Comprehensive Study Notes on Electrochemistry

Introduction to Electrochemistry

• Definition: Electrochemistry is the study of the production of electricity from energy released during spontaneous chemical reactions and the use of electrical energy to facilitate non-spontaneous chemical transformations.

• Importance and Applications:

  • Industrial Production: Used for the production of metals (like sodium, magnesium, and aluminum), sodium hydroxide ($NaOH$), chlorine ($Cl_2$), and fluorine ($F_2$).

  • Energy Storage: Batteries and fuel cells convert chemical energy into electrical energy for use in various devices.

  • Environmental Impact: Electrochemical reactions are often energy-efficient and less polluting, aiding in the development of eco-friendly technologies.

  • Biological Systems: Sensory signals (from cells to the brain and back) and cellular communication have an electrochemical origin.

• Interdisciplinary Nature: It is a vast subject connecting chemistry, physics, and biological sciences.

Electrochemical Cells and the Daniell Cell

• Daniell Cell Basics: This cell converts chemical energy from a redox reaction into electrical energy.

  • Overall Reaction: $Zn(s) + Cu^{2+}(aq) \rightarrow Zn^{2+}(aq) + Cu(s)$.

  • Standard Potential: The cell produces an electrical potential of $1.1\,V$ when the concentrations of $Zn^{2+}$ and $Cu^{2+}$ ions are unity ($1\,mol\,dm^{-3}$).

• External Potential ($E_{ext}$) Effects:

  • Condition 1 (E_{ext} < 1.1\,V): The cell functions as a galvanic cell. Electrons flow from the zinc rod to the copper rod (current flows from copper to zinc). Zinc dissolves at the anode; copper deposits at the cathode.

  • Condition 2 ($E_{ext} = 1.1\,V$): The reaction stops entirely. No flow of electrons or current occurs; no chemical reaction takes place.

  • Condition 3 (E_{ext} > 1.1\,V): The cell functions as an electrolytic cell. The reaction reverses. Electrons flow from copper to zinc (current flows from zinc to copper). Zinc deposits at the zinc electrode; copper dissolves at the copper electrode.

Galvanic Cells

• Function: Converts Gibbs energy of a spontaneous redox reaction into electrical work (e.g., to run motors, heaters, etc.).

• Half-Cell Reactions: A galvanic cell is comprised of two half-reactions (redox couples).

  • Oxidation Half-Reaction (at Anode): $Zn(s) \rightarrow Zn^{2+}(aq) + 2e^{-}$.

  • Reduction Half-Reaction (at Cathode): $Cu^{2+}(aq) + 2e^{-} \rightarrow Cu(s)$.

• Cell Construction:

  • Each half-cell consists of a metal electrode dipped in an electrolyte.

  • External connection: Metallic wire through a voltmeter and switch.

  • Internal connection: Salt bridge connecting the two electrolytes (prevents electrolyte mixing while allowing ion migration).

  • In some cases, both electrodes may share the same electrolyte, eliminating the need for a salt bridge.

• Electrode Potential:

  • At the interface of the electrode and electrolyte, metal ions tend to deposit (making it positive) while metal atoms tend to go into solution (leaving electrons, making the electrode negative).

  • Electrode Potential: The potential difference between the electrode and the electrolyte at equilibrium.

  • Standard Electrode Potential ($E^o$): The potential when the concentrations of all species are unity. By IUPAC convention, standard reduction potentials are used as standard electrode potentials.

  • Anode has a negative potential relative to the solution; Cathode has a positive potential.

Measurement of Electrode Potential

• Cell Potential / EMF:

  • Cell Potential: The difference between the reduction potentials of the cathode and anode ($E_{cell} = E_{right} - E_{left}$).

  • Electromotive Force (EMF): The cell potential when no current is drawn through the cell.

• Representation Convention:

  • Anode (left), Cathode (right).

