Electrochemistry: The Ultimate Text

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Electrochemistry: Complete Treatise

From Fundamentals to Advanced Kinetics

Chapter 1

Fundamentals of Electrochemistry

1.1 Introduction to Redox

Electrochemistry is the study of the interchange between chemical energy and electrical energy. At its core lies the Redox Reaction (Reduction-Oxidation). Unlike simple acid-base reactions, redox involves the actual transfer of electrons from one species to another.

Oxidation: The loss of electrons (increase in oxidation number).
Reduction: The gain of electrons (decrease in oxidation number).
Mnemonic: OIL RIG (Oxidation Is Loss, Reduction Is Gain).

Consider the classic reaction between Zinc and Copper Sulfate. When a Zinc rod is dipped into $CuSO_4$, the blue color fades, and reddish copper precipitates. This is a Direct Redox reaction. The energy is released as heat. Electrochemistry aims to separate these two half-reactions in space, forcing the electrons to travel through a wire, thereby creating Indirect Redox or electricity.

1.2 The Galvanic Cell Construction

To harness the electron flow, we build a Galvanic (Voltaic) Cell. The standard example is the Daniel Cell.

Anode (Left): Zinc rod in $ZnSO_4$. Oxidation occurs here: $Zn \to Zn^{2+} + 2e^-$. The electrode becomes negative as electrons are left behind on the metal.
Cathode (Right): Copper rod in $CuSO_4$. Reduction occurs here: $Cu^{2+} + 2e^- \to Cu$. The electrode becomes positive as it consumes electrons.
Salt Bridge: An inverted U-tube containing an inert electrolyte (like KCl or $KNO_3$) in agar-agar jelly.

Deep Dive: Why KCl in Salt Bridge?

The salt bridge has a specific function: to maintain electrical neutrality and minimize Liquid Junction Potential (LJP). KCl is chosen because the Ionic Mobility of $K^+$ and $Cl^-$ are almost identical. If ions move at different speeds, a charge separation occurs at the junction of the two liquids, creating a potential that opposes the cell voltage.

Advanced Note: If the electrodes contain Silver (Ag), Lead (Pb), or Mercury (Hg), KCl cannot be used because $Cl^-$ would precipitate $AgCl$, $PbCl_2$, or $Hg_2Cl_2$, clogging the bridge. In such cases, $NH_4NO_3$ or $KNO_3$ is used.

Chapter 2

Electrode Potential & Thermodynamics

2.1 The Concept of Potential

Why do electrons move? Because of a potential difference. When a metal $M$ is placed in a solution of its own ions $M^{n+}$, a potential difference develops at the interface. This is called Single Electrode Potential.

We cannot measure the potential of a single half-cell in isolation. We need a reference. The Standard Hydrogen Electrode (SHE) is arbitrarily assigned a potential of 0.00 V at all temperatures.

2.2 Nernst Equation: Derivation

The potential depends on concentration and temperature. Thermodynamics gives us the relation between Gibbs Free Energy ($\Delta G$) and Reaction Quotient ($Q$):

$\Delta G = \Delta G^\circ + RT \ln Q$

We know that electrical work done is equal to the decrease in Gibbs energy: $\Delta G = -nFE_{cell}$. Substituting this into the thermodynamic equation:

$-nFE_{cell} = -nFE^\circ_{cell} + RT \ln Q$

Dividing by $-nF$:

$E_{cell} = E^\circ_{cell} - \frac{RT}{nF} \ln Q$

At 298K, substituting values for $R$ (8.314), $T$ (298), and $F$ (96500) and converting $\ln$ to $\log_{10}$:

$E_{cell} = E^\circ_{cell} - \frac{0.0591}{n} \log Q$

2.3 Thermodynamics of Cells

A cell is a thermodynamic engine. We can calculate fundamental properties from EMF data.

Gibbs Energy: $\Delta G = -nFE_{cell}$. This predicts spontaneity. If $E_{cell} > 0$, reaction is spontaneous.
Entropy ($\Delta S$): Since $\Delta G = \Delta H - T\Delta S$, and $d(\Delta G)/dT = -\Delta S$, we get:
$\Delta S = nF \left( \frac{\partial E_{cell}}{\partial T} \right)_P$
Here, $\frac{\partial E}{\partial T}$ is the Temperature Coefficient of the cell.
Enthalpy ($\Delta H$): The total heat content change.
$\Delta H = nF \left[ T \left( \frac{\partial E}{\partial T} \right) - E \right]$

Chapter 3

Electrolytic Conductance

3.1 Mechanisms of Conduction

Unlike metallic conductors (where electrons flow), electrolytic conductors rely on the movement of ions.

