Electrochemistry Study Guide: Theory, Conductance, and Applications

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 bring about non-spontaneous chemical transformations.

• Importance and Applications:

  • Production of metals such as sodium, and chemicals like sodium hydroxide ($NaOH$), chlorine ($Cl_2$), and fluorine ($F_2$).

  • Usage of batteries and fuel cells to convert chemical energy into electrical energy for various devices.

  • Eco-friendly technology: Electrochemical reactions are often more energy-efficient and less polluting.

  • Biological Basis: Transmission of sensory signals through cells to the brain and cell-to-cell communication have electrochemical origins.

Electrochemical Cells and the Daniell Cell

• Daniell Cell Overview: This specific galvanic cell converts the chemical energy liberated during the redox reaction between zinc and copper ions into electrical energy.

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

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

• Influence of External Voltage ($E_{ext}$):

  • Case 1 (E_{ext} < 1.1\,V): Electrons flow from the zinc rod to the copper rod; current flows from copper to zinc. Zinc dissolves at the anode, and copper deposits at the cathode.

  • Case 2 ($E_{ext} = 1.1\,V$): Equilibrium is reached. There is no flow of electrons or current, and no chemical reaction occurs.

  • Case 3 (E_{ext} > 1.1\,V): The cell functions as an electrolytic cell. Electrons flow from copper to zinc, and current flows from zinc to copper. Zinc is deposited at the zinc electrode, and copper dissolves at the copper electrode.

Galvanic Cells: Theory and Measurement

• Basic Principles: A galvanic cell converts Gibbs energy of a spontaneous redox reaction into electrical work (e.g., to run motors or heaters).

• Half-Cells and Redox Couples: The redox reaction is split into two half-reactions:

  • Oxidation (Anode): $Zn(s) \rightarrow Zn^{2+}(aq) + 2e^{-}$ (occurring on the zinc electrode).

  • Reduction (Cathode): $Cu^{2+}(aq) + 2e^{-} \rightarrow Cu(s)$ (occurring on the copper electrode).

  • Electrodes are connected externally by a wire through a voltmeter, and electrolytes are connected internally via a salt bridge.

• Electrode Potential: A potential difference established between the electrode and the electrolyte due to charge separation at the interface. According to IUPAC, standard reduction potentials are now referred to as standard electrode potentials.

• Cell Potential (EMF):

  • The potential difference between the two electrodes of a galvanic cell is the cell potential, measured in volts ($V$).

  • It is called the Electromotive Force (EMF) when no current is drawn.

  • Convention: The anode is on the left and the cathode is on the right. $E_{cell} = E_{right} - E_{left}$.

  • Representation: $Cu(s) | Cu^{2+}(aq) || Ag^{+}(aq) | Ag(s)$, where single lines denote phase boundaries and double lines denote a salt bridge.

• Standard Hydrogen Electrode (SHE):

  • Used as a reference electrode with a potential assigned as $0.00\,V$ at all temperatures.

  • Representation: $Pt(s) | H_2(g) | H^{+}(aq)$.

  • Consists of a platinum electrode coated with platinum black dipped in an acidic solution ($1\,M$) with pure hydrogen gas bubbled at $1\,bar$.

• Inert Electrodes: Metals like platinum or gold that do not participate in the reaction but provide a surface for electron transfer. Examples include the hydrogen electrode and bromine electrode ($Pt(s) | Br_2(aq) | Br^{-}(aq)$).

The Nernst Equation and Thermodynamics

• Nernst Equation for a Single Electrode: Relates electrode potential to concentration.

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

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

• Nernst Equation for a Cell (at $298\,K$):

  • $E_{cell} = E^{\circ}_{cell} - \frac{0.059}{n} \log Q$

  • For the Daniell cell: $E_{cell} = E^{\circ}_{cell} - \frac{0.059}{2} \log \frac{[Zn^{2+}]}{[Cu^{2+}]}$

• Equilibrium Constant ($K_c$): At equilibrium, $E_{cell} = 0$.

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

  • Example: For the Daniell cell, $K_c = 2 \times 10^{37}$ at $298\,K$.

