Electrochemistry Class 12 – Notes, NCERT Solutions, Formulas & CBSE PYQs | Unit 3 Chemistry Guide

Unit 3 – Electrochemistry

3.1 Electrochemical Cells

3.2 Galvanic Cells

3.3 Nernst Equation

3.4 Conductance of Electrolytic Solutions

3.5 Electrolytic Cells and Electrolysis

3.6 Batteries

3.7 Fuel Cells

3.8 Corrosion

1. Introduction to Electrochemistry

Electrochemistry is a branch of chemistry that studies the relationship between electrical energy and chemical reactions.

Definition: It involves two main aspects:
- The production of electricity from the energy released during spontaneous chemical reactions.
- The use of electrical energy to drive non-spontaneous chemical transformations.
Significance: Electrochemistry is important for both theoretical and practical considerations.
- Industrial Applications: Many metals (like sodium), sodium hydroxide, chlorine, fluorine, and other chemicals are produced using electrochemical methods.
- Energy Conversion: Batteries and fuel cells are devices that convert chemical energy into electrical energy and are widely used in various instruments and devices.
- Environmental Benefits: Electrochemical reactions can be energy-efficient and less polluting, making the study of electrochemistry crucial for developing eco-friendly technologies.
- Biological Relevance: The transmission of sensory signals in the body and communication between cells have electrochemical origins.
Nature of the Subject: Electrochemistry is a vast and interdisciplinary subject.

2. Electrochemical Cells

Electrochemical cells consist of two metallic electrodes immersed in electrolytic solutions. They are broadly classified into two types:

2.1. Galvanic (Voltaic) Cells

These cells convert the chemical energy of a spontaneous redox reaction into electrical energy.

Function: In a galvanic cell, the Gibbs energy of a spontaneous redox reaction is converted into electrical work, which can power motors or other electrical devices.
Example: Daniell Cell:
- A Daniell cell (Fig. 2.1 in sources) uses zinc and copper electrodes dipping in solutions of their respective salts.
- The spontaneous reaction is Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s).
- When concentrations of Zn²⁺ and Cu²⁺ ions are 1 mol dm⁻³, the cell has an electrical potential (EMF) of 1.1 V.
- Anode (Negative Potential): Zinc dissolves (oxidation). Electrons flow from the Zn rod to the Cu rod.
- Cathode (Positive Potential): Copper deposits (reduction).
- Current Flow: Current flows from Cu to Zn (opposite to electron flow).
Effect of External Potential:
- If an external opposite potential less than 1.1 V is applied, the galvanic cell reaction continues.
- If the external potential equals 1.1 V, the reaction stops, and no current flows.
- If the external potential exceeds 1.1 V, the reaction reverses, and the cell functions as an electrolytic cell.

2.2. Electrolytic Cells

These cells use electrical energy to drive non-spontaneous chemical reactions.

Function: Electrical energy is supplied to the cell to bring about a desired chemical change.
Example: Electrolysis of copper sulphate solution using copper strips, where Cu²⁺ ions discharge at the cathode.
Industrial Applications: Used for producing metals like sodium and magnesium from their fused chlorides, and aluminum from aluminum oxide.

3. Electrode Potentials

A potential difference develops between an electrode and its electrolyte, which is known as electrode potential.