  • Format: $M(s) | M^{n+}(aq) || X^{n+}(aq) | X(s)$.

  • A single vertical line represents a phase boundary; a double vertical line represents a salt bridge.

• Standard Hydrogen Electrode (SHE):

  • Acts as a reference electrode. Represented as $Pt(s) | H_2(g) | H^+(aq)$.

  • Assigned a potential of $0.00\,V$ at all temperatures.

  • Consists of a platinum electrode coated with platinum black, dipped in $1\,M\,H^+$ solution with pure $H_2$ gas bubbled at $1\,bar$.

• Calculating Potential relative to SHE:

  • If the SHE is the anode, the measured cell EMF equals the standard reduction potential of the cathode.

  • Example: $Pt(s) | H_2(g, 1\,bar) | H^+(aq, 1\,M) || Cu^{2+}(aq, 1\,M) | Cu$ has an EMF of $0.34\,V$.

  • Example: $Pt(s) | H_2(g, 1\,bar) | H^+(aq, 1\,M) || Zn^{2+}(aq, 1\,M) | Zn$ has an EMF of $-0.76\,V$.

• Chemical Implications of $E^o$:

  • Positive $E^o$: The reduced form is more stable than hydrogen gas; the oxidised form is easily reduced.

  • Negative $E^o$: Hydrogen ions can oxidise the metal; the metal can reduce hydrogen ions.

• Inert Electrodes: Metals like platinum ($Pt$) or gold ($Au$) that do not participate in reaction but provide a surface for electron transfer and conduction (e.g., in Hydrogen or Bromine electrodes).

Standard Electrode Potentials (Table 2.1 Data Summary)

• Strongest Oxidising Agent: Fluorine gas ($F_2$) with $E^o = 2.87\,V$.

• Strongest Reducing Agent: Lithium metal ($Li(s)$) with $E^o = -3.05\,V$.

• Top to bottom in standard reduction potential tables: Oxidising power of the species on the left decreases; reducing power of the species on the right increases.

The Nernst Equation

• Equation for an Electrode: For $M^{n+}(aq) + ne^{-} \rightarrow M(s)$, the potential is:

  • $E_{(M^{n+}/M)} = E^o_{(M^{n+}/M)} - \frac{RT}{nF} \ln \frac{1}{[M^{n+}]}$

  • Where $R = 8.314\,JK^{-1}mol^{-1}$, $F = 96487\,C\,mol^{-1}$, and $T$ is temperature in Kelvin.

• Simplified Equation at 298 K: Using base 10 log and the consolidated constants:

  • $E_{(M^{n+}/M)} = E^o_{(M^{n+}/M)} - \frac{0.059}{n} \log \frac{1}{[M^{n+}]}$

• Cell Potential Calculation: For a cell like the Daniell cell:

  • $E_{cell} = E^o_{cell} - \frac{0.059}{2} \log \frac{[Zn^{2+}]}{[Cu^{2+}]}$

• General Reaction: For $aA + bB + ne^{-} \rightarrow cC + dD$:

  • $E_{cell} = E^o_{cell} - \frac{RT}{nF} \ln \frac{[C]^c [D]^d}{[A]^a [B]^b}$

• Equilibrium Constant ($K_c$):

  • At equilibrium, $E_{cell} = 0$.

  • $E^o_{cell} = \frac{2.303RT}{nF} \log K_c$

  • At $298\,K$: $E^o_{cell} = \frac{0.059}{n} \log K_c$

  • Example: For Daniell cell, $E^o_{cell} = 1.1\,V$, leading to $K_c = 2 \times 10^{37}$ at $298\,K$.

Electrochemical Cell and Gibbs Energy

• Relationship: Electrical work ($\\Delta_rG$) is the negative of the cell EMF times the charge passed.

