Electrochemistry

Electrochemistry: Study of chemical changes producing/accompanying electrical energy and vice versa.

Electrolytes: Conduct electricity in molten/aqueous state due to ions. Two types:

• Strong: Completely dissociate (NaCl, HCl, NaOH, $H_2SO_4$)
• Weak: Partially dissociate ($CH_3COOH, NH_4OH$)

Non-electrolytes: Do not conduct (e.g., glucose, urea).

Conductance: Reciprocal of resistance, $G = 1/R$. Unit: siemens (S) or $\Omega^{-1}$.

Specific Conductance (Conductivity, $\kappa$ "kappa"): $$\kappa = \frac{1}{\rho} = \frac{l}{RA}$$

• $\kappa$ unit: S/m or S·cm⁻¹
• Conductance of 1 cm cube of solution

Cell Constant ($l/A$): Geometric factor of conductivity cell; constant for a given cell.

Molar Conductivity ($\Lambda_m$): Conductance of all ions from 1 mole of electrolyte: $$\Lambda_m = \frac{\kappa \times 1000}{c}$$ where $c$ = concentration in mol/L. Unit: S·cm²/mol.

Equivalent Conductivity ($\Lambda_{eq}$): Conductance for 1 equivalent. $\Lambda_{eq} = \kappa \times 1000/N$.

Variation with concentration:

• $\kappa$ decreases with dilution (fewer ions per cm³)
• $\Lambda_m$ increases with dilution (more dissociation in weak electrolytes; more freedom of ion movement in strong)

Strong vs Weak Electrolyte Behavior:

For strong electrolytes, Debye-Hückel-Onsager: $\Lambda_m = \Lambda_m^\ominus - A\sqrt{c}$ (linear with $\sqrt c$).

• Extrapolation to $c = 0$ gives $\Lambda_m^\ominus$ (limiting molar conductivity, at infinite dilution).

For weak electrolytes: $\Lambda_m$ increases sharply at low $c$ (more dissociation). Cannot find $\Lambda_m^\ominus$ by extrapolation; use Kohlrausch's law.

Kohlrausch's Law of Independent Ion Migration: At infinite dilution, each ion contributes independently to $\Lambda_m^\ominus$: $$\Lambda_m^\ominus = \nu_+ \lambda_+^\ominus + \nu_- \lambda_-^\ominus$$

where $\nu$ = number of cations/anions, $\lambda^\ominus$ = limiting ionic conductivity.

Application: Find $\Lambda_m^\ominus$ for weak electrolytes: $\Lambda_m^\ominus(CH_3COOH) = \Lambda_m^\ominus(CH_3COONa) + \Lambda_m^\ominus(HCl) - \Lambda_m^\ominus(NaCl)$.

Degree of Dissociation ($\alpha$) of Weak Electrolyte: $$\alpha = \frac{\Lambda_m}{\Lambda_m^\ominus}$$

For acid HA: $K_a = c\alpha^2/(1-\alpha)$.

Electrochemical Cells: Devices for interconversion of chemical and electrical energy.

Two Types:

Galvanic Cell Components:

• Anode: Oxidation (loss of e⁻); negative terminal in galvanic cell
• Cathode: Reduction (gain of e⁻); positive terminal in galvanic cell
• Salt bridge: Maintains electrical neutrality; contains KCl or KNO₃ in agar
• External circuit: Wire connecting electrodes

Daniell Cell:

• Anode: Zn rod in ZnSO₄ solution; Zn → Zn²⁺ + 2e⁻
• Cathode: Cu rod in CuSO₄ solution; Cu²⁺ + 2e⁻ → Cu
• Overall: $\text{Zn} + \text{Cu}^{2+} \to \text{Zn}^{2+} + \text{Cu}$
• $E^\ominus_{cell} = 1.10$ V

Cell Notation: Anode | Anode soln || Cathode soln | Cathode. Daniell: $\text{Zn(s)} | \text{Zn}^{2+}(1M) || \text{Cu}^{2+}(1M) | \text{Cu(s)}$

EMF (Electromotive Force): Potential difference between electrodes when no current flows; max work obtainable. $$E_{cell} = E_{cathode} - E_{anode}$$

Always: $E_{cathode} > E_{anode}$ for spontaneous cell, so $E_{cell} > 0$.

Standard Electrode Potential ($E^\ominus$): Potential of electrode at $1$ M concentration, $1$ bar, $298$ K, relative to SHE.

Standard Hydrogen Electrode (SHE): Reference; $E^\ominus = 0$ V.

• Half-reaction: $2H^+ + 2e^- \rightleftharpoons H_2$; $H_2$ gas at $1$ bar, $H^+$ at $1$ M

Electrochemical Series: Half-cells arranged by decreasing $E^\ominus$:

Higher $E^\ominus$: Better oxidizing agent (gets reduced). Lower $E^\ominus$ (more negative): Better reducing agent (gets oxidized; better at giving electrons).

Free Energy and EMF: $$\Delta G^\ominus = -nFE^\ominus_{cell}$$

• $n$: moles of electrons transferred
• $F$ = $96500$ C/mol (Faraday constant)

Nernst Equation: Relates cell EMF to concentration (non-standard conditions).