Standard Electrode Potential (E°):
- Defined when the concentrations of all species involved in a half-cell are unity.
- According to IUPAC convention, standard reduction potentials are called standard electrode potentials.
Calculation of Cell Potential (EMF):
- The cell potential (E_cell) is the difference between the potentials of the two half-cells: E_cell = E_right - E_left.
- Example: For Cu(s) + 2Ag⁺(aq) → Cu²⁺(aq) + 2 Ag(s), E_cell = E°_Ag⁺/Ag - E°_Cu²⁺/Cu.
- Individual half-cell potentials cannot be measured directly; only their difference can be determined.
Measurement of Electrode Potential using Standard Hydrogen Electrode (SHE):
- The Standard Hydrogen Electrode (SHE) is assigned an arbitrary potential of zero volts at 298 K. It is represented by Pt(s)|H₂(g)|H⁺(aq).
- To measure the standard electrode potential of another half-cell, it is coupled with a SHE acting as the anode (reference).
- The measured EMF of the cell then equals the standard reduction potential of the other half-cell, because E°_L for SHE is zero.
- Example:
  - Pt(s)|H₂(g, 1 bar)|H⁺(aq, 1 M)||Cu²⁺(aq, 1 M)|Cu gives 0.34 V, which is E° for Cu²⁺(aq) + 2e⁻ → Cu(s).
  - Pt(s)|H₂(g, 1 bar)|H⁺(aq, 1 M)||Zn²⁺(aq, 1 M)|Zn gives -0.76 V, which is E° for Zn²⁺(aq) + 2e⁻ → Zn(s).
- For the Daniell cell, E°_cell = E°_Cu²⁺/Cu - E°_Zn²⁺/Zn = 0.34V - (-0.76V) = 1.10 V.
Inert Electrodes: Metals like platinum or gold are used as inert electrodes, providing a surface for reactions and electron conduction without participating chemically. Examples include hydrogen and bromine electrodes.
Interpretation of Standard Electrode Potentials:
- If E° > 0, the reduced form is more stable than hydrogen gas.
- If E° < 0, hydrogen gas is more stable than the reduced form.
- Strongest Oxidizing Agent: Species with the highest positive E° (e.g., F₂ gas, E° = 2.87 V).
- Weakest Reducing Agent: The corresponding reduced form of the strongest oxidizing agent (e.g., F⁻ ion).
- Most Powerful Reducing Agent: Species with the lowest (most negative) E° (e.g., Lithium metal, E° = -3.05 V).
- Weakest Oxidizing Agent: The corresponding oxidized form of the most powerful reducing agent (e.g., Li⁺ ion).
- Moving down Table 2.1 (decreasing E°), oxidizing power decreases, and reducing power increases.
Applications: Electrochemical cells and electrode potentials are used to determine pH, solubility products, equilibrium constants, and for potentiometric titrations.

4. Nernst Equation

The Nernst equation describes how electrode potential varies with concentration when it's not at standard conditions (unity concentration).

For a Half-Cell Reaction: For Mⁿ⁺(aq) + ne⁻ → M(s), the electrode potential (E) is given by: E_Mⁿ⁺/M = E°_Mⁿ⁺/M - (RT/nF) ln(1/[Mⁿ⁺]) Where:
- E° is the standard electrode potential.
- R is the gas constant (8.314 JK⁻¹ mol⁻¹).
- F is the Faraday constant (96487 C mol⁻¹).
- T is the temperature in Kelvin.
- n is the number of electrons involved in the reaction.
- [Mⁿ⁺] is the concentration of the species. (Concentration of solid M is taken as unity).
For a Full Cell Reaction: For Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s), the cell potential E(cell) is given by: E(cell) = E°(cell) - (RT/2F) ln([Zn²⁺]/[Cu²⁺]) (at 298K, this simplifies to E(cell) = E°(cell) - (0.059V/n) log([Products]/[Reactants]))
Relation to Gibbs Energy: The electrical work done by a galvanic cell (maximum work obtained reversibly) is equal to the decrease in its Gibbs energy (Δ_r G). Δ_r G = -nFE Under standard conditions: Δ_r G° = -nFE°(cell). For the Daniell cell, Δ_r G° = -2 × 1.1V × 96487 C mol⁻¹ = -212.27 kJ mol⁻¹.

5. Conductance of Electrolytic Solutions

5.1. Basic Definitions and Units

Electrical Resistance (R): Measured in ohm (Ω).
- Formula: R = ρ (l/A), where ρ is resistivity, l is length, A is area of cross-section.
Resistivity (ρ): Also known as specific resistance.
- Definition: Resistance of a substance when it is one meter long and has an area of cross-section of one m².
- Units: Ohm metre (Ω m) or ohm centimeter (Ω cm). (1 Ω m = 100 Ω cm).
Conductance (G): The inverse of resistance.
- Formula: G = 1/R = κ (A/l), where κ is conductivity.
- Units: Siemens (S), equal to ohm⁻¹ (mho) or Ω⁻¹.
Conductivity (κ): Also known as specific conductance.
- Definition: The inverse of resistivity. It is the conductance of a material when it is 1m long and its area of cross-section is 1 m².
- Units: S m⁻¹ or S cm⁻¹ (1 S cm⁻¹ = 100 S m⁻¹).

5.2. Types of Conductors

Conductors: Materials with very large conductivity (e.g., metals like copper, silver, gold, and some non-metals like graphite).
Insulators: Materials with very low conductivity (e.g., glass, ceramics, teflon).
Semiconductors: Materials with conductivity between conductors and insulators (e.g., silicon, gallium arsenide).
Superconductors: Materials with zero resistivity or infinite conductivity.

