries) carries 2-3 NEET questions per year and about 7 marks in CBSE Class 12 boards. JEE frequently asks Nernst equation numericals. The battery types are factual recall; EMF calculations need practice.

Question Type	NEET Frequency	JEE Frequency
Cell EMF calculation	Every year	Every year
Battery type identification	Most years	Occasional
Nernst equation numerical	Occasional	Every year
Fuel cell principle	Every 2 years	Occasional
Lead-acid reactions	Most years	Occasional

For NEET, memorise the three battery types with their electrode materials, EMF, and one application each. For JEE, also practise Nernst equation problems with non-standard concentrations.

Practice Questions

Q1. Calculate the EMF of a cell with Ag+/Ag (+0.80 V) and Zn2+/Zn (-0.76 V).

$E°_{cell} = E°_{cathode} - E°_{anode} = 0.80 - (-0.76) = 1.56$ V. Silver is the cathode (higher reduction potential, reduction happens here). Zinc is the anode (lower reduction potential, oxidation happens here).

Q2. Why does a car battery’s performance drop in cold weather?

Chemical reactions slow down at lower temperatures (lower kinetic energy of molecules). In the lead-acid battery, the rate of the redox reaction decreases, producing less current. Additionally, the electrolyte (H2SO4 solution) becomes more viscous at low temperatures, reducing ion mobility and internal conductivity.

Q3. What advantage does a hydrogen fuel cell have over burning hydrogen as fuel?

A fuel cell converts chemical energy directly to electrical energy, bypassing the heat-to-work conversion that limits combustion engines (Carnot efficiency limit). Fuel cells can achieve 60-80% efficiency; combustion engines manage only 25-35%. Also, fuel cells produce only water — no NOx or other pollutants.

FAQs

Why does a battery have a fixed voltage but variable current?

The voltage (EMF) depends on the electrode materials and is determined by thermodynamics (electrode potentials). The current depends on the external circuit’s resistance (Ohm’s law: I = V/R). A battery can deliver more current to a low-resistance circuit, but its voltage stays roughly constant until nearly discharged.

What happens if you try to recharge a primary cell?

The reactions are not easily reversible. Attempting to recharge can cause gas buildup (H2), overheating, leaking of corrosive electrolyte, and in extreme cases, explosion. Never recharge a primary cell.

Why are lithium-ion batteries sometimes in the news for fires?

Li-ion batteries contain flammable organic solvents as the electrolyte. If damaged (punctured, overcharged, or overheated), internal short circuits can cause thermal runaway — a rapid, uncontrolled temperature increase that ignites the solvent. This is why airline regulations restrict lithium batteries.

Memorise three battery types — dry cell, lead-acid, Li-ion — with anode, cathode and EMF. Covers most PYQs.

Relationship Between Gibbs Energy and Cell Potential

\Delta G = -nFE_{cell}

where $\Delta G$ = Gibbs free energy change, $n$ = moles of electrons transferred, $F$ = Faraday constant (96485 C/mol), $E_{cell}$ = cell potential.

For a spontaneous cell reaction, $E_{cell} > 0$ and $\Delta G < 0$ . The more positive the cell potential, the more energy the battery can deliver.

Worked example: For the Daniell cell ( $E°_{cell} = 1.10$ V, $n = 2$ ):

\Delta G° = -(2)(96485)(1.10) = -212,267 \text{ J/mol} = -212.3 \text{ kJ/mol}

This large negative value confirms the reaction is strongly spontaneous — which is why the Daniell cell produces a reliable voltage.

Faraday’s Laws of Electrolysis

These laws apply to rechargeable batteries during the charging process:

m = \frac{MIt}{nF}

where $m$ = mass deposited, $M$ = molar mass, $I$ = current, $t$ = time, $n$ = electrons per ion, $F$ = Faraday constant.

The mass of substance deposited at an electrode is proportional to the charge passed.

Example: How long does it take to deposit 1 g of copper ( $M = 63.5$ , $n = 2$ ) from CuSO4 using a current of 2 A?

t = \frac{mNF}{MI} = \frac{1 \times 2 \times 96485}{63.5 \times 2} = 1520 \text{ seconds} \approx 25 \text{ minutes}

Why Battery Technology Matters for India

India aims to have 30% electric vehicles by 2030. This requires massive battery production capacity. The choice between lead-acid (cheap but heavy) and lithium-ion (light but expensive) has enormous economic implications. Indian companies are investing in sodium-ion batteries as a potential alternative — sodium is abundant in India while lithium must be imported.

Batteries are redox chemistry packaged for portability. Understand the two half-reactions and the rest is engineering.