For: $aA + bB \to cC + dD$: $$E_{cell} = E^\ominus_{cell} - \frac{RT}{nF}\ln\frac{[C]^c[D]^d}{[A]^a[B]^b}$$

At $25°$C ($T = 298$ K), using base-10 log and $R = 8.314$: $$E_{cell} = E^\ominus_{cell} - \frac{0.0591}{n}\log\frac{[C]^c[D]^d}{[A]^a[B]^b}$$

Note: Activities of pure solids and pure liquids = 1.

For a single electrode (e.g., $M^{n+} + ne^- \to M$): $$E_{M^{n+}/M} = E^\ominus_{M^{n+}/M} + \frac{0.0591}{n}\log[M^{n+}]$$

(Positive sign because we use reduction potential and concentration of the oxidized form increases potential.)

Equilibrium Constant Relation: At equilibrium, $E_{cell} = 0$: $$E^\ominus_{cell} = \frac{0.0591}{n}\log K_c$$

So $K_c = 10^{nE^\ominus/0.0591}$.

Effects of Concentration:

• $E_{cell}$ varies if concentrations are not 1 M
• Diluting cathode side decreases $E_{cell}$
• Diluting anode side increases $E_{cell}$

Concentration Cells: Same electrode in two different concentrations. $E^\ominus_{cell} = 0$. $$E_{cell} = \frac{0.0591}{n}\log\frac{[M^{n+}]_{conc}}{[M^{n+}]_{dilute}}$$

Electrolysis: Non-spontaneous chemical change driven by passage of electric current.

Electrolytic Cell:

• Anode (positive, connected to + terminal of battery): Oxidation
• Cathode (negative): Reduction

Products of Electrolysis:

For solution of NaCl (brine):

• Anode: $2Cl^- \to Cl_2 + 2e^-$ (not $O_2$ because of overpotential)
• Cathode: $2H_2O + 2e^- \to H_2 + 2OH^-$ (Na⁺ has lower $E^\ominus$ than H₂O)

For molten NaCl:

• Anode: $2Cl^- \to Cl_2 + 2e^-$
• Cathode: $Na^+ + e^- \to Na$

For copper sulfate (with Cu electrodes — refining):

• Anode: $Cu \to Cu^{2+} + 2e^-$
• Cathode: $Cu^{2+} + 2e^- \to Cu$

(Used in electrorefining of copper.)

Faraday's Laws of Electrolysis:

1st Law: Amount of substance liberated at electrode $\propto$ quantity of charge: $$w = ZIt = ZQ$$ where $Z$ = electrochemical equivalent (g/C), $I$ = current (A), $t$ = time (s), $Q$ = charge.

2nd Law: When same charge passes through different electrolytes, masses of substances deposited are in ratio of equivalent weights: $$\frac{w_1}{w_2} = \frac{E_1}{E_2}$$

Faraday constant: $F = 96500$ C/mol $= eN_A$. Charge of 1 mole of electrons.

Mass deposited: $w = E \cdot Q/F = E \cdot I \cdot t/F$ $w = (M/n) \cdot I t/96500$, where $M$ = molar mass, $n$ = valence change.

Corrosion: Oxidation of metals in environment.

Rusting of Iron: Electrochemical process.

• Anode: $Fe \to Fe^{2+} + 2e^-$
• Cathode: $O_2 + 4H^+ + 4e^- \to 2H_2O$ (or $O_2 + 2H_2O + 4e^- \to 4OH^-$)
• Further: $Fe^{2+}$ oxidized to $Fe^{3+}$; with $H_2O$ → $Fe_2O_3 \cdot xH_2O$ (rust, hydrated $Fe(III)$ oxide)

Conditions: Moisture + air (especially with $CO_2$ or salts dissolved).

Prevention:

• Painting, galvanising (Zn coating), tin plating, electroplating
• Cathodic protection: Connect Fe to a more active metal (Zn, Mg) that corrodes preferentially (sacrificial anode)
• Anodising (Al with $Al_2O_3$ layer)
• Alloying (stainless steel: Fe + Cr + Ni)

Batteries (Commercial Galvanic Cells):

1. Primary cells (non-rechargeable):

Reactions (dry cell):

• Anode: $Zn \to Zn^{2+} + 2e^-$
• Cathode: $2MnO_2 + 2NH_4^+ + 2e^- \to Mn_2O_3 + 2NH_3 + H_2O$

2. Secondary cells (rechargeable):

Lead acid cell (car battery):

• Anode: $Pb + SO_4^{2-} \to PbSO_4 + 2e^-$
• Cathode: $PbO_2 + 4H^+ + SO_4^{2-} + 2e^- \to PbSO_4 + 2H_2O$
• Reverses on charging

Fuel Cells: Convert chemical energy from fuel directly to electricity. $H_2$-$O_2$ fuel cell:

• Anode: $H_2 + 2OH^- \to 2H_2O + 2e^-$
• Cathode: $O_2 + 2H_2O + 4e^- \to 4OH^-$
• Used in space programs (Apollo missions); produces drinkable water!