JEE Chemistry Electrochemistry Notes Set 07

Galvanic Cell, Representation and Salt Bridge

An electrochemical cell interconverts chemical and electrical energy. In a galvanic (voltaic) cell a spontaneous redox reaction produces current; in an electrolytic cell an external source forces a non-spontaneous reaction to occur.
At the anode oxidation takes place (electrons are released, polarity negative in a galvanic cell). At the cathode reduction takes place (electrons are consumed, polarity positive in a galvanic cell). Electrons always flow in the external wire from anode to cathode, and conventional current flows the opposite way.

In the cell notation the anode half-cell is written on the left and the cathode half-cell on the right. A single vertical line separates two phases, a comma separates species in the same phase, and a double vertical line stands for the salt bridge. For a gas electrode the gas is written next to the inert platinum, for example \( \ce{Pt | H2(g) | H+(aq) || Cu^{2+}(aq) | Cu(s)} \).

The salt bridge is a U-tube containing an inert electrolyte in agar or gel. It completes the circuit, keeps each half-cell electrically neutral, and reduces the liquid junction potential. The cation and anion of the electrolyte should have nearly equal mobilities, which is why KCl, \( \ce{KNO3} \) or \( \ce{NH4NO3} \) are used. If the cell contains \( \ce{Ag+} \), \( \ce{Pb^{2+}} \) or \( \ce{Hg2^{2+}} \), KCl cannot be used because it would precipitate the chloride. Removing the bridge makes the measured voltage drop to zero.

Example. The reaction \( \ce{Sn^{2+} + 2Ag+ -> Sn^{4+} + 2Ag} \) has tin(II) oxidised on an inert electrode, so the cell is \( \ce{Pt | Sn^{2+}, Sn^{4+} || Ag+ | Ag} \).

Electrode Potential and the Electrochemical Series

A metal dipping in a solution of its own ions sets up an electrical double layer, and the resulting potential difference is the electrode potential. It depends on the nature of the metal, the concentration of ions, the temperature and, for gases, the pressure. The potential of one electrode cannot be measured alone, so the standard hydrogen electrode (SHE) (Pt, \( \ce{H2} \) at 1 atm, \( \ce{H+} \) at 1 M) is defined as 0.00 V at all temperatures and every other electrode is measured against it.

Electrodes arranged by their standard reduction potentials give the electrochemical series. A species lower in the series (more negative \( E^\circ \)) is a stronger reducing agent; a species higher up (more positive \( E^\circ \)) is a stronger oxidising agent. Selected values at 298 K: Li⁺/Li -3.05 V, K⁺/K -2.93 V, Na⁺/Na -2.71 V, Mg²⁺/Mg -2.37 V, Zn²⁺/Zn -0.76 V, Fe²⁺/Fe -0.44 V, Cu²⁺/Cu +0.34 V, Ag⁺/Ag +0.80 V, Cl₂/Cl^- +1.36 V, MnO₄^-/Mn²⁺ +1.51 V, F₂/F^- +2.87 V.

Cell potential: \( E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode} \) (both as reduction potentials). It is an intensive property, so multiplying a cell reaction by a number does not change it. For Zn-Cu: \( E^\circ_{cell} = 0.34 - (-0.76) = 1.10\ \text{V} \). A positive value means the reaction is spontaneous as written. A metal displaces from solution any metal with a higher reduction potential and displaces hydrogen from acids only if its own reduction potential is below zero.

Free Energy, Equilibrium Constant and Work

The driving force of a cell reaction is linked to thermodynamics through \( \Delta G = -nFE \) and \( \Delta G^\circ = -nFE^\circ = -RT\ln K \), where \( F = 96500 \) C per mole of electrons. At 298 K this gives \( \log K = \dfrac{nE^\circ}{0.059} \). The maximum electrical work obtainable from a cell is \( nFE \).

Example. For the Zn-Cu cell, \( \Delta G^\circ = -2 \times 96500 \times 1.10 = -212.3\ \text{kJ} \) and \( \log K = 2 \times 1.10/0.059 \approx 37.3 \), so the reaction goes essentially to completion.

When combining half-reactions, potentials are not additive but free energies are. To find an unknown potential, add the \( nE^\circ \) values: \( n_3E_3 = n_1E_1 + n_2E_2 \).

Nernst Equation and Concentration Cells

For a half-reaction \( \text{Ox} + ne^- \rightarrow \text{Red} \) at 298 K, \( E = E^\circ - \dfrac{0.059}{n}\log\dfrac{[\text{Red}]}{[\text{Ox}]} \). Pure solids and liquids are taken as activity 1 and gases enter as partial pressures. For a full cell, \( E_{cell} = E^\circ_{cell} - \dfrac{0.059}{n}\log Q \); at equilibrium \( E_{cell}=0 \) and \( Q=K \). A discharged battery is a cell at equilibrium.

Example. For \( \ce{Cu^{2+} + 2e- -> Cu} \) with \( [\ce{Cu^{2+}}] = 0.01\ \text{M} \): \( E = 0.34 - \dfrac{0.059}{2}\log\dfrac{1}{0.01} = 0.281\ \text{V} \).

Hydrogen electrode: \( E = -0.059\,\text{pH} \) for \( \ce{H+/H2} \) at 1 atm. A concentration cell uses the same electrode material at two concentrations (or pressures), so \( E^\circ_{cell}=0 \) and \( E_{cell} = \dfrac{0.059}{n}\log\dfrac{C_{cathode}}{C_{anode}} \) for ions; the dilute half-cell is the anode and the concentrated half-cell is the cathode.