5.3. Electronic (Metallic) Conductance

Mechanism: Due to the movement of electrons.
Dependence on Factors:
- Nature and structure of the metal.
- Number of valence electrons per atom.
- Temperature: Decreases with an increase in temperature.
- Composition: Remains unchanged as electrons pass through.

5.4. Electrolytic (Ionic) Conductance

Mechanism: Due to the movement of ions present in solutions.
Influence of Electrolytes: When electrolytes are dissolved in water, they furnish ions, increasing the solution's conductivity.
Dependence on Factors:
- Nature of the electrolyte added.
- Size of the ions produced and their solvation.
- Nature of the solvent and its viscosity.
- Concentration of the electrolyte.
- Temperature: Increases with an increase in temperature.
Effect of DC Current: Prolonged passage of direct current through an ionic solution can change its composition due to electrochemical reactions.

5.5. Measurement of Conductivity of Ionic Solutions

Conductivity Cell: Consists of two platinum electrodes (platinized Pt) with a specific area (A) separated by a distance (l).
- The solution between electrodes forms a column whose resistance is R = (l/A)κ⁻¹ = (l/A)ρ.
Cell Constant (G)*: The ratio l/A.
- Determination: Usually determined by measuring the resistance (R) of the cell containing a solution of known conductivity (κ), typically KCl solutions. G = κR*.
- Its dimension is length⁻¹.

6. Variation of Conductivity and Molar Conductivity with Concentration

6.1. Conductivity (κ)

Trend: Always decreases with a decrease in concentration for both weak and strong electrolytes.
Reason: Dilution reduces the number of ions per unit volume, which are responsible for carrying current in the solution.
Definition: The conductivity of a solution at a given concentration is the conductance of one unit volume of solution placed between two platinum electrodes with unit area of cross-section and at a unit distance. So, κ = G (when A and l are unity).

6.2. Molar Conductivity (Λm)

Definition: Conductance of the volume (V) of solution containing one mole of electrolyte placed between two electrodes with area A and unit distance.
- Formula: Λm = κV (where V is the volume containing 1 mole of electrolyte).
- Alternatively, Λm (S cm² mol⁻¹) = (κ (S cm⁻¹) × 1000 (cm³ L⁻¹)) / molarity (mol/L).
- Units: S m² mol⁻¹ or S cm² mol⁻¹ (1 S m² mol⁻¹ = 10⁴ S cm² mol⁻¹).
Trend: Increases with a decrease in concentration (dilution).
Reason: Although conductivity (κ) decreases, the total volume (V) containing one mole of electrolyte increases significantly with dilution, compensating for the decrease in κ.
Limiting Molar Conductivity (Λ°m): The molar conductivity when the concentration approaches zero (infinite dilution).

6.3. Strong Electrolytes

Behavior: Λm increases slowly with dilution.
Equation (Debye-Hückel-Onsager equation for strong electrolytes): Λm = Λ°m - A c^½.
- A plot of Λm versus c^½ yields a straight line.
- The intercept of this line is Λ°m.
- The slope is -A.
- The constant 'A' depends on the solvent, temperature, and type of electrolyte (e.g., 1-1, 2-1, 2-2 electrolytes like NaCl, CaCl₂, MgSO₄).
- Example: For KCl, Λ°m was determined to be 150.0 S cm² mol⁻¹ from the intercept of the Λm vs c^½ plot.
Kohlrausch's Law of Independent Migration of Ions:
- Statement: At infinite dilution, the molar conductivity of an electrolyte is the sum of the limiting molar conductivities of its individual cations and anions.
- Formula: Λ°m = n₊λ°₊ + n₋λ°₋.
  - λ°₊ and λ°₋ are the limiting molar conductivities of the cation and anion, respectively.
  - n₊ and n₋ are the number of cations and anions produced per formula unit of the electrolyte.
- Application: Can be used to determine Λ°m for weak electrolytes. Example: Λ°m for acetic acid (HAc) can be calculated from Λ°m values of strong electrolytes like HCl, NaAc, and NaCl.

6.4. Weak Electrolytes

Behavior: Λm increases steeply with dilution, especially at lower concentrations.
Reason: This increase is primarily due to an increase in the degree of dissociation of the weak electrolyte as dilution increases the number of ions in the solution.
Determining Λ°m: Cannot be obtained by direct extrapolation of Λm to zero concentration because of the steep increase and very low conductivity at extreme dilution. It is instead determined using Kohlrausch's Law.
Degree of Dissociation (α): Can be calculated as α = Λm / Λ°m.
Dissociation Constant (K): Can then be calculated using K = (cα²)/(1-α).

