Electrochemical Cells and Electrode Potential — Notes

Electrochemical (galvanic/voltaic) cell: spontaneous redox reaction → electrical energy; anode negative, cathode positive. Electrolytic cell: electrical energy drives a non-spontaneous reaction; anode positive, cathode negative. In both, oxidation at the anode, reduction at the cathode.

Daniell cell: $\ce{Zn(s) + Cu^2+(aq) -> Zn^2+(aq) + Cu(s)}$; anode $\ce{Zn -> Zn^2+ + 2e-}$, cathode $\ce{Cu^2+ + 2e- -> Cu}$; $E^\circ_\text{cell} = 1.10\ \text{V}$. Electrons flow in the external circuit from Zn to Cu; current flows from Cu to Zn.

Salt bridge (KCl, KNO₃ or NH₄NO₃ in agar): completes the circuit, maintains electrical neutrality, prevents mixing of solutions, minimises liquid junction potential.

Cell notation: anode | anode electrolyte || cathode electrolyte | cathode; $E_\text{cell} = E_\text{right} - E_\text{left}$.

An electrode in contact with its ions sets up $\ce{M^{n+} + ne- <=> M}$; the resulting potential difference is the electrode potential. Absolute values cannot be measured, so potentials are measured against the standard hydrogen electrode (E° = 0 V at all temperatures) and quoted as reduction potentials (IUPAC). Standard conditions: 1 M ions, 1 bar gases, 298 K.

SHE: Pt foil coated with platinum black in 1 M H⁺, pure H₂ at 1 bar bubbled over it; $\ce{2H+(aq) + 2e- <=> H2(g)}$. Limitations: difficult to maintain exactly 1 M H⁺ and 1 bar H₂; Pt easily poisoned; cannot be used in the presence of oxidising agents; cumbersome.

Measuring E°: Zn | Zn²⁺(1 M) || SHE gives 0.76 V with Zn as anode, so $E^\circ_{\ce{Zn^2+/Zn}} = -0.76\ \text{V}$; SHE || Cu²⁺(1 M) | Cu gives 0.34 V with Cu as cathode, so $E^\circ_{\ce{Cu^2+/Cu}} = +0.34\ \text{V}$.

• Concentration of ions: for $\ce{M^{n+} + ne- -> M}$, $E = E^\circ + \dfrac{0.059}{n}\log[\ce{M^{n+}}]$ at 298 K; higher [Mⁿ⁺] gives a more positive E.
• Temperature: the Nernst factor $2.303RT/nF$ increases with $T$.
• Nature of the electrode: metals with low sublimation and ionisation enthalpies and high hydration enthalpy of their ions lose electrons easily and have more negative E°.

Electrodes arranged in order of standard reduction potential (F₂/F⁻ +2.87 … Li⁺/Li −3.05 V).

Applications: (1) relative strengths of oxidising and reducing agents (more positive E° → stronger oxidant); (2) a metal with lower E° displaces one with higher E° from its salt solution; (3) metals with negative E° liberate H₂ from dilute acids; (4) $E^\circ_\text{cell} = E^\circ_\text{cathode} - E^\circ_\text{anode}$; (5) feasibility: a redox reaction is spontaneous if $E^\circ_\text{cell} > 0$.

E° is an intensive property: it is not multiplied by stoichiometric coefficients.

Nernst equation: $E_\text{cell} = E^\circ_\text{cell} - \dfrac{2.303RT}{nF}\log Q = E^\circ_\text{cell} - \dfrac{0.059}{n}\log Q$ (298 K); $Q$ = products ÷ reactants, pure solids omitted. For the hydrogen electrode, $E = -0.059\,\text{pH}$ (1 bar H₂).

Gibbs energy: $\Delta G = -nFE_\text{cell}$, $\Delta G^\circ = -nFE^\circ_\text{cell}$; spontaneous if $E > 0$ ($\Delta G < 0$).

Equilibrium constant: at equilibrium $E_\text{cell} = 0$, so $E^\circ_\text{cell} = \dfrac{2.303RT}{nF}\log K = \dfrac{0.059}{n}\log K$ (298 K); also $\Delta G^\circ = -2.303RT\log K$.