• Gibbs Energy and Electrical Work:

  • Electrical work done in one second equals potential multiplied by total charge passed.

  • $\Delta_rG = -nFE_{cell}$

  • Standard Gibbs Energy: $\Delta_rG^{\circ} = -nFE^{\circ}_{cell}$

  • Relationship with equilibrium: $\Delta_rG^{\circ} = -RT \ln K$

Conductance of Electrolytic Solutions

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

• Resistivity ($\rho$): Specific resistance of a substance $1\,m$ long with cross-section $1\,m^2$. Units: $\Omega\,m$.

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

• Conductivity ($\kappa$): Inverse of resistivity. Unit: $S\,m^{-1}$ or $S\,cm^{-1}$. $1\,S\,cm^{-1} = 100\,S\,m^{-1}$.

• Factors Affecting Conductance:

  1. Metallic Conductance: Nature/structure of metal, valence electrons, and temperature (conductance decreases as temperature increases).

  2. Ionic (Electrolytic) Conductance: Nature of electrolyte, ion size/solvation, solvent nature/viscosity, concentration, and temperature (conductance increases as temperature increases).

• Cell Constant ($G^*$): Defined as $l/A$. Usually determined by measuring the resistance of a cell with a solution of known conductivity (like $KCl$). $G^* = R \times \kappa$.

• Molar Conductivity ($\Lambda_m$):

  • $\Lambda_m = \frac{\kappa}{c}$

  • Units: $S\,m^2\,mol^{-1}$ or $S\,cm^2\,mol^{-1}$.

  • $1\,S\,m^2\,mol^{-1} = 10^{4}\,S\,cm^2\,mol^{-1}$.

Variation of Conductivity and Kohlrausch Law

• Concentration Dependence:

  • Conductivity ($\kappa$) decreases with dilution because the number of ions per unit volume decreases.

  • Molar conductivity ($\Lambda_m$) increases with dilution (decrease in concentration) because the volume containing 1 mole of electrolyte increases more than $\kappa$ decreases.

• Limiting Molar Conductivity ($\Lambda_m^{\circ}$): The molar conductivity at infinite dilution (as concentration approaches zero).

• Strong Electrolytes: $\Lambda_m$ increases slowly with dilution following the Debye-Hückel-Onsager equation: $\Lambda_m = \Lambda_m^{\circ} - A c^{1/2}$.

• Weak Electrolytes: $\Lambda_m$ increases steeply at low concentrations. $\Lambda_m^{\circ}$ cannot be determined by extrapolation. It is found using Kohlrausch Law.

• Kohlrausch Law of Independent Migration of Ions: The limiting molar conductivity of an electrolyte is the sum of limiting molar conductivities of its constituent ions.

  • $\Lambda_m^{\circ} = \nu_+ \lambda_+^{\circ} + \nu_- \lambda_-^{\circ}$

  • Application: Determining the degree of dissociation ($\alpha = \Lambda_m / \Lambda_m^{\circ}$) and the dissociation constant ($K_a = \frac{c \alpha^2}{1-\alpha}$).

Electrolysis and Faraday's Laws

• Process: Using an external voltage to force a non-spontaneous chemical reaction.

• Commercial Production: Metals like $Na$, $Mg$, and $Al$ are produced by electrolysis of their fused salts or oxides.

• Faraday's First Law: The amount of chemical reaction at an electrode is proportional to the quantity of electricity passed through the electrolyte ($Q = It$).

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

• Quantity of Electricity:

  • Charge on 1 mole of electrons is the Faraday constant ($F \approx 96500\,C\,mol^{-1}$, exactly $96487\,C\,mol^{-1}$).

  • Example: Reduction of $Cu^{2+}$ requires $2\,F$ per mole.

• Products of Electrolysis: Depend on the nature of material and electrodes (inert vs. reactive) and electrode potentials.

  • Electrolysis of Brine ($NaCl$ solution): Products are $H_2(g)$, $Cl_2(g)$, and $NaOH(aq)$. Although water oxidation to $O_2$ has a lower potential ($1.23\,V$) compared to chloride oxidation ($1.36\,V$), chloride is oxidized due to the overpotential of oxygen.

