Electrochemistry

Electrochemical Cells

**Definition**: An electrochemical cell is a device that either converts chemical energy into electrical energy (galvanic cell) or uses electrical energy to drive non-spontaneous chemical reactions (electrolytic cell).

**Key distinction**: In a galvanic (voltaic) cell, a spontaneous redox reaction produces electrical energy. In an electrolytic cell, external electrical energy drives a non-spontaneous reaction.

**Example**: The Daniell cell converts the spontaneous reaction Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s) into electrical energy, generating an emf of 1.1 V at standard conditions.

**Important exam points**:

Galvanic cells have positive emf values and operate spontaneously

Electrolytic cells require external voltage greater than the cell's emf to operate

When applied external voltage equals the cell emf, no reaction occurs (equilibrium state)

Electron flow is always from anode to cathode through external circuit

Current flow (conventional) is opposite to electron flow

Galvanic Cells: Construction and Function

**Cell components**:

Two half-cells, each containing a metallic electrode immersed in an electrolyte

External circuit: metallic wire connecting electrodes through voltmeter and switch

Internal connection: salt bridge connecting the two electrolyte solutions (or single electrolyte if both electrodes are in same solution)

**Half-cell reactions** (using Daniell cell example):

**Reduction half-reaction (Cathode)**: Cu²⁺(aq) + 2e⁻ → Cu(s)

**Oxidation half-reaction (Anode)**: Zn(s) → Zn²⁺(aq) + 2e⁻

**Electrode definition**:

**Anode**: Electrode where oxidation occurs; negative with respect to solution in galvanic cell

**Cathode**: Electrode where reduction occurs; positive with respect to solution in galvanic cell

**Cell notation convention** (IUPAC):

Format: Anode(left) | Anode electrolyte || Cathode electrolyte | Cathode(right)

Example: Zn(s)|Zn²⁺(aq)||Cu²⁺(aq)|Cu(s)

Double vertical line (||) represents salt bridge

**Cell potential (emf)**:

The potential difference between cathode and anode, measured in volts when no current flows:

**E°cell = E°cathode − E°anode = E°right − E°left**

**Exam-critical points**:

Salt bridge prevents charge accumulation and maintains electrical neutrality

Electron flow direction: anode → cathode (through external wire)

Current direction: cathode → anode (opposite to electron flow)

Standard conditions: all ion concentrations = 1 M, gas pressure = 1 bar, T = 298 K

Standard Electrode Potential and Standard Hydrogen Electrode

**Standard Electrode Potential (E°)**: The potential of a half-cell measured against the standard hydrogen electrode under standard conditions (all concentrations 1 M, gases 1 bar pressure, 298 K).

**Standard Hydrogen Electrode (SHE)**:

Representation: Pt(s) | H₂(g, 1 bar) | H⁺(aq, 1 M)

Half-reaction: H⁺(aq) + e⁻ → ½H₂(g)

**Assigned potential: 0.00 V at all temperatures** (reference electrode)

Construction: Platinum electrode coated with platinum black, dipped in 1 M H⁺ solution with pure H₂ gas bubbling through

**Measuring standard electrode potential**:

When a half-cell is connected with SHE as anode and the half-cell as cathode, the measured emf equals the standard electrode potential of that half-cell:

**E°cell = E°half-cell − E°SHE = E°half-cell − 0 = E°half-cell**

**Examples from standard table**:

Cu²⁺(aq) + 2e⁻ → Cu(s): E° = +0.34 V (Cu²⁺ more easily reduced than H⁺)

Zn²⁺(aq) + 2e⁻ → Zn(s): E° = −0.76 V (H⁺ more easily reduced than Zn²⁺)

**Interpretation of electrode potential values**:

**Positive E°**: Reduced form more stable than H₂ gas; species is better oxidizing agent than H⁺

**Negative E°**: Oxidized form more stable; species is stronger reducing agent than H⁺/H₂ couple

**Trends in standard electrode potentials table**:

F₂/F⁻ has highest E° (+2.87 V): strongest oxidizing agent in aqueous solution

Li⁺/Li has lowest E° (−3.05 V): strongest reducing agent

As E° increases: oxidizing power increases, reducing power of right-side species decreases

As E° decreases (going down): reducing power of left-side species increases

**Real-life application**: Cu does not dissolve in dilute HCl because E°(H⁺/H₂) = 0.00 V > E°(Cu²⁺/Cu) = +0.34 V, meaning H⁺ cannot oxidize Cu. However, HNO₃ oxidizes Cu because NO₃⁻ is a stronger oxidizing agent than H⁺.

