Electrochemistry (ISC Class 12): The Complete Chapter 2 Guide with Formulas, Exam Traps and Practice Questions

Electrochemistry is one of those chapters that ISC Class 12 students either love or quietly dread. There is no middle ground. The reason is simple: it sits at the junction of physical chemistry’s two most demanding skills—conceptual clarity about what happens inside a cell, and numerical accuracy in applying formulas that all look deceptively similar.

The good news is that the entire chapter is built on a very small number of ideas. Once you see how conductance, electrode potential, the Nernst equation and free energy are all describing the same story from different angles, the numericals stop being a memory test and start being obvious.

This guide walks through the whole of Chapter 2: Electrochemistry in the order it should be understood — not the order it is usually crammed. It is aligned with the ISC Chemistry (Class XII) syllabus for the Examination Year 2027.

1. Start Here: What Electrochemistry Actually Studies

Electrochemistry is the branch of chemistry that examines the relationship between electrical energy and the chemical changes in a redox reaction.

That relationship runs in two directions, and those two directions give us the two types of cells the entire chapter revolves around.

2. Conductance: What Makes a Solution Conduct Well?

Before touching any formula, understand the three interactions that decide how easily ions move.

(a) Solute–solute interactions (interionic attraction). Dissociated ions attract each other because of opposite charges. The stronger this pull, the harder it is for ions to move. This is the basis on which electrolytes are classified as strong or weak.

(b) Solute–solvent interactions (solvation). Solvent molecules surround the ions, keeping them apart and preventing recombination.

(c) Solvent–solvent interactions (viscosity). A more viscous solvent physically restricts ionic movement.

All three of these resisting effects weaken as temperature rises. Hence:

The four factors, stated the way examiners want them

• Nature of the electrolyte — strong electrolytes ionise almost completely and conduct much better than weak electrolytes.
• Nature of the solvent — the greater the polarity of the solvent, the greater the ionisation, and hence the greater the conduction.
• Concentration — higher concentration means stronger interionic attraction and lower conduction. On dilution, conduction increases.
• Temperature — higher temperature increases dissociation and ionic mobility, so conduction increases.

Metallic vs Electrolytic Conductance

3. Conductivity, Cell Constant and the Two “Conductivities”

Resistance of a conductor is directly proportional to length and inversely proportional to area of cross-section:

Here ρ (rho) is the resistivity or specific resistance — a constant for a given material. A 10 cm copper wire and a 20 cm copper wire have exactly the same resistivity.

Its reciprocal is conductivity (specific conductivity), denoted by κ (kappa):

The term l / A is fixed for a given conductivity cell and is called the cell constant (unit: cm^–1).

If l = 1 cm and A = 1 cm², then κ = G. So:

Equivalent and molar conductivity

Equivalent conductivity (Λ_eq) is the conductance of all the ions produced from one gram equivalent of electrolyte dissolved in V cm³ of solution, with the electrodes 1 cm apart and large enough to contain the whole solution.

Molar conductivity (Λ_m) is the same idea, but for one mole of electrolyte:

The units table you must not confuse

4. Faraday’s Laws of Electrolysis

First Law

W ∝ Q, or W = ZQ = Z × I × t

Z is the electrochemical equivalent — the mass deposited when one coulomb of electricity is passed (i.e., 1 ampere for 1 second).

Second Law

Where 96500 comes from

Consider the electrolysis of molten NaCl: Na⁺ + e^– → Na. One electron produces one atom of sodium, so one mole of electrons produces one mole of sodium.

Charge on one mole of electrons = (1.6023 × 10^–19 C) × (6.023 × 10²³ mol^–1) = 96490 C mol^–1 ≈ 96500 C mol^–1

This is one faraday (F). So 1 F deposits 1/n mole = one gram equivalent of a substance, where n is the number of electrons involved in the electrode reaction.

5. Galvanic Cells, Salt Bridge and Cell Notation

A voltaic cell has two half-cells. Oxidation happens at the anode; reduction at the cathode. Two mnemonics worth keeping:

Functions of the salt bridge

1. To complete the electrical circuit by allowing ions to flow without the two solutions mixing.
2. To maintain the electrical neutrality of the solutions in the two half-cells.

Cell representation

The Daniell cell is written as:

A single vertical line (or forward slash) separates the electrode from the electrolyte. The double line represents the salt bridge. Anode always on the left, cathode always on the right. Get this habit right, and the E°_cell formula never trips you up.

In the Daniell cell:

• Anode: Zn(s) → Zn²⁺ + 2e^–
• Cathode: Cu²⁺ + 2e^– → Cu(s)

Electrons flow from anode to cathode through the external circuit.