Electrolysis and Faraday's Laws

In an electrolytic cell the anode is positive and the cathode negative. With inert electrodes (Pt, graphite) the species with the more favourable potential reacts: at the cathode the one with the higher reduction potential is reduced first, at the anode the one with the lower reduction potential is oxidised first. With attackable electrodes (Cu in \( \ce{CuSO4} \) for example) the anode metal itself dissolves, which is the basis of electrorefining and electroplating. In aqueous \( \ce{NaCl} \) the cathode product is hydrogen, because water is reduced more easily than \( \ce{Na+} \), and the anode product is chlorine, because of the overpotential of oxygen evolution; molten NaCl gives sodium and chlorine.

First law: mass deposited is proportional to the charge passed, \( w = ZIt \). Second law: for the same charge, masses deposited are proportional to equivalent weights, \( w = \dfrac{E\,I\,t}{96500} \) where \( E=M/n \). One faraday (96500 C) deposits one gram-equivalent of any substance. Charge of one mole of electrons is 96500 C; charge on one electron is \( 1.6\times10^{-19} \) C.

Example. Passing 9650 C through molten alumina deposits \( w = \dfrac{27}{3} \times \dfrac{9650}{96500} = 0.9\ \text{g} \) of aluminium.

Commercial Cells and Corrosion

Primary cells cannot be recharged: the dry (Leclanche) cell has a zinc container as anode and a carbon rod surrounded by \( \ce{MnO2} \) and carbon as cathode, with an ammonium chloride paste. The alkaline cell replaces the acidic paste with KOH, and the mercury cell (steady 1.35 V) uses a Zn(Hg) anode and HgO cathode. Secondary cells can be recharged: the lead storage battery has Pb as anode and \( \ce{PbO2} \) as cathode in about 38 percent \( \ce{H2SO4} \), and discharges by forming \( \ce{PbSO4} \) at both plates with consumption of acid, so the electrolyte density falls. Fuel cells (for example the hydrogen-oxygen cell) convert the energy of fuel directly to electricity with higher efficiency than combustion.

Corrosion of iron is an electrochemical process. At the anodic region \( \ce{Fe -> Fe^{2+} + 2e-} \), and at the cathodic region oxygen is reduced in the presence of moisture, \( \ce{O2 + 4H+ + 4e- -> 2H2O} \). The Fe(II) is further oxidised and hydrated to rust, \( \ce{Fe2O3.xH2O} \). Protection methods: painting or coating, galvanising with zinc, and cathodic protection with a more reactive sacrificial metal such as Mg or Zn.

Electrolytic Conductance

Resistance is \( R = \rho\,\dfrac{l}{a} \) and conductance is \( G = 1/R \) (siemens). Specific conductance (conductivity) is \( \kappa = G\,\dfrac{l}{a} \), where \( l/a \) is the cell constant. Conductivity decreases on dilution because fewer ions are present per unit volume. Molar conductivity is \( \Lambda_m = \dfrac{\kappa \times 1000}{M} \) with \( \kappa \) in S cm^-1 and M in mol L^-1; it rises on dilution because ionic interactions weaken and, for weak electrolytes, dissociation increases.

Example. A cell with resistance 50 ohm and cell constant 0.5 cm^-1 filled with 0.1 M solution gives \( \kappa = 0.5/50 = 0.01\ \text{S cm}^{-1} \) and \( \Lambda_m = 0.01\times1000/0.1 = 100\ \text{S cm}^2\text{mol}^{-1} \).

Temperature raises the conductivity of an electrolyte (ions move faster, viscosity drops), whereas the conductivity of a metal falls with temperature. Smaller ions are more heavily hydrated, so their effective size is larger and mobility lower; this is why among alkali metal ions the aqueous mobility order is Li⁺ < Na⁺ < K⁺ < Rb⁺ < Cs⁺. Hydrogen and hydroxide ions have abnormally high mobility because of proton hopping (Grotthuss mechanism).

Kohlrausch Law

For strong electrolytes, \( \Lambda_m = \Lambda_m^\circ - A\sqrt{C} \) (Debye-Huckel-Onsager equation), so extrapolating to zero concentration gives the limiting value. For weak electrolytes the curve is steep at low concentration and the limiting value cannot be found by extrapolation. Kohlrausch's law of independent migration states that at infinite dilution each ion contributes a fixed amount to \( \Lambda^\circ_m \) regardless of its partner: \( \Lambda^\circ_m = \nu_+\lambda^\circ_+ + \nu_-\lambda^\circ_- \).

Uses: finding the limiting molar conductivity of a weak electrolyte, for example \( \Lambda^\circ(\text{CH}_3\text{COOH}) = \Lambda^\circ(\text{HCl}) + \Lambda^\circ(\text{CH}_3\text{COONa}) - \Lambda^\circ(\text{NaCl}) \); degree of dissociation \( \alpha = \Lambda_m/\Lambda_m^\circ \); and the dissociation constant of a weak electrolyte \( K_a = \dfrac{C\alpha^2}{1-\alpha} \), and solubility of a sparingly soluble salt from \( \kappa \) of its saturated solution (since the solution is very dilute, \( \Lambda_m \approx \Lambda_m^\circ \)).

Example. With \( \Lambda^\circ \) values of 426 (HCl), 91 (sodium acetate) and 126.5 (NaCl) S cm² mol^-1, \( \Lambda^\circ(\text{CH}_3\text{COOH}) = 426 + 91 - 126.5 = 390.5 \). If the measured \( \Lambda_m \) is 39.05, then \( \alpha = 0.1 \).