Electrochemical Cells

Electrochemical cells convert chemical energy into electrical energy (galvanic cells) or use electrical energy to drive non-spontaneous chemical reactions (electrolytic cells). A galvanic cell, like the Daniell cell (Zn-Cu), utilizes a spontaneous redox reaction to generate electricity. An electrolytic cell uses an external voltage source to force a non-spontaneous reaction to occur.

A galvanic cell comprises two half-cells, each consisting of an electrode immersed in an electrolyte. The two half-cells are connected externally by a wire (with a voltmeter) and internally by a salt bridge or by dipping both electrodes in the same electrolyte. The half-cell where oxidation occurs is the anode (negative potential), and where reduction occurs is the cathode (positive potential). The potential difference between electrodes is the cell potential (emf), measured in volts. The standard cell potential ($E^o_{cell}$) is measured when all species are at unit concentration and gases are at 1 bar pressure.

The standard hydrogen electrode (SHE), with a standard electrode potential of 0 V, serves as a reference to measure the standard electrode potentials ($E^o$) of other half-cells.

Galvanic Cells

Galvanic cells convert chemical energy from spontaneous redox reactions into electrical energy. The Daniell cell (Zn + Cu²⁺ → Zn²⁺ + Cu) is a common example, with a standard cell potential ($E^o_{cell}$) of 1.1 V. It's represented as Zn(s)|Zn²⁺(aq)||Cu²⁺(aq)|Cu(s), where the anode (oxidation) is on the left and the cathode (reduction) is on the right. The cell potential is $E_{cell} = E_{cathode} - E_{anode}$.

Measurement Of Electrode Potential

The potential difference between an electrode and its electrolyte solution is the electrode potential. Standard electrode potential ($E^o$) is measured when concentrations of all species are unity and temperature is 298 K. The Standard Hydrogen Electrode (SHE), Pt(s)|H₂(g, 1 bar)|H⁺(aq, 1 M), is assigned a standard electrode potential of 0 V. By combining a half-cell with SHE, its standard electrode potential can be measured. A positive $E^o$ indicates the reduced form is more stable than H₂ (stronger oxidizing agent), while a negative $E^o$ indicates H₂ is more stable than the reduced form (stronger reducing agent). Standard electrode potentials help predict the feasibility of reactions and compare the oxidizing/reducing strengths of species.

Nernst Equation

The Nernst equation relates the electrode potential ($E$) of a half-cell or the cell potential ($E_{cell}$) to the concentrations of the species involved and the standard electrode potential ($E^o$). For a general electrode reaction $M^{n+} + ne^- \rightarrow M(s)$, the electrode potential is $E_{M^{n+}/M} = E^o_{M^{n+}/M} - \frac{RT}{nF} \ln \frac{1}{[M^{n+}]}$. For a cell reaction, $aA + bB \rightarrow cC + dD$, the cell potential is $E_{cell} = E^o_{cell} - \frac{RT}{nF} \ln Q$, where $Q = \frac{[C]^c [D]^d}{[A]^a [B]^b}$ is the reaction quotient.

At 298 K, the equation simplifies to $E_{cell} = E^o_{cell} - \frac{0.0591}{n} \log Q$. The cell potential is positive and the reaction is spontaneous as long as $E_{cell} > 0$. As the reaction proceeds, concentrations change, $E_{cell}$ decreases, and eventually, $E_{cell}$ becomes zero at equilibrium.

Equilibrium Constant From Nernst Equation

At equilibrium, $E_{cell} = 0$ and $Q = K_c$ (equilibrium constant). Substituting these into the Nernst equation gives $E^o_{cell} = \frac{2.303RT}{nF} \log K_c$. At 298 K, $E^o_{cell} = \frac{0.0591}{n} \log K_c$. This equation allows calculation of the equilibrium constant from the standard cell potential.

Electrochemical Cell And Gibbs Energy Of The Reaction

The standard Gibbs energy change ($Δ^o_rG$) of a cell reaction is related to the standard cell potential ($E^o_{cell}$) by the equation $Δ^o_rG = -nFE^o_{cell}$, where $n$ is the number of moles of electrons transferred and $F$ is the Faraday constant. Gibbs energy also relates to the equilibrium constant ($Δ^o_rG = -RT \ln K_c$). Thus, $E^o_{cell}$ provides thermodynamic information about the reaction.

Conductance Of Electrolytic Solutions

Electrolytic solutions conduct electricity due to the movement of ions. Conductivity ($κ$) is the inverse of resistivity ($ρ$), and molar conductivity ($Λ_m$) is the conductivity per mole of electrolyte. Both decrease with decreasing concentration for strong electrolytes (due to decreased number of ions per unit volume) and increase steeply for weak electrolytes (due to increased dissociation).

Measurement Of The Conductivity Of Ionic Solutions

The resistance of an electrolytic solution is measured using a conductivity cell with two platinum electrodes coated with platinum black, immersed in the solution. The cell constant ($G^* = l/A$) is determined by measuring the resistance of a solution with known conductivity. The conductivity ($κ$) is then calculated as $κ = G^* / R$, where $R$ is the measured resistance.

