Electrolytic Conductance, Electrolysis, Batteries and Corrosion — Notes

Metallic conductance: by electrons, no chemical change, decreases with rise in temperature. Electrolytic conductance: by ions, chemical change at electrodes, increases with temperature.

$R = \rho\,l/A$; conductance $G = 1/R$ (S); specific conductance $\kappa = 1/\rho$ (S cm⁻¹); cell constant $G^* = l/A$ (cm⁻¹); $\kappa = G^*/R$. The cell constant is found with a KCl solution of known $\kappa$; AC is used to avoid electrolysis.

$\Lambda_\text{m} = \dfrac{1000\,\kappa}{M}$ (S cm² mol⁻¹); $\Lambda_\text{eq} = \dfrac{1000\,\kappa}{N}$ (S cm² eq⁻¹); $\Lambda_\text{m} = n\,\Lambda_\text{eq}$.

On dilution: $\kappa$ decreases (fewer ions per cm³); $\Lambda_\text{m}$ and $\Lambda_\text{eq}$ increase (greater ion mobility; for weak electrolytes, more dissociation).

Strong electrolytes: $\Lambda_\text{m} = \Lambda^\circ_\text{m} - A\sqrt{c}$ — a straight line extrapolated to $c = 0$. Weak electrolytes: low $\Lambda_\text{m}$ rising steeply at high dilution; $\Lambda^\circ_\text{m}$ cannot be found by extrapolation.

At infinite dilution each ion makes a definite contribution independent of the other ion: $\Lambda^\circ_\text{m} = \nu_+\lambda^\circ_+ + \nu_-\lambda^\circ_-$.

Applications: $\Lambda^\circ_\text{m}$ of weak electrolytes by combining strong ones, e.g. $\Lambda^\circ(\ce{CH3COOH}) = \Lambda^\circ(\ce{HCl}) + \Lambda^\circ(\ce{CH3COOK}) - \Lambda^\circ(\ce{KCl})$; degree of dissociation $\alpha = \Lambda_\text{m}/\Lambda^\circ_\text{m}$; dissociation constant $K_\text{a} = c\alpha^2/(1-\alpha)$; solubility of sparingly soluble salts ($S = 1000\kappa/\Lambda^\circ_\text{m}$).

First law: $m = ZQ = ZIt$ ($Z$ = electrochemical equivalent). Second law: for the same charge, $m_1/m_2 = E_1/E_2$ (equivalent masses).

$F = N_\text{A}e = 6.022 \times 10^{23} \times 1.602 \times 10^{-19} \approx 96500\ \text{C mol}^{-1}$: the charge on one mole of electrons, which deposits one gram equivalent of any substance.

Working: $Q = It$ (t in seconds) → moles of e⁻ $= Q/F$ → moles of product $= Q/(nF)$ → mass $= MQ/(nF)$.

Primary cells (not rechargeable): Leclanché dry cell — anode $\ce{Zn -> Zn^2+ + 2e-}$; cathode $\ce{MnO2 + NH4+ + e- -> MnO(OH) + NH3}$; about 1.5 V. Mercury cell — anode $\ce{Zn + 2OH- -> ZnO + H2O + 2e-}$ (zinc amalgam); cathode $\ce{HgO + H2O + 2e- -> Hg + 2OH-}$; overall $\ce{Zn + HgO -> ZnO + Hg}$; constant 1.35 V.

Secondary cells (rechargeable): lead storage battery — anode $\ce{Pb + SO4^2- -> PbSO4 + 2e-}$; cathode $\ce{PbO2 + SO4^2- + 4H+ + 2e- -> PbSO4 + 2H2O}$; acid density falls on discharge. Ni–Cd cell.

H₂–O₂ fuel cell: anode $\ce{2H2 + 4OH- -> 4H2O + 4e-}$; cathode $\ce{O2 + 2H2O + 4e- -> 4OH-}$; about 70% efficient; product water.

Corrosion of iron: anode $\ce{Fe -> Fe^2+ + 2e-}$; cathode $\ce{O2 + 4H+ + 4e- -> 2H2O}$; Fe²⁺ → rust (Fe₂O₃·xH₂O). Promoted by moisture, O₂, electrolytes, CO₂/SO₂, contact with less active metals. Prevention: barrier coatings, galvanising (Zn), sacrificial anodes (Mg, Zn), alloying (stainless steel), anti-rust solutions.