Chemistry: Class 121 — Chapter 2: Electrochemistry

The Daniell cell converts chemical energy liberated during the redox reaction:

The electrical potential of this cell is $1.1\text{ V}$ when the concentration of $Zn^{2+}$ and $Cu^{2+}$ ions is unity ($1\text{ mol dm}^{-3}$). The cell behavior changes under an external opposing potential ($E_{ext}$):

• Case 1: $E_{ext} < 1.1\text{ V}$
  • Electrons flow from $Zn$ rod to $Cu$ rod (current flows from $Cu$ to $Zn$).
  • $Zn$ dissolves at the anode and $Cu$ deposits at the cathode.
• Case 2: $E_{ext} = 1.1\text{ V}$
  • No flow of electrons or current.
  • No chemical reaction occurs.
• Case 3: $E_{ext} > 1.1\text{ V}$
  • Electrons flow from $Cu$ to $Zn$ (current flows from $Zn$ to $Cu$).
  • The cell functions as an electrolytic cell where zinc is deposited at the zinc electrode and copper dissolves at the copper electrode.

A galvanic cell is a combination of two half-cells or redox couples:

• Reduction Half-Reaction (at Cathode): Cathode has a positive potential with respect to the solution.
  $$Cu^{2+}(aq) + 2e^- \rightarrow Cu(s)$$
• Oxidation Half-Reaction (at Anode): Anode has a negative potential with respect to the solution.
  $$Zn(s) \rightarrow Zn^{2+}(aq) + 2e^-$$
• Electrode Potential: A potential difference that develops between the electrode and the electrolyte. When concentrations of all species are unity, it is called the Standard Electrode Potential.

The absolute potential of an individual half-cell cannot be measured. It is measured with respect to a reference electrode called the Standard Hydrogen Electrode (SHE).

The SHE is assigned a zero potential ($0.00\text{ V}$) at all temperatures corresponding to the reaction:

The cell potential (EMF) is given by:

For a general electrode reaction: $M^{n+}(aq) + ne^- \rightarrow M(s)$, the Nernst equation is:

At $298\text{ K}$, substituting the values of $R$, $F$, and $T$, it reduces to:

For a general electrochemical reaction of the type: $aA + bB \xrightarrow{ne^-} cC + dD$:

• Equilibrium Constant ($K_c$): At equilibrium, $E_{cell} = 0$. The Nernst equation becomes:
  $$E^\circ_{cell} = \frac{2.303 RT}{nF} \log K_c$$
  At $298\text{ K}$:
  $$E^\circ_{cell} = \frac{0.059}{n} \log K_c$$
• Gibbs Energy of Reaction ($\Delta_r G$): Reversible work done by a galvanic cell is equal to the decrease in its Gibbs energy:
  $$\Delta_r G = -nFE_{cell}$$
  Under standard conditions:
  $$\Delta_r G^\circ = -nFE^\circ_{cell} = -RT \ln K_c$$

• Resistance ($R$): Measured in ohms ($\Omega$). $R = \rho \frac{l}{A}$.
• Resistivity ($\rho$): Specific resistance, measured in $\Omega\text{ m}$ or $\Omega\text{ cm}$.
• Conductance ($G$): Inverse of resistance. $G = \frac{1}{R} = \kappa \frac{A}{l}$. Measured in Siemens ($S$) or $\Omega^{-1}$.
• Conductivity ($\kappa$): Inverse of resistivity. $\kappa = G \cdot \frac{l}{A}$. Measured in $S\text{ m}^{-1}$ or $S\text{ cm}^{-1}$.
• Molar Conductivity ($\Lambda_m$): Conductance of a solution containing one mole of electrolyte.
  $$\Lambda_m = \frac{\kappa}{c}$$
  Units are $S\text{ m}^2\text{ mol}^{-1}$ or $S\text{ cm}^2\text{ mol}^{-1}$.