**Exam-important fact**: Standard electrode potentials are reduction potentials—they always represent the reduction half-reaction. To find cell emf: E°cell = E°(cathode, reduction) − E°(anode, oxidation)

Nernst Equation

**Definition**: The Nernst equation relates electrode potential under non-standard conditions to the standard electrode potential and the concentration of reactants and products.

**For a single electrode** (reduction half-reaction: Mⁿ⁺ + ne⁻ → M):

**E = E° − (RT/nF) ln(1/[Mⁿ⁺])**

Or equivalently:

**E = E° − (RT/nF) ln[M]/[Mⁿ⁺]** (concentration of solid M = 1)

**For a complete cell reaction**:

**Ecell = E°cell − (RT/nF) ln Q**

Where:

**R** = Gas constant = 8.314 J K⁻¹ mol⁻¹

**F** = Faraday constant = 96,487 C mol⁻¹ (charge of 1 mole of electrons)

**T** = Temperature in Kelvin

**n** = Number of electrons transferred

**Q** = Reaction quotient = [Products]/[Reactants] with stoichiometric coefficients

**At 298 K, converting to base-10 logarithm**:

**E = E° − (0.0592/n) log Q**

**Nernst equation for Daniell cell** (n = 2):

**Ecell = 1.10 − (0.0592/2) log([Zn²⁺]/[Cu²⁺])**

**Nernst equation for Ni|Ni²⁺||Ag⁺|Ag cell** (n = 2):

**Ecell = E°cell − (0.0592/2) log([Ni²⁺]/[Ag⁺]²)**

**Important observations**:

Ecell increases with increasing [Cu²⁺] and decreasing [Zn²⁺] in Daniell cell

When Q = 1 (standard conditions), Ecell = E°cell

When Q = K (equilibrium), Ecell = 0

The equation shows how concentration changes affect cell potential

**Example calculation**: For Mg(s) + 2Ag⁺(0.0001 M) → Mg²⁺(0.130 M) + 2Ag(s)

Q = [Mg²⁺]/[Ag⁺]² = 0.130/(0.0001)² = 1.3 × 10⁷

E°cell = E°(Ag⁺/Ag) − E°(Mg²⁺/Mg) = 0.80 − (−2.36) = 3.16 V

Ecell = 3.16 − (0.0592/2) log(1.3 × 10⁷) = 3.16 − 0.224 = 2.94 V

Relationship Between E°cell, ΔG°, and Equilibrium Constant

**Thermodynamic relationship**:

The Gibbs free energy change is directly related to the electrical work done by the cell:

**ΔG° = −nFE°cell**

Where:

**ΔG°** = Standard Gibbs free energy change

**n** = Number of moles of electrons transferred

**F** = Faraday constant

**E°cell** = Standard cell potential

**Derivation of relationship with Kc**:

At equilibrium, Ecell = 0 and Q = Kc, so:

0 = E°cell − (0.0592/n) log Kc

Rearranging:

**E°cell = (0.0592/n) log Kc**

Or in terms of natural logarithm:

**E°cell = (2.303RT/nF) ln Kc**

**Interpretation**:

**E°cell > 0**: ΔG° < 0; reaction is spontaneous; Kc > 1

**E°cell = 0**: ΔG° = 0; system at equilibrium; Kc = 1

**E°cell < 0**: ΔG° > 0; reaction is non-spontaneous; Kc < 1

**Example**: For Daniell cell reaction:

E°cell = 1.10 V, n = 2

log Kc = (1.10 × 2)/0.0592 = 37.16

Kc = 1.45 × 10³⁷ (extremely large, reaction goes nearly to completion)

**Exam importance**: This relationship allows calculation of equilibrium constants from electrochemical data—useful when direct measurement is difficult.