  • $\Delta_rG = -nFE_{cell}$

• Standard Gibbs Energy: $\Delta_rG^o = -nFE^o_{cell}$

• extensive vs. Intensive: $E_{cell}$ is intensive (does not scale with amount), but $\Delta_rG$ is extensive (depends on $n$). If reaction coefficients are doubled, $\Delta_rG$ doubles, but $E_{cell}$ remains constant.

• Connectivity: $\Delta_rG^o = -RT \ln K$.

Conductance of Electrolytic Solutions

• Resistance ($R$): Measured in Ohms ($\Omega$). $R = \rho \frac{l}{A}$.

• Resistivity ($\rho$): Specific resistance in $\Omega\,m$. Submultiple: $\Omega\,cm$.

• Conductance ($G$): Inverse of resistance. $G = 1/R$. Unit: Siemens ($S$) or $ohm^{-1}$.

• Conductivity (Specific Conductance, $\kappa$): Inverse of resistivity ($1/\rho$). Unit: $S\,m^{-1}$ or $S\,cm^{-1}$.

  • $1\,S\,cm^{-1} = 100\,S\,m^{-1}$.

• Material Classification:

  • Conductors: Metals, alloys, graphite, conducting polymers (e.g., polyaniline, polythiophene).

  • Insulators: Glass, ceramics, Teflon.

  • Semiconductors: Silicon, Germanium, Gallium Arsenide.

  • Superconductors: Materials with zero resistivity. Previously limited to 0–15 K; modern ceramic superconductors work up to 150 K.

• Factors Affecting Conductance:

  • Electronic (Metallic) Conductance: Depends on metal nature, valence electrons, and temperature (conductivity decreases as temperature increases).

  • Ionic (Electrolytic) Conductance: Movement of ions in solution. Depends on electrolyte nature, ion size/solvation, solvent viscosity, concentration, and temperature (conductivity increases as temperature increases).

Measurement of Conductivity

• Challenges:

  1. Direct current change solution composition (solved by using Alternating Current).

  2. Connecting liquid solution to a bridge (solved by using a Conductivity Cell).

• Cell Constant ($G^*$): Defined as $l/A$. Usually determined using a standard solution like $KCl$.

  • $G^* = R \times \kappa$

• Molar Conductivity ($\Lambda_m$):

  • $\Lambda_m = \frac{\kappa}{c}$

  • Units Conversion: $\Lambda_m\,(S\,cm^2\,mol^{-1}) = \frac{\kappa\,(S\,cm^{-1}) \times 1000\,(cm^3/L)}{Molarity\,(mol/L)}$.

• Variation with Concentration:

  • Conductivity ($\kappa$): Decreases with dilution for both strong and weak electrolytes because the number of ions per unit volume decreases.

  • Molar Conductivity ($\Lambda_m$): Increases with dilution.

Strong and Weak Electrolytes

• Strong Electrolytes: $\Lambda_m$ increases slowly with dilution.

  • Kohlrausch’s Equation: $\Lambda_m = \Lambda_m^o - A c^{1/2}$.

  • $\Lambda_m^o$ is limiting molar conductivity (at zero concentration).

  • Constant $A$ depends on stoichiometry (1-1, 1-2, etc.) and solvent/temperature.

• Weak Electrolytes: $\Lambda_m$ increases steeply with dilution near zero concentration due to an increase in degree of dissociation ($\alpha$).

  • $\alpha = \frac{\Lambda_m}{\Lambda_m^o}$.

  • Dissociation constant: $K_a = \frac{c\alpha^2}{(1 - \alpha)}$.

• Kohlrausch Law of Independent Migration of Ions: Limiting molar conductivity is the sum of the individual contributions of the anion and cation.

  • $\Lambda_m^o = \nu_+ \lambda_+^o + \nu_- \lambda_-^o$

  • Example: $\Lambda_m^o(CaCl_2) = \lambda^o(Ca^{2+}) + 2\lambda^o(Cl^-)$.

Electrolysis and electrolytic Cells

• Mechanism: uses an external voltage source to drive non-spontaneous reactions.