7. Electrolytic Cells and Electrolysis

Electrolysis involves using an external voltage source to drive a non-spontaneous chemical reaction.

7.1. Faraday's Laws of Electrolysis

First Law: The amount of chemical reaction occurring at any electrode during electrolysis is proportional to the quantity of electricity passed through the electrolyte.
Second Law: The amounts of different substances liberated by the same quantity of electricity passing through electrolytic solutions are proportional to their chemical equivalent weights (Atomic Mass of Metal ÷ Number of electrons required to reduce the cation).
Quantity of Electricity (Q): Q = It (where I is current in amperes, t is time in seconds, and Q is in coulombs).
Faraday Constant (F): The charge on one mole of electrons is approximately 96487 C mol⁻¹. This is equivalent to Avogadro's number (N_A) multiplied by the charge on one electron (1.6021 × 10⁻¹⁹ C).

7.2. Products of Electrolysis

The products depend on the oxidizing and reducing species present in the cell and their standard electrode potentials.

Overpotential: Sometimes, an extra potential (overpotential) must be applied for kinetically slow processes to occur, even if thermodynamically feasible.
Examples:
- Molten NaCl: Produces sodium metal at cathode (Na⁺ + e⁻ → Na) and Cl₂ gas at anode (Cl⁻ → ½Cl₂ + e⁻) because only Na⁺ and Cl⁻ ions are present.
- Aqueous NaCl Solution: Produces NaOH, Cl₂, and H₂.
  - At Cathode: H⁺(aq) + e⁻ → ½ H₂(g) is preferred over Na⁺(aq) + e⁻ → Na(s) because H⁺ has a higher (less negative) standard reduction potential (0.00 V vs -2.71 V). The net reaction involves H₂O dissociation: H₂O(l) + e⁻ → ½H₂(g) + OH⁻.
  - At Anode: Cl⁻(aq) → ½ Cl₂(g) + e⁻ (E° = 1.36 V) is preferred over 2H₂O(l) → O₂(g) + 4H⁺(aq) + 4e⁻ (E° = 1.23 V) due to the overpotential of oxygen.
  - Net Reaction: NaCl(aq) + H₂O(l) → Na⁺(aq) + OH⁻(aq) + ½H₂(g) + ½Cl₂(g).
- Sulphuric Acid Electrolysis: For dilute H₂SO₄, O₂ is preferred at the anode. At higher concentrations, S₂O₈²⁻ may be formed instead.

8. Batteries and Fuel Cells

Batteries and fuel cells are practical applications of galvanic cells that convert chemical energy into electrical energy.

8.1. Primary Batteries

Characteristics: Used once and cannot be recharged.
Examples:
- Dry Cell (Leclanché cell):
  - Anode: Zinc container (Zn(s) → Zn²⁺ + 2e⁻).
  - Cathode: Graphite (carbon) rod packed with MnO₂ and NH₄⁺ (MnO₂ + NH₄⁺ + e⁻ → MnO(OH) + NH₃).
  - Electrolyte: A moist paste.
  - Potential: Approximately 1.5 V.
  - Ammonia forms a complex with Zn²⁺ to give [Zn(NH₃)₄]²⁺.
- Mercury Cell:
  - Anode: Zinc-mercury amalgam (Zn(Hg) + 2OH⁻ → ZnO(s) + H₂O + 2e⁻).
  - Cathode: Paste of HgO and carbon (HgO + H₂O + 2e⁻ → Hg(l) + 2OH⁻).
  - Electrolyte: Paste of KOH and ZnO.
  - Overall Reaction: Zn(Hg) + HgO(s) → ZnO(s) + Hg(l).
  - Potential: Approximately 1.35 V, which remains constant because the overall reaction does not involve ions whose concentration changes. Suitable for low-current devices (e.g., hearing aids, watches).

