Electrochemistry — Notes

A galvanic (voltaic) cell converts the Gibbs energy of a spontaneous redox reaction into electrical energy. In the Daniell cell, zinc is oxidised at the anode ($\ce{Zn -> Zn^2+ + 2e-}$) and copper(II) ions are reduced at the cathode ($\ce{Cu^2+ + 2e- -> Cu}$); with 1 M solutions the EMF is 1.10 V. A salt bridge (KCl or $\ce{NH4NO3}$ in agar) completes the internal circuit and keeps the solutions electrically neutral.

Cell notation: anode | anode solution || cathode solution | cathode, e.g. $\ce{Zn(s) | Zn^2+(aq) || Cu^2+(aq) | Cu(s)}$. $E_\text{cell} = E_\text{right} - E_\text{left} = E_\text{cathode} - E_\text{anode}$.

Electrode potential is measured against the standard hydrogen electrode (Pt, platinum black, $\ce{H2}$ at 1 bar, $[\ce{H+}] = 1\ \text{M}$), assigned $E^\circ = 0$. Standard conditions: 1 M, 1 bar, 298 K. The electrochemical series lists standard reduction potentials: the more positive $E^\circ$, the stronger the oxidising agent (F₂ +2.87 V); the more negative, the stronger the reducing agent (Li −3.05 V). A metal with a lower $E^\circ$ displaces the ions of one with a higher $E^\circ$; metals with negative $E^\circ$ liberate hydrogen from dilute acids. $E^\circ$ values are intensive: never multiply them by stoichiometric coefficients.

For $\ce{M^{n+} + ne- -> M}$: $E = E^\circ - \dfrac{2.303RT}{nF}\log\dfrac{1}{[\ce{M^{n+}}]}$. At 298 K, $\dfrac{2.303RT}{F} = 0.059\ \text{V}$.

For a cell, $E_\text{cell} = E^\circ_\text{cell} - \dfrac{0.059}{n}\log Q$, where $Q$ = products over reactants (pure solids omitted). For the Daniell cell $Q = [\ce{Zn^2+}]/[\ce{Cu^2+}]$. For a hydrogen electrode at 1 bar, $E = -0.059\,\text{pH}$.

Gibbs energy: $\Delta_\text{r}G = -nFE_\text{cell}$ and $\Delta_\text{r}G^\circ = -nFE^\circ_\text{cell}$ ($F = 96500\ \text{C mol}^{-1}$). Positive $E$ ⇒ negative $\Delta G$ ⇒ spontaneous.

Equilibrium: at equilibrium $E_\text{cell} = 0$ and $Q = K$, so $E^\circ_\text{cell} = \dfrac{0.059}{n}\log K$ and $\Delta_\text{r}G^\circ = -2.303RT\log K$. For the Daniell cell $\Delta_\text{r}G^\circ = -212.3\ \text{kJ mol}^{-1}$ and $K \approx 10^{37}$.

$R = \rho\dfrac{l}{A}$; conductance $G = 1/R$ (S); conductivity $\kappa = 1/\rho$ ($\text{S cm}^{-1}$ or $\text{S m}^{-1}$). In a conductivity cell, $\kappa = G^*/R$ where the cell constant $G^* = l/A$ is found with a standard KCl solution; alternating current is used.

Molar conductivity $\Lambda_\text{m} = \dfrac{\kappa \times 1000}{c}$ ($\text{S cm}^2\ \text{mol}^{-1}$, with κ in S cm⁻¹ and c in mol L⁻¹). On dilution κ decreases (fewer ions per unit volume) but Λm increases.

• Strong electrolytes: $\Lambda_\text{m} = \Lambda^\circ_\text{m} - A\sqrt{c}$; $\Lambda^\circ_\text{m}$ by extrapolation to $c = 0$.
• Weak electrolytes: Λm rises steeply at low c because the degree of dissociation increases; $\Lambda^\circ_\text{m}$ cannot be extrapolated.

Kohlrausch’s law: $\Lambda^\circ_\text{m} = \nu_+\lambda^\circ_+ + \nu_-\lambda^\circ_-$. Uses: $\Lambda^\circ_\text{m}$ of weak electrolytes from strong ones (e.g. $\Lambda^\circ(\ce{NH4OH}) = \Lambda^\circ(\ce{NH4Cl}) + \Lambda^\circ(\ce{NaOH}) - \Lambda^\circ(\ce{NaCl})$); degree of dissociation $\alpha = \Lambda_\text{m}/\Lambda^\circ_\text{m}$; and $K_\text{a} = \dfrac{c\alpha^2}{1 - \alpha}$.

In an electrolytic cell, an external source drives a non-spontaneous reaction: reduction at the cathode (negative), oxidation at the anode (positive).

Faraday’s first law: $m = ZIt$ (mass ∝ charge $Q = It$). Second law: for the same charge, masses deposited are proportional to $M/n$. One faraday ($F \approx 96500\ \text{C}$) is one mole of electrons: it deposits 1 mol Ag, ½ mol Cu, ⅓ mol Al.

Products depend on the electrolyte’s state, the electrodes and $E^\circ$ values (with overpotential):

• molten NaCl: Na at cathode, Cl₂ at anode;
• concentrated aqueous NaCl: H₂ at cathode (water reduced), Cl₂ at anode (oxygen has a high overpotential);
• dilute H₂SO₄ (Pt): H₂ and O₂; concentrated H₂SO₄: H₂ and peroxodisulfate ions;
• aqueous CuSO₄: Cu at cathode; with a copper anode the anode dissolves (refining, plating), with Pt the anode gives O₂.

Primary batteries (not rechargeable): dry (Leclanché) cell — zinc container anode, carbon rod cathode with $\ce{MnO2}$, paste of $\ce{NH4Cl}$ and $\ce{ZnCl2}$; about 1.5 V. Mercury cell — Zn–Hg amalgam anode, HgO + carbon cathode, KOH/ZnO electrolyte; about 1.35 V, constant over its life because no ion concentration changes.

Secondary batteries (rechargeable): lead storage battery — Pb anode, $\ce{PbO2}$ cathode, about 38% $\ce{H2SO4}$. Discharge: $\ce{Pb + PbO2 + 2H2SO4 -> 2PbSO4 + 2H2O}$; the acid’s density falls. Charging reverses it. Nickel–cadmium cells last longer but cost more.

Fuel cells convert the energy of a fuel directly into electricity with continuous feed. H₂–O₂ cell: anode $\ce{2H2 + 4OH- -> 4H2O + 4e-}$, cathode $\ce{O2 + 2H2O + 4e- -> 4OH-}$, overall $\ce{2H2 + O2 -> 2H2O}$; about 70% efficient, pollution-free, used in spacecraft.

Corrosion is the slow destruction of a metal by its surroundings; rusting of iron is an electrochemical process. At an anodic spot: $\ce{2Fe -> 2Fe^2+ + 4e-}$. Electrons flow through the metal to a cathodic spot: $\ce{O2 + 4H+ + 4e- -> 2H2O}$ ($\ce{H+}$ from $\ce{H2CO3}$ formed by dissolved $\ce{CO2}$). Overall: $\ce{2Fe + O2 + 4H+ -> 2Fe^2+ + 2H2O}$. $\ce{Fe^2+}$ is oxidised further to rust, $\ce{Fe2O3.xH2O}$. Salt water speeds corrosion by increasing conductivity.

Prevention: barrier coatings (paint, oil, grease, plastic); galvanising (zinc coat, which corrodes preferentially even when scratched); sacrificial anodes (magnesium or zinc blocks on ships and pipelines); anti-rust chemicals (e.g. phosphate coatings).