6. Electrode Potential and the Standard Hydrogen Electrode

Electrode potential (E) is the tendency of an electrode to lose or gain electrons when it is in contact with a solution of its own ions.

Standard electrode potential (E°) is measured with the metal dipped in a 1 M solution of its ions at a specified temperature. For gases, the standard conditions are 1 atmosphere pressure and 1 M ion concentration.

Here is the conceptual problem: oxidation and reduction always occur together, so a single electrode’s absolute potential can never be measured. We need a reference — the Standard Hydrogen Electrode (SHE), also called the Normal Hydrogen Electrode (NHE).

SHE construction: hydrogen gas at 1 atm bubbled into 1 M HCl, over a foil of platinised platinum. Represented as Pt, H₂(g) | H⁺(1 M), with its potential taken as zero at any specified temperature.

It is reversible with respect to H⁺ ions, working as an anode (H₂ → 2H⁺ + 2e^–) or as a cathode (2H⁺ + 2e^– → H₂) depending on the other half-cell.

Limitations of the SHE

This is a frequently asked short-answer question:

• Difficult to set up and maintain — requires pure H₂ at exactly 1 atmosphere pressure.
• The platinum electrode is easily poisoned by traces of impurities in the gas or solution.
• Maintaining exactly 1 M H⁺ concentration is experimentally difficult.
• Cannot be used with strong oxidising or reducing agents that would react with hydrogen gas.

Because of these, secondary reference electrodes — the calomel electrode and the silver–silver chloride electrode, both calibrated against the SHE — are more commonly used in practice.

How the Zn and Cu potentials were found

Coupling a Zn electrode in 1 M ZnSO₄ with the SHE gives an EMF of 0.76 V, with zinc as the negative electrode. Hence E°(Zn²⁺|Zn) = – 0.76 V.

Coupling a Cu electrode in 1 M CuSO₄ with the SHE gives 0.34 V, with copper as the positive electrode (cathode), since Cu²⁺ is reduced more readily than H⁺. Hence E°(Cu²⁺|Cu) = + 0.34 V.

Copper is reduced in preference to hydrogen; zinc is oxidised in preference to hydrogen. That difference in sign is exactly what allows metals to be ranked in the electrochemical series.

7. The Electrochemical Series and Its Applications

Arranging electrodes in order of increasing standard reduction potential gives the electrochemical series. A selection of values at 298 K:

Four applications of the electrochemical series

1. Comparing oxidising and reducing powers — species at the top (very negative E°) are strong reducing agents; those at the bottom (very positive E°) are strong oxidising agents. F₂ is the strongest oxidising agent in the list; Li the strongest reducing agent.
2. Comparing the relative activities of metals.
3. Predicting the feasibility of a redox reaction — the reaction is spontaneous if the species being reduced has the more positive standard reduction potential than the species being oxidised. Equivalently, E°_cell must come out positive.
4. Calculating the standard EMF of any cell.

8. Cell Potential, EMF and Potential Difference

The EMF of a cell depends on the nature of the reactants, the concentration of the solutions in the two half-cells, and the temperature.

9. The Nernst Equation

Standard potentials assume 1 M concentration at 298 K. Real cells rarely oblige. The Nernst equation tells us what happens otherwise.

For a single electrode

For Mⁿ⁺ + ne^– → M:

where E is the electrode potential at the given concentration, E° the standard electrode potential, R the gas constant, T the temperature in kelvin, F the faraday, and n the number of electrons involved in the electrode reaction.

Since the concentration of a pure solid or liquid is taken as unity, [M] = 1:

Substituting R = 8.314 J K^–1 mol^–1, F = 96500 C and T = 298 K:

For a cell reaction

For the general reaction aA + bB → xX + yY:

Worked example — the Daniell cell. For Zn + Cu²⁺ → Zn²⁺ + Cu, n = 2, and with [Zn] = [Cu] = 1:

Second example. For 2Cr + 3Fe²⁺ → 2Cr³⁺ + 3Fe, n = 6:

For gases, partial pressure in atmospheres replaces concentration.

10. Equilibrium Constant and Gibbs Free Energy

K_c from the Nernst equation

As a Daniell cell runs, [Cu²⁺] falls and [Zn²⁺] rises. Eventually the two electrode potentials become equal, the current stops flowing, and E_cell = 0. The cell reaction has reached equilibrium. Substituting E_cell = 0:

So the standard EMF of a cell directly gives its equilibrium constant.