• Conductivity ($\kappa$): Always decreases with a decrease in concentration (dilution) because the number of ions per unit volume decreases.
• Molar Conductivity ($\Lambda_m$): Increases with dilution because the total volume containing one mole of electrolyte increases.
• Strong Electrolytes: $\Lambda_m$ increases slowly with dilution and follows the equation:
  $$\Lambda_m = \Lambda_m^\circ - A c^{1/2}$$
• Weak Electrolytes: $\Lambda_m$ increases steeply at lower concentrations. Limiting Molar Conductivity ($\Lambda_m^\circ$) cannot be obtained by extrapolation. It is calculated using Kohlrausch Law.
• Degree of Dissociation ($\alpha$):
  $$\alpha = \frac{\Lambda_m}{\Lambda_m^\circ}$$
• Dissociation Constant ($K_a$):
  $$K_a = \frac{c\alpha^2}{1-\alpha}$$

The law states that limiting molar conductivity of an electrolyte can be represented as the sum of the individual contributions of the anion and cation of the electrolyte:

Where $\lambda_+^\circ$ and $\lambda_-^\circ$ are the limiting molar conductivities of the cation and anion respectively, and $\nu_+$ and $\nu_-$ are their stoichiometric coefficients.

1. First Law: The mass of chemical reaction occurring at any electrode during electrolysis is directly proportional to the quantity of electricity passed through the electrolyte.
   $$Q = I \cdot t$$
2. Second Law: The amounts of different substances liberated by the same quantity of electricity are proportional to their chemical equivalent weights.

The charge on one mole of electrons is equal to the Faraday Constant ($F \approx 96487\text{ C mol}^{-1}$, approximated as $96500\text{ C mol}^{-1}$).

Products depend on the nature of the material being electrolyzed and the electrode potentials of competing reactions:

• Molten $NaCl$: Produces sodium metal at the cathode and chlorine gas at the anode.
• Aqueous $NaCl$: Produces hydrogen gas at the cathode (due to higher reduction potential of $H^+$ over $Na^+$) and chlorine gas at the anode (due to oxygen overpotential).

The reaction occurs only once; the battery becomes dead after use and cannot be recharged.

• Dry Cell (Leclanche Cell): Anode is Zinc container; Cathode is Carbon (graphite) rod surrounded by $MnO_2$. Cell potential is $\approx 1.5\text{ V}$.
• Mercury Cell: Anode is Zinc-mercury amalgam; Cathode is paste of $HgO$ and carbon. Cell potential is $1.35\text{ V}$ and remains constant.

Can be recharged by passing current in the opposite direction.

• Lead Storage Battery: Used in automobiles. Anode is Lead ($Pb$); Cathode is grid of lead packed with lead dioxide ($PbO_2$); Electrolyte is $38\%$ sulfuric acid ($H_2SO_4$).
• Nickel-Cadmium Cell: Has a longer life than lead storage but is more expensive.

Galvanic cells designed to convert the energy of combustion of fuels like hydrogen, methane, or methanol directly into electrical energy. The most successful is the $H_2-O_2$ Fuel Cell, operating with an efficiency of about $70\%$.

• Anode (Oxidation):
  $$2Fe(s) \rightarrow 2Fe^{2+} + 4e^- \quad (E^\circ = -0.44\text{ V})$$
• Cathode (Reduction):
  $$O_2(g) + 4H^+(aq) + 4e^- \rightarrow 2H_2O(l) \quad (E^\circ = 1.23\text{ V})$$
• Overall Reaction:
  $$2Fe(s) + O_2(g) + 4H^+(aq) \rightarrow 2Fe^{2+}(aq) + 2H_2O(l) \quad (E^\circ_{cell} = 1.67\text{ V})$$
• The $Fe^{2+}$ ions are further oxidized by atmospheric oxygen to form rust as hydrated ferric oxide ($Fe_2O_3 \cdot xH_2O$).

• Covering the surface with paint or chemicals (e.g., bisphenol).
• Plating with inert metals or sacrificial coating with active metals like Zinc (Galvanization) or Magnesium.