Resistance (R): Obstruction to flow. $R \propto \frac{l}{A}$. Unit: Ohm ($\Omega$).
Conductance (G): Ease of flow. $G = 1/R$. Unit: Siemens (S).
Conductivity ($\kappa$): The conductance of 1 unit volume ($1 cm^3$) of solution. $\kappa = G \times \frac{l}{A}$. The term $\frac{l}{A}$ is the Cell Constant.

3.2 Molar Conductivity ($\Lambda_m$)

Conductivity ($\kappa$) isn't great for comparing electrolytes because it depends on concentration. We normalize this by defining Molar Conductivity: the conducting power of all ions produced by 1 mole of electrolyte.

$\Lambda_m = \frac{\kappa \times 1000}{Molarity}$

3.3 Variation with Dilution (Deep Concept)

This is a critical concept. Upon dilution (adding water):

Conductivity ($\kappa$) DECREASES: Because the number of ions per unit volume decreases.
Molar Conductivity ($\Lambda_m$) INCREASES:
- For Strong Electrolytes (e.g., KCl), inter-ionic attraction decreases, increasing mobility. This follows the Debye-Hückel-Onsager equation: $\Lambda_m = \Lambda_m^\infty - A\sqrt{c}$.
- For Weak Electrolytes (e.g., CH3COOH), the Degree of Dissociation ($\alpha$) increases drastically. The increase is steep (Hyperbolic curve).

3.4 Kohlrausch's Law

Since weak electrolytes never fully dissociate at measurable concentrations, we cannot find their Limiting Molar Conductivity ($\Lambda_m^\infty$) graphically. We use Kohlrausch's Law of Independent Migration of Ions:

"At infinite dilution, each ion makes a definite contribution to the total molar conductivity of the electrolyte, irrespective of the nature of the other ion."

Example Application: To find $\Lambda^\infty$ for Acetic Acid (HAc):
$\Lambda^\infty_{HAc} = \Lambda^\infty_{NaAc} + \Lambda^\infty_{HCl} - \Lambda^\infty_{NaCl}$

Chapter 4

Electrolysis & Commercial Cells

4.1 Quantitative Electrolysis (Faraday's Laws)

Michael Faraday established the quantitative relationship between electricity and chemical change.

First Law: The mass deposited ($W$) is directly proportional to charge passed ($Q$). $W = ZQ = ZIt$.

Second Law: When the same charge is passed through different electrolytes, the mass deposited is proportional to their Equivalent Weights ($E$). $\frac{W_1}{W_2} = \frac{E_1}{E_2}$

4.2 Qualitative Electrolysis (Predicting Products)

This is often called the "Preferential Discharge Theory". When multiple ions compete at an electrode, thermodynamic and kinetic factors decide the winner.

At Anode (Oxidation):

The species with lower Oxidation Potential (higher SRP) is harder to oxidize. However, water complicates things.

Halides (Cl, Br, I): Oxidize preferentially over water to form gas.
Spectator Ions (SO4, NO3): Do not oxidize. Water oxidizes instead ($E^\circ_{ox} = -1.23V$).

At Cathode (Reduction):

Active Metals (Li, K, Na, Ca, Mg, Al): Have very low SRP. They do NOT reduce in aqueous solution. Water reduces to $H_2$ gas instead.
Noble Metals (Cu, Ag, Au): Have high SRP. They reduce and deposit.

4.3 Commercial Batteries

Lead Storage Battery (Secondary Cell): Used in automobiles.
Anode: Pb (s)
Cathode: $PbO_2$ (s)
Electrolyte: 38% $H_2SO_4$
Key Feature: During discharge, $H_2SO_4$ is consumed, lowering density. Charging reverses this.

Fuel Cells ($H_2-O_2$):
Combustion energy is directly converted to electrical energy.
Anode Reaction: $2H_2 + 4OH^- \to 4H_2O + 4e^-$
Cathode Reaction: $O_2 + 2H_2O + 4e^- \to 4OH^-$
Efficiency is very high (~70%) compared to thermal plants (~40%).

Chapter 5

Advanced Topics (The Deepest Dive)

5.1 Transport Numbers & Ionic Mobility

Total current is carried by both cations and anions. The fraction of total current carried by an ion is its Transport Number (t).

$t_+ = \frac{u_+}{u_+ + u_-}$ and $t_- = \frac{u_-}{u_+ + u_-}$

Where $u$ is Ionic Mobility (speed under unit potential gradient).
Hittorf's Rule: The loss of concentration around any electrode is proportional to the speed of the ion moving away from it.

5.2 Concentration Cells

A galvanic cell where the electrodes and electrolyte are the same material, but concentrations differ.
Example: $Pt, H_2(P_1) | H^+(C_1) || H^+(C_2) | H_2(P_2), Pt$
Since $E^\circ = 0$, the cell works purely on entropy (concentration gradient).

Electrochemistry