Free energy

In an electrochemical cell, the electrical work done by the cell equals the decrease in free energy of the system. Since one mole of electrons carries one faraday, n moles carry nF:

Combining this with the expression above:

Predicting spontaneity — the table to memorise

11. Variation of Molar Conductivity with Concentration

Strong electrolytes

Molar conductivity varies with concentration according to Kohlrausch’s equation:

where Λ°_m is the molar conductivity at infinite dilution and b is a constant depending on the nature of the solvent and the temperature. A plot of Λ_m against √c is linear at low concentration and deviates from linearity at higher concentrations. Extrapolating this line to c = 0 gives Λ°_m directly.

Weak electrolytes

Weak electrolytes furnish far fewer ions, so their conductance is much lower than that of a strong electrolyte at the same concentration. For CH₃COOH, molar conductivity rises steeply on dilution — especially near infinite dilution — because dilution increases ionisation and therefore the number of ions in solution. But the curve runs almost parallel to the Λ_m axis and never reaches a limiting value, so it cannot be extrapolated. Λ°_m for a weak electrolyte must be obtained indirectly.

12. Kohlrausch’s Law of Independent Migration of Ions

For an electrolyte A_xB_y:

Application 1 — Λ°_m for a weak electrolyte

For acetic acid, write the three strong-electrolyte equations:

• Λ°_m(KCl) = λ°(K⁺) + λ°(Cl^–)
• Λ°_m(CH₃COOK) = λ°(CH₃COO^–) + λ°(K⁺)
• Λ°_m(HCl) = λ°(H⁺) + λ°(Cl^–)

Then:

The K⁺ and Cl^– terms cancel, leaving exactly λ°(CH₃COO^–) + λ°(H⁺). Elegant, and very examinable.

Application 2 — degree of dissociation

This gives the fraction of ions actually available at concentration c out of the total number possible at infinite dilution. It holds good only for weak electrolytes.

13. Batteries and Fuel Cells

A battery is a galvanic cell, or a series of cells, designed to be self-contained.

Lead storage battery

Six cells in series; lead anode, 38% H₂SO₄, PbO₂ cathode.

Rechargeable, because both reactions are reversible. Its state of charge can be checked by testing the density of the electrolyte — H₂SO₄ is progressively replaced by water as the battery discharges.

Dry cell

Zn can as anode; moist paste of MnO₂, NH₄Cl and ZnCl₂ in starch; carbon rod cathode.

Alkaline battery

NH₄Cl replaced by KOH or NaOH. The Zn anode corrodes less, and the cell voltage stays more constant because all species in the net reaction are condensed phases.

Mercury battery

Zn/Hg amalgam anode, paste of KOH, Zn(OH)₂ and HgO, steel cathode.

Voltage remains constant until the reactants are spent, again because all species are in condensed phases.

Ni-Cad battery

Rechargeable, since both reactions are reversible.

Fuel cell

A galvanic cell in which the reactants are supplied continuously. In the H₂–O₂ fuel cell, porous carbon electrodes with Ni and NiO catalysts sit in hot KOH solution; E° = 1.23 V.

• Anode: 2H₂(g) → 4H⁺(aq) + 4e^–
• Cathode: O₂(g) + 4H⁺(aq) + 4e^– → 2H₂O(l)

The steam generated is condensed and used as drinking water — which is why fuel cells were used on space missions.

14. Corrosion

Corrosion is the undesired oxidation of metals to oxides and other compounds. When the metal is iron, we call the process rusting.

The surface of a metal acts as a tiny voltaic cell wherever there is a difference in potential between two points — caused by water vapour, impurities in the metal, or stressed regions created during machining.

Oxidation half-reaction: Fe(s) → Fe²⁺(aq) + 2e^–    E°_ox = 0.44 V

The reduction half-reaction depends on the pH and on the availability of oxygen. Under normal conditions, water in contact with air carries enough dissolved oxygen for:

Combining the two gives the net rusting reaction:

which is further oxidised:

Fe(OH)₃ is an idealised formula, often written Fe₂O₃·3H₂O. Losing variable amounts of water gives the familiar rust, Fe₂O₃(H₂O)_x.

Methods of preventing corrosion

• Plating with an inert metal such as chromium — but only if the plating is free of cracks. Tin cans work this way; once scratched, however, rusting is rapid, with iron acting as the anode and tin as the cathode.
• Sacrificial protection — coating with zinc, which oxidises more readily than iron and is “sacrificed”. Zn acts as a sacrificial anode, so no rusting occurs even if the coating is scratched. This is galvanisation.
• Self-protective coatings — aluminium forms a stable Al₂O₃ layer; copper forms a green CuCO₃ patina.
• Protective coatings such as the paints used on titanium alloys.
• Annealing — heating followed by slow cooling — slows down the rate of corrosion.