Batteries and Fuel Cells

• Primary Batteries: Reaction occurs only once; battery becomes dead after use.

  • Dry Cell (Leclanché Cell): Anode is zinc container; Cathode is graphite rod surrounded by $MnO_2$. Potential is approx. $1.5\,V$.

  • Mercury Cell: Anode: Zinc-mercury amalgam; Cathode: Paste of $HgO$ and carbon. Produces constant $1.35\,V$ throughout its life.

• Secondary Batteries: Can be recharged by passing current in the opposite direction.

  • Lead Storage Battery: Used in automobiles. Anode: Lead; Cathode: Grid of lead packed with $PbO_2$. Electrolyte: $38\%$ solution of $H_2SO_4$. On discharge: $Pb(s) + PbO_2(s) + 2H_2SO_4(aq) \rightarrow 2PbSO_4(s) + 2H_2O(l)$.

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

• Fuel Cells: Convert the energy of combustion of fuels (e.g., $H_2$, methane) directly into electricity.

  • $H_2-O_2$ Fuel Cell: Used in the Apollo space program. Efficiency is approx. $70\%$ (compared to $40\%$ for thermal plants). Electrodes are porous carbon containing catalysts like platinum or palladium.

Corrosion

• Definition: Oxidation of metal surfaces into oxides or other salts (e.g., rusting of iron, tarnishing of silver).

• Electrochemical Mechanism of Rusting:

  • Anode spot: $2Fe(s) \rightarrow 2Fe^{2+} + 4e^{-}$ ($E^{\circ} = -0.44\,V$).

  • Cathode spot: $O_2(g) + 4H^{+}(aq) + 4e^{-} \rightarrow 2H_2O(l)$ ($E^{\circ} = 1.23\,V$).

  • Overall Reaction: $2Fe(s) + O_2(g) + 4H^{+}(aq) \rightarrow 2Fe^{2+}(aq) + 2H_2O(l)$ ($E^{\circ}_{cell} = 1.67\,V$).

  • $Fe^{2+}$ is further oxidized to $Fe_2O_3 \cdot xH_2O$ (rust).

• Prevention:

  • Barrier methods (painting, chemicals like bisphenol).

  • Sacrificial protection: Coating with more reactive metals like zinc (galvanization) or magnesium.

Questions & Discussion

• Question 2.1: How would you determine the standard electrode potential of the system $Mg^{2+}|Mg$?

• Response: Construct a cell with the $Mg^{2+}|Mg$ electrode as the cathode and the Standard Hydrogen Electrode (SHE) as the anode. Measure the cell EMF under standard conditions ($1\,M$ concentration, $298\,K$). The measured EMF will be the standard reduction potential of the magnesium system, as the anode potential is zero.

• Question 2.2: Can you store copper sulphate solutions in a zinc pot?

• Response: No. Zinc has a lower (more negative) reduction potential ($-0.76\,V$) compared to copper ($0.34\,V$). Therefore, zinc is more reactive and will undergo a spontaneous redox reaction, displacing copper from the solution ($Zn + CuSO_4 \rightarrow ZnSO_4 + Cu$), which would corrode the pot.

• Question 2.4: Calculate the potential of a hydrogen electrode in contact with a solution whose pH is 10.

• Response: For the reaction $H^{+}(aq) + e^{-} \rightarrow \frac{1}{2}H_2(g)$, the Nernst equation is $E = E^{\circ} - 0.059 \log(1/[H^{+}])$. Since $E^{\circ} = 0$ and $-\log[H^{+}] = pH = 10$, the potential is $E = -0.059 \times 10 = -0.59\,V$.

• Question 2.15: Discuss the rusting of iron as an electrochemical cell.

• Response: Rusting occurs when specific spots on an iron object act as anodes where iron is oxidized. Electrons move through the metal to other spots acting as cathodes, where oxygen is reduced in the presence of $H^{+}$ ions. The electrolyte is typically a thin film of water containing dissolved acidic gases like $CO_2$ (forming $H_2CO_3$).