Electrolytic Cells

**Definition**: An electrolytic cell uses external electrical energy to drive non-spontaneous chemical reactions.

**Comparison with galvanic cells**:

| Feature | Galvanic | Electrolytic |

|---------|----------|-------------|

| **Spontaneity** | Spontaneous (ΔG° < 0) | Non-spontaneous (ΔG° > 0) |

| **E°cell** | Positive | Negative |

| **Anode** | Negative (oxidation occurs) | Positive (oxidation occurs) |

| **Cathode** | Positive (reduction occurs) | Negative (reduction occurs) |

| **External voltage** | None needed | Eext > E°cell required |

| **Power source** | Produces electrical energy | Consumes electrical energy |

**Operating principle**: When external voltage applied equals cell emf, reaction stops (I = 0). When external voltage exceeds cell emf (Eext > E°cell), reaction reverses, and the cell now functions as an electrolytic cell.

**Electrolysis of ionic solutions**: The actual products depend on the relative positions of ions in the electrochemical series and their concentrations. Ions that are easier to oxidize/reduce (higher/lower E° values) preferentially react.

**Exam-critical concept**: In an electrolytic cell, the anode is connected to the positive terminal of the external source, and the cathode to the negative terminal—opposite to the galvanic cell configuration.

Faraday's Laws of Electrolysis

**First Law of Electrolysis**: The amount of substance deposited (or dissolved) at an electrode during electrolysis is directly proportional to the quantity of electricity passed through the cell.

Mathematically: **m ∝ Q**, or **m = (M × Q)/(n × F)**

Where:

**m** = mass of substance deposited (in grams)

**M** = Molar mass of the substance (g/mol)

**Q** = Total charge passed (in coulombs)

**n** = Number of electrons involved in the reduction/oxidation

**F** = Faraday constant = 96,487 C/mol

Also expressed in terms of current and time:

**m = (M × I × t)/(n × F)**

Where **I** = current (in amperes) and **t** = time (in seconds)

**Second Law of Electrolysis**: When the same amount of charge is passed through different electrolytes, the masses of substances deposited at the electrodes are proportional to their chemical equivalent weights (molar mass/number of electrons).

**m₁/m₂ = (M₁/n₁)/(M₂/n₂)**

Or equivalently: **m₁/m₂ = (Eq₁)/(Eq₂)** where Eq = equivalent weight

**Practical applications**:

Electrorefining of metals (purification)

Electroplating (coating objects with metal)

Electrolytic production of chemicals (NaOH, Cl₂, F₂)

Metal extraction from ores

**Example problem**: Calculate mass of Cu deposited when 5 A current passes through CuSO₄ solution for 2 hours.

n = 2 (Cu²⁺ + 2e⁻ → Cu)

Q = I × t = 5 A × (2 × 3600 s) = 36,000 C

m = (64 × 36,000)/(2 × 96,487) = 11.9 g

Conductance and Conductivity

**Electrical conductivity (κ)**: The ability of a solution to conduct electric current; measured in siemens per meter (S m⁻¹) or siemens per centimeter (S cm⁻¹).

**Resistance (R)** and **Resistivity (ρ)** relationship:

**R = ρ × (l/A)**

Where:

**l** = length of conductor (cm)

**A** = cross-sectional area (cm²)

**ρ** = resistivity (Ω cm)

**Conductance (G)**: Reciprocal of resistance:

**G = 1/R** (measured in siemens, S)

**Conductivity (κ)**: Reciprocal of resistivity:

**κ = 1/ρ** (measured in S cm⁻¹)

Therefore: **κ = G × (l/A)** or **G = κ × (A/l)**

**Molar conductivity (Λₘ)**: The conductivity of solution containing 1 mole of electrolyte; measured in S cm² mol⁻¹.

**Λₘ = κ × (1000/c)**

Where:

**c** = concentration of electrolyte in mol L⁻¹ (or M)

The factor 1000 converts cm³ to mL in a liter

Alternative expression:

**Λₘ = (κ/c) × 1000** (when c is in mol dm⁻³)

**Measurement of conductivity**:

Use **conductivity cell** containing two platinum electrodes separated by fixed distance

Cell constant (l/A) is determined using standard KCl solution: **Cell constant = κ(KCl) × G(measured)**

Then for unknown solution: κ = G(measured) × Cell constant

**Variation with concentration**:

**Conductivity (κ)** decreases with dilution (fewer ions per unit volume)

**Molar conductivity (Λₘ)** increases with dilution (ions have more space, less inter-ionic interference)

At infinite dilution (c → 0), molar conductivity approaches maximum value **Λ°ₘ** (molar conductivity at infinite dilution)

**Exam-important distinctions**:

**Electrolytic (ionic) conductivity**: Due to movement of ions in solution

**Electronic conductivity**: Due to movement of free electrons in metals

Kohlrausch's Law

**Statement**: The molar conductivity of an electrolyte at infinite dilution is equal to the sum of molar conductivities of its constituent ions at infinite dilution.

**Mathematical form**: **Λ°ₘ = λ°₊ + λ°₋**

Where:

**Λ°ₘ** = Molar conductivity at infinite dilution

**λ°₊** = Molar conductivity of cation at infinite dilution

**λ°₋** = Molar conductivity of anion at infinite dilution

**For compounds with polyatomic ions**:

**Λ°ₘ(NaCl) = λ°(Na⁺) + λ°(Cl⁻)**

**Λ°ₘ(CaCl₂) = λ°(Ca²⁺) + 2λ°(Cl⁻)**

**Important applications**:

1. **Determination of degree of dissociation (α)**:

**α = Λₘ/Λ°ₘ** (at any concentration)

Where Λₘ is molar conductivity at concentration c, and Λ°ₘ is at infinite dilution

2. **Calculation of unknown molar conductivity**:

If Λ°ₘ of an unknown electrolyte cannot be directly measured, it can be calculated from known ionic conductivities.

3. **Determination of Ka for weak electrolytes**:

For weak electrolyte HA:

**Ka = (α² × c)/(1 − α)** where **α = Λₘ/Λ°ₘ**

Or: **Ka = (Λₘ)² × c / (Λ°ₘ × (Λ°ₘ − Λₘ))**

**Example**: For acetic acid (weak acid):

If Λₘ = 50 S cm² mol⁻¹ at 0.01 M and Λ°ₘ = 390.5 S cm² mol⁻¹

α = 50/390.5 = 0.128

Ka = (0.128)² × 0.01 / (1 − 0.128) = 1.87 × 10⁻⁵

**Exam-critical points**:

Kohlrausch's law applies only at infinite dilution

At finite concentrations, interionic forces cause deviations

Strong electrolytes follow the law more accurately than weak electrolytes

The law is additive—different electrolytes with common ions can be related

Batteries

**Definition**: A battery is a galvanic cell (or combination of cells) that converts chemical energy directly into electrical energy through spontaneous redox reactions.

Lead Storage Battery (Lead-Acid Battery)

**Construction**:

**Anode**: Lead (Pb) plates containing spongy lead

**Cathode**: Lead dioxide (PbO₂) plates

**Electrolyte**: Dilute sulfuric acid (H₂SO₄), approximately 4 M

**Number of cells**: 6 cells in series (each producing ~2.1 V), total ~12 V

**Electrode reactions during discharge**:

**At anode (oxidation)**:

Pb(s) + SO₄²⁻ → PbSO₄(s) + 2e⁻

**At cathode (reduction)**:

PbO₂(s) + 4H⁺ + SO₄²⁻ + 2e⁻ → PbSO₄(s) + 2H₂O(l)

**Overall cell reaction**:

Pb(s) + PbO₂(s) + 2H₂SO₄(aq) → 2PbSO₄(s) + 2H₂O(l)

