The Electrochemistry Inside a Lithium-Ion Battery
A lithium-ion cell is not a new kind of chemistry. It is a galvanic cell governed by ΔG = −nFE, with a charge bookkeeping given by Faraday's Q = It — the same two equations you use for a Daniell cell and for electrolysis numericals. What makes it unusual is that neither electrode dissolves. Lithium ions simply move into and out of the layered structures of the two electrodes, so the cell can be run backwards thousands of times. This article computes the numbers a cell datasheet quotes, then explains honestly why a real cell delivers well under half of what the formulas promise.
The formulas you already know
Faraday: Q = It = nF with F = 96 485 C/mol
Specific capacity (mAh/g) = n·F / (3.6 × M) Energy (Wh) = capacity (Ah) × average voltage (V)
What actually happens on charge and discharge
The two electrodes are hosts. On charge, lithium is pulled out of the layered metal oxide and pushed between the graphene sheets of graphite; on discharge it goes back. This is called intercalation, and it is why the cell is often described as a "rocking chair". With a common layered oxide as the positive electrode:
Negative (anode on discharge): LixC₆ → C₆ + x Li⁺ + x e⁻
Overall (discharge): LixC₆ + Li1−xCoO₂ → C₆ + LiCoO₂
Notice that lithium is never present as the metal, and that cobalt is the element actually being reduced and oxidised — it moves between the +3 and +4 states while lithium stays as Li⁺ throughout. Electrons travel through the external circuit and do the useful work; Li⁺ travels through a non-aqueous electrolyte, typically a lithium salt in an organic carbonate solvent mixture, because water would be reduced long before lithium chemistry could happen.
Worked example 1 — theoretical specific capacity of graphite
Fully lithiated graphite is LiC₆: one lithium, and therefore one electron, per six carbons. Using C = 12.011 g/mol, what is the theoretical capacity per gram of carbon?
M(C₆) = 6 × 12.011 = 72.066 g/mol · n = 1
Charge per gram = 96 485 ÷ 72.066 = 1338.85 C/g
Convert to mAh: 1 mAh = 3.6 C, so 1338.85 ÷ 3.6 = 372 mAh/g
Cross-check by moles. 1 g of C₆ units is 1 ÷ 72.066 = 0.013876 mol, giving 0.013876 mol of electrons. In ampere-hours: 0.013876 × 96 485 ÷ 3600 = 0.3719 Ah = 372 mAh ✔
Worked example 2 — the cathode is the limiting side
Now do the same for LiCoO₂, taking Li = 6.94, Co = 58.933 and O = 15.999 g/mol.
M(LiCoO₂) = 6.94 + 58.933 + (2 × 15.999) = 6.94 + 58.933 + 31.998 = 97.871 g/mol
For one electron per formula unit: 96 485 ÷ 97.871 = 985.84 C/g
985.84 ÷ 3.6 = 274 mAh/g if all the lithium could be removed
In practice only about half the lithium is cycled, because removing more destabilises the
layered structure and the electrode degrades. Taking x ≈ 0.5:
usable ≈ 0.5 × 274 ≈ 137 mAh/g
Put the two together and the arithmetic of cell design appears. Per gram of active material the cathode delivers roughly 137 mAh against the anode's 372 mAh, so a balanced cell needs something like 2.7 times as much cathode mass as anode mass. That is why so much effort in the field goes into the positive electrode: it is the heavier, more expensive, capacity-limiting half.
Worked example 3 — charge, lithium moved, and energy stored
A cell is charged at a constant 1.5 A for 2.0 hours. Its nominal voltage is 3.7 V. How much charge passed, how many moles of lithium moved, and how much energy is stored?
Charge: Q = It = 1.5 × 2.0 = 3.0 Ah = 3.0 × 3600 = 10 800 C
Lithium shuttled: n = Q ÷ F = 10 800 ÷ 96 485 = 0.1119 mol
mass = 0.1119 × 6.94 = 0.777 g of lithium moved from one electrode to the other
Energy: E = 3.0 Ah × 3.7 V = 11.1 Wh (= 11.1 × 3600 = 3.996 × 10⁴ J)
ΔG for the cell reaction at 3.7 V with n = 1:
ΔG = −nFE = −1 × 96 485 × 3.7 = −3.57 × 10⁵ J = −357 kJ per mole of lithium —
strongly spontaneous on discharge, which is exactly what a battery must be.