8.2. Secondary Batteries

Characteristics: Can be recharged by passing current in the opposite direction. Can undergo multiple discharge and charge cycles.
Examples:
- Lead Storage Battery:
  - Components: Lead anode, lead dioxide (PbO₂) packed lead grid cathode, and 38% sulphuric acid electrolyte.
  - Discharging Reactions:
    - Anode: Pb(s) + SO₄²⁻(aq) → PbSO₄(s) + 2e⁻.
    - Cathode: PbO₂(s) + SO₄²⁻(aq) + 4H⁺(aq) + 2e⁻ → PbSO₄(s) + 2H₂O(l).
    - Overall: Pb(s) + PbO₂(s) + 2H₂SO₄(aq) → 2PbSO₄(s) + 2H₂O(l).
  - Charging: The reaction is reversed, converting PbSO₄ back to Pb and PbO₂. Commonly used in automobiles and inverters.
- Nickel-Cadmium Cell: Longer life than lead-acid batteries but more expensive.
  - Overall Discharge Reaction: Cd(s) + 2Ni(OH)₃(s) → CdO(s) + 2Ni(OH)₂(s) + H₂O(l).

8.3. Fuel Cells

Function: Convert the chemical energy of fuels directly into electrical energy, similar to galvanic cells.
Advantages:
- More energy-efficient than thermal power plants (which have ~40% efficiency).
- Pollution-free.
Example: Hydrogen-Oxygen Fuel Cell:
- Reactants: H₂ and O₂.
- Products: Water (H₂O).
- Electrode materials, catalysts, and electrolytes are continuously being developed to increase efficiency.
- Used experimentally in automobiles.

9. Corrosion

Corrosion is an electrochemical phenomenon that involves the slow oxidation of metallic surfaces, forming oxides or other salts of the metal.

Examples: Rusting of iron, tarnishing of silver, green coating on copper and bronze.
Economic Impact: Causes significant damage to infrastructure and leads to substantial financial losses.
Mechanism (Rusting of Iron): Occurs in the presence of water and air.
- Anode (Oxidation): Iron loses electrons to form ferrous ions (Fe(s) → Fe²⁺(aq) + 2e⁻).
- Cathode (Reduction): Oxygen gains electrons (O₂(g) + 4H⁺(aq) + 4e⁻ → 2H₂O(l)).
- Overall Initial Reaction: 2Fe(s) + O₂(g) + 4H⁺(aq) → 2Fe²⁺(aq) + 2 H₂O(l) (E°_cell = 1.67 V).
- Further Oxidation: Ferrous ions (Fe²⁺) are further oxidized by atmospheric oxygen to ferric ions, which then form hydrated ferric oxide (Fe₂O₃.xH₂O), commonly known as rust. This process also regenerates hydrogen ions.
Prevention: Crucial for safety and economic reasons.
- Barrier Methods: Preventing contact with the atmosphere (e.g., painting, chemical coatings).
- Metallic Coatings: Covering the surface with other inert metals (like tin, zinc) or metals that react preferentially to protect the object (e.g., galvanization with zinc).
- Sacrificial Protection (Electrochemical Method): Connecting a more reactive metal (like Mg or Zn) that corrodes instead of the protected object.

10. The Hydrogen Economy

The concept of a "Hydrogen Economy" envisions a future where hydrogen serves as a primary source of energy.

Current Energy Sources: Currently, fossil fuels (coal, oil, gas) are the main energy drivers, but their combustion produces carbon dioxide, leading to the "Greenhouse Effect". This causes global temperature rise, polar ice melt, and rising ocean levels.
Hydrogen as an Alternative: Hydrogen is an ideal alternative because its combustion only produces water, making it a non-polluting fuel.
Electrochemical Relevance: Both the production of hydrogen via water electrolysis (using solar energy for sustainability) and its use in fuel cells are based on electrochemical principles, making electrochemistry vital for the realization of a hydrogen economy.

Analogy: Think of electrochemistry as a grand orchestra where chemical reactions are the musical notes and electrical energy is the conductor's baton. A galvanic cell is like a spontaneous, harmonious composition that naturally produces electricity (music) as the chemicals react. An electrolytic cell, on the other hand, is like a controlled composition where we have to use external electricity (the conductor's strong hand) to force non-spontaneous chemical changes (complex, deliberate musical phrases). Electrode potentials are the tuning forks, setting the standard for how much "potential" each half of the reaction has, while the Nernst equation is the sheet music, telling us how these potentials change if the "audience" (concentrations) isn't exactly where we want it to be. The conductance is the smooth flow of the music, and Faraday's laws are the strict rules ensuring that the amount of music produced matches the effort put in. Finally, batteries and fuel cells are like portable music players, storing or generating music efficiently, while corrosion is the unwelcome rust on the instruments, degrading their performance over time, and highlighting the importance of understanding and preventing such processes.

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