**Standard cell potential**: E°cell = 2.1 V per cell

**Charging process**: When connected to external source, reactions reverse (electrolytic mode):

PbSO₄ at anode → Pb + SO₄²⁻

PbSO₄ at cathode → PbO₂ + 4H⁺ + SO₄²⁻

**Advantages**:

High cell potential per unit

Can be recharged many times

Can deliver large currents due to low internal resistance

Relatively inexpensive

Reliable and long-lasting

**Disadvantages**:

Heavy (lead is dense)

Cannot be stored indefinitely without maintenance

Sulfation occurs if left uncharged

Produces hydrogen and oxygen gases during overcharging (explosion hazard)

**Exam importance**: Lead storage battery is the most common secondary battery (rechargeable cell) in vehicles.

Hydrogen-Oxygen Fuel Cell

**Definition**: A fuel cell is a galvanic cell in which chemical energy of fuel combustion is directly converted to electrical energy without heat generation.

**Construction of H₂-O₂ fuel cell**:

**Anode (negative electrode)**: Porous carbon electrode where H₂ is oxidized

**Cathode (positive electrode)**: Porous carbon electrode where O₂ is reduced

**Electrolyte**: Acidic or alkaline aqueous solution

**Catalyst**: Platinum or other catalyst to increase reaction rate

**Electrode reactions in acidic medium**:

**At anode (oxidation)**:

H₂(g) → 2H⁺(aq) + 2e⁻ (E° = 0.00 V)

**At cathode (reduction)**:

O₂(g) + 4H⁺(aq) + 4e⁻ → 2H₂O(l) (E° = 1.23 V)

**Overall cell reaction**:

2H₂(g) + O₂(g) → 2H₂O(l)

**Standard cell potential**:

E°cell = 1.23 − 0.00 = 1.23 V

**Electrode reactions in alkaline medium**:

**At anode**:

2H₂(g) + 4OH⁻(aq) → 4H₂O(l) + 4e⁻

**At cathode**:

O₂(g) + 2H₂O(l) + 4e⁻ → 4OH⁻(aq)

**Overall reaction**: Same as acidic medium: 2H₂ + O₂ → 2H₂O

**Advantages of fuel cells**:

High energy density

Environmentally clean—only product is water

Silent operation (no moving parts)

Can operate continuously as long as fuel supplied

High efficiency (up to 60-70%)

Produce no air pollution or greenhouse gases

**Disadvantages**:

High initial cost

Hydrogen storage and safety concerns

Need for catalyst

Slow start-up compared to batteries

Requires pure hydrogen (expensive purification)

**Real-world applications**:

Space programs (Apollo missions used H₂-O₂ fuel cells)

Electric vehicles

Portable power generation

Backup power systems

Future sustainable energy source

**Exam-critical concept**: Fuel cells are non-rechargeable galvanic cells that consume reactants and cannot be regenerated by reversing the reaction with external voltage.

Corrosion and Its Prevention

**Definition**: Corrosion is the spontaneous electrochemical degradation of metals and their alloys when exposed to environmental conditions (moisture, oxygen, etc.).

**Types of corrosion**:

1. **Electrochemical corrosion** (most common)

2. **Direct chemical attack**

**Mechanism of electrochemical corrosion** (rusting of iron example):

Iron corrodes in presence of water and oxygen:

**4Fe(s) + 3O₂(g) + 6H₂O(l) → 4Fe(OH)₃(s)** (overall)

Or: 4Fe(s) + 3O₂(g) + 2H₂O(l) → 4FeO·OH(s) (hydrated iron oxide)

This involves two half-reactions:

**Anode reaction (oxidation)**:

2Fe(s) → 2Fe²⁺(aq) + 4e⁻

**Cathode reaction (reduction)**:

O₂(g) + 2H₂O(l) + 4e⁻ → 4OH⁻(aq)

The Fe²⁺ ions react with OH⁻ ions and oxygen to form rust (Fe₂O₃·nH₂O or FeO·OH).