• Faraday’s First Law: Mass of substance produced ($w$) is proportional to the quantity of electricity passed ($Q$). $Q = It$.

• Faraday’s Second Law: Amounts of different substances liberated by the same quantity of electricity are proportional to their chemical equivalent weights.

• Faraday Constant ($F$): Charge of 1 mole of electrons.

  • $F = N_A \times 1.6021 \times 10^{-19}\,C \approx 96487\,C\,mol^{-1}$ (usually taken as $96500\,C$).

• Metal Production: Electrolysis is used for Na, Mg, and Al (using fused chlorides or oxides in cryolite) where chemical reduction is not feasible.

Products of Electrolysis

• Depends on material nature, electrodes (inert vs. reactive), and standard potentials.

• Aqueous Salt Solutions: Competing reactions occur at electrodes.

  • Cathode: Species with higher $E^o$ (more positive) is reduced first. In water, $H^+$/$H_2O$ often competes with metal cations.

  • Anode: Species with lower $E^o$ should be oxidised, but kinetically slow reactions (like $O_2$ production) require overpotential. Thus, $Cl^-$ can be oxidised to $Cl_2$ instead of water to $O_2$ in aqueous $NaCl$.

• Sulfuric Acid: Dilute $H_2SO_4$ yields $O_2$ at the anode; concentrated $H_2SO_4$ yields $S_2O_8^{2-}$ (peroxodisulphate).

Batteries

• Primary Batteries (Non-rechargeable):

  • Dry Cell (Leclanche): Zn anode, graphite cathode with $MnO_2$. Potential: $1.5\,V$.

  • Mercury Cell: Zn-Hg amalgam anode, $HgO$/carbon cathode. Potential: $1.35\,V$ (constant during life).

• Secondary Batteries (Rechargeable):

  • Lead Storage Battery: Pb anode, $PbO_2$ cathode, $38\%\,H_2SO_4$ electrolyte. Discharges to $PbSO_4$. Reverses during charging.

  • Nickel-Cadmium Cell: Longer life, more expensive. Overall: $Cd + 2Ni(OH)_3 \rightarrow CdO + 2Ni(OH)_2 + H_2O$.

Fuel Cells

• Mechanism: Converts energy of combustion (e.g., $H_2, CH_4$) directly into electricity.

• Efficiency: ~70% (vs. 40% for thermal plants).

• Hydrogen-Oxygen Fuel Cell: Use porous carbon electrodes with catalysts ($Pt/Pd$). Operation produces water vapor (used by Apollo astronauts).

• Reactions:

  • Anode: $2H_2 + 4OH^- \rightarrow 4H_2O + 4e^-$

  • Cathode: $O_2 + 2H_2O + 4e^- \rightarrow 4OH^-$

Corrosion

• Mechanism: Essentially an electrochemical phenomenon (rusting of iron).

• Chemistry:

  • Anodic Spot: Iron is oxidised: $Fe(s) \rightarrow Fe^{2+}(aq) + 2e^-$.

  • Cathodic Spot: Oxygen is reduced in presence of $H^+$ (from $CO_2$ or pollutants): $O_2 + 4H^+ + 4e^- \rightarrow 2H_2O$.

  • Rust Formation: $Fe^{2+}$ is further oxidised to ferric ions, forming hydrated oxide ($Fe_2O_3 \cdot xH_2O$).

• Prevention: Painting, coating with chemicals (bisphenol), galvanizing (coating with Zn/Sn), or sacrificial protection (using sacrificial Mg/Zn anodes).

The Hydrogen Economy

• Vision: To replace polluting fossil fuels ($CO_2$ production leading to Greenhouse Effect) with hydrogen.

• The Advantage: Hydrogen combustion produces only water.

• The Process: Producing hydrogen by splitting water via solar energy, followed by use in fuel cells. Both rely heavily on electrochemical principles.