Variation Of Conductivity And Molar Conductivity With Concentration

Conductivity ($κ$): Decreases with dilution because the number of ions per unit volume decreases. This trend holds for both strong and weak electrolytes.

Molar Conductivity ($Λ_m$): Increases with dilution. For strong electrolytes, this increase is gradual ($Λ_m = Λ^o_m - A\sqrt{c}$), attributed to increased volume of solution per mole of electrolyte. For weak electrolytes, the increase is steep, mainly due to increased dissociation. The molar conductivity at infinite dilution ($Λ^o_m$) is the theoretical maximum value where dissociation is complete.

Kohlrausch's Law: States that the limiting molar conductivity of an electrolyte is the sum of the contributions of its individual ions ($Λ^o_m = ν_+ λ^o_+ + ν_- λ^o_-$). This law is useful for calculating $Λ^o_m$ for weak electrolytes and determining ionic conductivities.

Electrolytic Cells And Electrolysis

Electrolytic cells use external electrical energy to drive non-spontaneous redox reactions. Electrolysis involves using direct current to decompose electrolytes. The products formed depend on the electrolyte's nature, concentration, and the electrode material (inert vs. reactive).

Faraday's Laws of Electrolysis:

• First Law: The amount of chemical reaction at an electrode is proportional to the quantity of electricity passed ($Q = It$).
• Second Law: The amounts of different substances liberated by the same quantity of electricity are proportional to their equivalent weights.

One Faraday of charge (96487 C) deposits or liberates one equivalent weight of substance. For instance, depositing 1 mole of Cu requires 2 moles of electrons (2F), while 1 mole of Ag requires 1 mole of electron (1F).

Products Of Electrolysis

The products of electrolysis depend on factors like the ions present, their standard electrode potentials ($E^o$), and overpotential. For example, electrolysis of aqueous NaCl yields H₂ at the cathode and Cl₂ at the anode (due to overpotential of oxygen making Cl⁻ oxidation more favorable than water oxidation). Electrolysis of molten NaCl yields Na metal and Cl₂ gas. The electrolysis of aqueous solutions can also produce or consume H⁺/OH⁻ ions, affecting the solution's pH.

Batteries

Batteries are galvanic cells used as portable sources of electrical energy. They convert chemical energy into electrical energy through spontaneous redox reactions.

Primary Batteries

Primary cells are used once and cannot be recharged. The redox reaction is irreversible. Examples include the:

• Dry Cell (Leclanché cell): Zn anode, C (graphite) cathode with MnO₂ and C powder, electrolyte is NH₄Cl + ZnCl₂ paste. $E \approx 1.5 V$.
• Mercury Cell: Zn-amalgam anode, paste of HgO and C cathode, KOH+ZnO electrolyte. $E \approx 1.35 V$. It provides a constant voltage throughout its life.

Secondary Batteries

Secondary cells can be recharged by passing current in the reverse direction, allowing reuse. Examples include:

• Lead Storage Battery: Pb anode, PbO₂ cathode, H₂SO₄ electrolyte. Used in cars and inverters. The reaction involves PbSO₄ formation at both electrodes during discharge, which reverts to Pb and PbO₂ upon charging.
• Nickel-Cadmium (Ni-Cd) Cell: A rechargeable cell with a longer life than lead-acid batteries but is more expensive.

Fuel Cells

Fuel cells are galvanic cells that directly convert the chemical energy of fuel combustion into electrical energy, offering higher efficiency (~70%) and being pollution-free compared to thermal power plants (~40%). Reactants (fuel and oxidant) are continuously supplied, and products are removed. The most common fuel cell uses hydrogen and oxygen, producing water. Catalysts (like Pt or Pd) are used at porous electrodes to increase reaction rates. The reaction is $2H_2(g) + O_2(g) \rightarrow 2H_2O(l)$, generating electricity continuously as long as reactants are supplied.

Corrosion

Corrosion is the gradual destruction of metals through chemical or electrochemical reactions with their environment. Rusting of iron is a common example, involving the oxidation of iron and reduction of oxygen in the presence of water and electrolytes (like CO₂ dissolved in water forming carbonic acid).

Electrochemical Mechanism of Rusting: Iron acts as an anode where oxidation occurs: $Fe(s) \rightarrow Fe^{2+}(aq) + 2e^-$ ($E^o = -0.44$ V). Electrons flow through the metal to a cathodic region where reduction of oxygen occurs: $O_2(g) + 4H^+(aq) + 4e^- \rightarrow 2H_2O(l)$ ($E^o = +1.23$ V). The overall cell potential is $E^o_{cell} = 1.67$ V, indicating spontaneity. $Fe^{2+}$ ions are further oxidized to $Fe^{3+}$, which forms hydrated ferric oxide ($Fe_2O_3 \cdot xH_2O$), the rust.

Prevention: Corrosion can be prevented by preventing contact with the atmosphere (painting, coating with inert metals like tin) or by using sacrificial anodes (more reactive metals like Mg or Zn) that corrode preferentially, protecting the main object.

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