What speeds corrosion up

Salt (ocean spray, road de-icing salt), acid rain, and regions where the metal has been worked or stressed — the head or tip of a nail, or the point where a nail is bent.

15. Ten Mistakes That Cost Marks Every Year

1. Writing E°_cell = E°_anode – E°_cathode. It is cathode minus anode.
2. Getting n wrong in the Nernst equation. Use the number of electrons in the balanced cell reaction.
3. Confusing κ and Λ_m — and, worse, their units. κ is per cm; Λ_m is cm² per mole.
4. Forgetting the factor of 1000 in Λ_m = κ × 1000 / Molarity.
5. Applying α = Λ^c_m / Λ°_m to strong electrolytes. It is valid only for weak ones.
6. Claiming Λ°_m of a weak electrolyte can be found by extrapolation. It cannot — use Kohlrausch’s law.
7. Saying “conductivity increases on dilution.” κ decreases on dilution (fewer ions per cm³); Λ_m increases. Two different quantities, two opposite trends.
8. Saying electrons flow through the salt bridge. Ions do.
9. Sign errors when converting between oxidation and reduction potentials.
10. Writing log Q upside down — products belong in the numerator, reactants in the denominator.

16. Quick Formula Revision Sheet

17. Test Yourself

1. Why does electrolytic conductance increase with temperature while metallic conductance decreases?
2. A conductivity cell has a cell constant of 1.25 cm^–1. If the conductance of a 0.1 M solution is 2.5 × 10^–3 S, calculate κ and Λ_m.
3. State two limitations of the standard hydrogen electrode and name one secondary reference electrode.
4. Calculate E°_cell for the cell Zn | Zn²⁺(1 M) ‖ Cu²⁺(1 M) | Cu, and predict whether the reaction is spontaneous.
5. Write the Nernst equation for 2Cr + 3Fe²⁺ → 2Cr³⁺ + 3Fe and state the value of n.
6. Why can Λ°_m for acetic acid not be determined graphically? How is it determined?
7. Explain why a scratched galvanised iron sheet still resists rusting, while a scratched tin can rusts rapidly.
8. Given E°_cell = 1.10 V for the Daniell cell, calculate ΔG° and K_c at 298 K. (n = 2)

Frequently Asked Questions

Is Electrochemistry a difficult chapter in ISC Class 12 Chemistry?

It is demanding rather than difficult. The chapter has few independent ideas — most of it flows from conductance and electrode potential. Students find it hard mainly because the formulas look similar, so errors come from picking the wrong one rather than from not knowing the concept.

What is the difference between conductivity and molar conductivity?

Conductivity (κ) is the conductance of a solution held between electrodes 1 cm apart with 1 cm² area — it measures conduction per unit volume. Molar conductivity (Λ_m) is the conductance of all the ions from one mole of electrolyte. On dilution, κ decreases, but Λ_m increases.

Why is the Nernst equation important?

Standard electrode potentials only apply at 1 M concentration and 298 K. The Nernst equation lets you calculate the actual electrode potential or cell EMF at any concentration and temperature, and it is also the route to the equilibrium constant of the cell reaction.

Where does the value 0.0591 in the Nernst equation come from?

It is 2.303 RT / F evaluated at 298 K, with R = 8.314 J K^–1 mol^–1 and F = 96500 C mol^–1. It is valid only at 298 K — at any other temperature you must use the full 2.303 RT / nF form.

Why can the molar conductivity of a weak electrolyte at infinite dilution not be found graphically?

The plot of Λ_m against √c for a weak electrolyte is a steep curve that runs nearly parallel to the Λ_m axis near infinite dilution, so it cannot be extrapolated reliably to c = 0. Λ°_m is instead calculated using Kohlrausch’s law from strong electrolytes.

What is the main difference between a galvanic cell and an electrolytic cell?

A galvanic cell converts chemical energy into electrical energy through a spontaneous redox reaction. An electrolytic cell does the reverse: electrical energy is supplied from outside to drive a non-spontaneous redox reaction.

Final Thought

If you take one thing from this chapter, take this: electrochemistry is one story told four ways. E°_cell tells you whether a reaction will go. ΔG° tells you the same thing in energy units. K_c tells you how far it will go. And the Nernst equation tells you what happens when conditions are not standard. They are all connected by two short equations — ΔG° = – nFE°_cell and E°_cell = (0.0591/n) log K_c.

Learn the connections rather than the individual formulas, and the numericals will start solving themselves.