Consistency check: 0.1119 mol × 357 kJ/mol = 39.9 kJ, and the energy computed from Ah × V was 3.996 × 10⁴ J = 40.0 kJ ✔ The two routes agree, as they must, because Ah × V and nFE are the same product written in different units.
Where this is actually used
| Quantity | Where you meet it |
|---|---|
| Capacity in mAh or Ah | Printed on every phone, laptop and power-bank cell — it is charge, not energy |
| Energy in Wh or kWh | Electric-vehicle range and grid storage are quoted in energy, because that is what does work |
| C-rate | The current expressed as a multiple of capacity per hour; 2C on a 3 Ah cell is 6 A. Sets charging speed and heating |
| State of charge | Estimated by counting coulombs (Q = It) and correcting against the open-circuit voltage curve |
| Battery management systems | Keep every cell inside its voltage, current and temperature window — the electrochemistry above defines that window |
| Cell chemistry choice | Different cathode materials trade energy density against cost, thermal stability and cycle life |
| Recycling | Recovery of lithium, cobalt and nickel is itself a separation and electrochemistry problem |
Where the simple formula stops being valid
- An intercalation electrode has no single E°. The Nernst equation assumes a defined couple with well-defined activities. Here the electrode potential changes continuously as x changes, because the composition itself is the variable. That is why a real discharge curve slopes rather than sitting flat, and why "3.7 V" is a nominal average over the discharge, not a constant you can substitute with confidence.
- Aqueous standard-potential tables do not apply. Those E° values are defined against the standard hydrogen electrode in water. This cell runs in a non-aqueous electrolyte, so predicting its voltage by subtracting two numbers out of the Class 12 electrochemical series is not valid — the reference state is different.
- Theoretical capacity is never delivered. The 372 and 274 mAh/g above count only the active material. A real cell also carries binder, conductive additive, copper and aluminium current collectors, separator, electrolyte, casing and tabs — and a pack adds module structure, cooling and electronics. Pack-level energy per kilogram is far below electrode-level. Comparing an electrode number with a pack number is the most common way battery claims are made to look better than they are.
- Terminal voltage depends on current. What you measure is the open-circuit voltage minus IR drop and minus activation and concentration polarisation. Under load the voltage sags; at rest it recovers. A single "cell voltage" is meaningful only with a stated current and state of charge.
- Charge is not conserved in practice. Some lithium is consumed irreversibly forming the passivating layer on the anode surface during the first cycles, and more is lost slowly over life. That is the chemical origin of capacity fade, and no amount of coulomb counting recovers it.
- Thermodynamics gives no rate and no lifetime. ΔG = −nFE says the discharge is spontaneous. It says nothing about how fast lithium can diffuse through the solid, which is what actually limits fast charging, or about how many cycles the structure survives.
- Temperature moves everything. Cold slows ion transport and cuts usable capacity; heat accelerates every degradation reaction. Neither effect is in the equations above.
- Safety is not an academic footnote. These cells store large energy in a flammable electrolyte, and short-circuiting, puncturing, over-charging or heating one can cause a self-sustaining thermal runaway. Cells are not to be opened, dismantled or experimented on outside a properly equipped and supervised laboratory. Follow your institution's rules and the manufacturer's handling and disposal instructions.
Why this matters for JAM, GATE, NET and CUET-PG
| Exam area | What is typically asked |
|---|---|
| Electrochemistry | ΔG = −nFE; Ecell from half-cell potentials; Nernst equation with a reaction quotient |
| Faraday's laws | Q = It = nF; mass deposited or transferred; converting between C, Ah and mol |
| Solid-state / materials chemistry | Layered structures, intercalation, non-stoichiometric compounds, defect chemistry |
| Inorganic chemistry | Oxidation states of transition metals in mixed oxides; why Co goes +3 ⇌ +4 while Li stays +1 |
| Conceptual questions | Why a battery's rating is in mAh (charge) while its usefulness is in Wh (energy) |
Get the cell potential right under real conditions. The Nernst calculator takes E°, n and the reaction quotient and returns E, so you can see directly how the potential shifts as the composition of an electrode changes — the effect that turns a flat E° into a sloping discharge curve.
Open the Nernst Equation Calculator →Preparing for IIT-JAM, GATE, CSIR-NET or CUET-PG chemistry? ABC Chemistry runs dedicated competitive-exam batches at the coaching centre and online across India — details at abcchemistry.in.