**Electrochemical cell formation**:

**Anode**: Iron (site of oxidation/corrosion)

**Cathode**: Oxide layer, impurities, or nobler metal (site of O₂ reduction)

**Electrolyte**: Water with dissolved ions (salt, acids, etc.)

**Galvanic corrosion** (when two different metals in contact):

Nobler metal (higher E°) acts as cathode (protected)

More active metal (lower E°) acts as anode (corroded)

This occurs even without oxygen due to potential difference

**Factors affecting corrosion rate**:

**Oxygen availability**: Increased O₂ increases corrosion (faster cathode reaction)

**pH**: Acidic conditions accelerate corrosion

**Presence of salts**: Increases conductivity; NaCl especially increases corrosion

**Temperature**: Higher temperature increases reaction rates

**Nature of metal**: Metals with more negative E° corrode faster

**Presence of impurities**: Creates local galvanic cells

Prevention of Corrosion

**Method 1: Coating/Barrier protection**

**Paint**: Isolates metal from moisture and oxygen

**Oil/Grease**: Prevents water contact

**Plastic coating**: Protects from environment

**Enameling/Varnish**: Forms protective layer

Disadvantage: Must cover entire surface; even small breaks lead to corrosion

**Method 2: Sacrificial anode protection (Cathodic protection)**

**Principle**: Attach a more active metal (higher reducing power, lower E°) to the structure

The active metal oxidizes preferentially while the main metal (cathode) is protected

**Examples**:

Zinc or magnesium plates attached to iron pipes

Zinc coating on steel (galvanizing)

Sacrificial anodes on ship hulls

**Method 3: Impressed current cathodic protection**

**Method**: Apply external voltage to make the structure negative (cathode)

Used for pipelines, buried structures, and ships

Requires continuous power source

**Method 4: Alloying**

**Stainless steel**: Fe + Cr + Ni forms protective chromium oxide layer

**Aluminum alloys**: Form stable Al₂O₃ layer (self-passivating)

These metals develop passive films that prevent further corrosion

**Method 5: Corrosion inhibitors**

Chemical additives (e.g., silicates, phosphates) that:

Form protective films

Reduce electrochemical activity

Increase pH to reduce corrosion

Used in cooling systems and boilers

**Method 6: Environmental control**

Remove dissolved oxygen (deaeration)

Reduce salt concentration

Control pH (keep slightly alkaline)

Reduce temperature where possible

**Real-life example**: Protection of underground pipelines uses combination of:

External plastic coating (barrier)

Sacrificial magnesium anodes buried along pipeline

Impressed current cathodic protection at critical points

Corrosion inhibitors in the liquid being transported

**Exam-important points**:

Corrosion is spontaneous (E°cell > 0, ΔG° < 0) due to formation of lower energy products

Rusting of iron is not simple oxidation but an electrochemical process requiring both oxygen and moisture

Nobler metals (Au, Ag, Cu) corrode much more slowly than active metals (Fe, Zn)

Galvanic series shows relative activity: K > Na > Ca > Mg > Al > Zn > Fe > Ni > Sn > Pb > H > Cu > Hg > Ag > Au

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**Summary of Key Formulae for Board Exam**:

1. **Cell potential**: E°cell = E°cathode − E°anode

2. **Nernst equation**: Ecell = E°cell − (0.0592/n) log Q (at 298 K)

3. **Gibbs energy relation**: ΔG° = −nFE°cell

4. **Equilibrium constant**: E°cell = (0.0592/n) log Kc

5. **Conductivity**: κ = G × (l/A)

6. **Molar conductivity**: Λₘ = κ × (1000/c)

7. **Kohlrausch's law**: Λ°ₘ = λ°₊ + λ°₋

8. **Degree of dissociation**: α = Λₘ/Λ°ₘ

9. **Faraday's law**: m = (M × I × t)/(n × F)

10. **Ka from conductivity**: Ka = (Λₘ)² × c / (Λ°ₘ × (Λ°ₘ − Λₘ))