Cell Potentials & EMF

Charge Flow in Galvanic Cells

  • Electrons always move from anode → cathode.
    • Anode = site of oxidation (loss of e⁻)
    • Cathode = site of reduction (gain of e⁻)
  • Question addressed: How do we know which species is oxidized or reduced? → Use reduction potentials.

Reduction Potentials (General)

  • Reduction potential (E)
    • Electrical potential (measured in volts, V) assigned to a half-reaction written as a reduction.
    • Specifies the intrinsic “tendency” of a species to gain electrons.
  • Reference electrode: Standard Hydrogen Electrode (SHE)
    • Conventional value: ESHE=0  VE_{\text{SHE}} = 0\;\text{V}
  • Interpretation of sign/magnitude
    • More positive EredE_{\text{red}} → stronger drive to be reduced.
    • Less positive (or negative) EredE_{\text{red}} → species is more easily oxidized (acts as anode in a galvanic cell).

Standard Conditions

  • All tabulated "standard" values assume:
    • Temperature: 25  ∘C  (298  K)25\;^\circ\text{C} \;(298\;\text{K})
    • Pressure: 1  atm1\;\text{atm}
    • Concentrations: 1  M1\;\text{M} for all aqueous species.

Choosing Anode vs. Cathode with EredE_{\text{red}}

  • Galvanic cell (spontaneous)
    • Electrode with more positive EredE_{\text{red}} → cathode
    • Electrode with less positive EredE_{\text{red}} → anode
    • Overall cell free energy: \Delta G < 0
  • Electrolytic cell (non-spontaneous, driven by external voltage)
    • External source forces the electrode with the more positive EredE_{\text{red}} to be oxidized → becomes anode.
    • Electrode with the less positive EredE_{\text{red}} is forced to be reduced → cathode.
    • \Delta G > 0

Converting Reduction ↔ Oxidation Potentials

  • Oxidation potential = negative of the reduction potential for the reverse reaction.
    • Reverse the half-reaction and change the sign.
    • Example (from transcript)
    • Reduction: Ti++e−→Ti  Ered=−0.34  V\text{Ti}^{+} + e^- \rightarrow \text{Ti} \quad\; E_{\text{red}} = -0.34\;\text{V}
    • Oxidation: Ti→Ti++e−  Eox=+0.34  V\text{Ti} \rightarrow \text{Ti}^{+} + e^- \quad\; E_{\text{ox}} = +0.34\;\text{V}
  • MCAT & most tables supply only EredE_{\text{red}}; convert as needed.

Example 1 – Ag⁺ / Ti⁺ Half-Cells (Galvanic)

  • Given half-reactions (all as reductions):
    • Ag++e−→AgEred=+0.80  V\text{Ag}^+ + e^- \rightarrow \text{Ag} \quad E_{\text{red}} = +0.80\;\text{V}
    • Ti++e−→TiEred=−0.34  V\text{Ti}^+ + e^- \rightarrow \text{Ti} \quad E_{\text{red}} = -0.34\;\text{V}
  • Analysis
    • Ag⁺ has the more positive reduction potential → will be reduced (cathode).
    • Ti(s) will be oxidized to Ti+\text{Ti}^+ (anode).
  • Net ionic equation (spontaneous):
    Ag++Ti(s)  →  Ti++Ag(s)\text{Ag}^+ + \text{Ti(s)} \;\rightarrow\; \text{Ti}^+ + \text{Ag(s)}

Electromotive Force (EMF)

  • Definition: Voltage difference between two half-cells under standard conditions.
  • Formula (standard):
    E<em>cell∘=E</em>red,cathode∘−Ered,anode∘E<em>{\text{cell}}^{\circ} = E</em>{\text{red,cathode}}^{\circ} - E_{\text{red,anode}}^{\circ}
  • Do not multiply potentials by stoichiometric coefficients—potential depends on identity, not quantity, of species.

Example 2 – Sm³⁺ vs. RhCl63−\text{RhCl}_{6}^{3-}

  • Given EredE_{\text{red}} values
    • Sm3++3e−→SmEred=−2.41  V\text{Sm}^{3+} + 3e^- \rightarrow \text{Sm} \quad E_{\text{red}} = -2.41\;\text{V}
    • RhCl<em>63−+3e−→Rh+6Cl−E</em>red=+0.44  V\text{RhCl}<em>{6}^{3-} + 3e^- \rightarrow \text{Rh} + 6\text{Cl}^- \quad E</em>{\text{red}} = +0.44\;\text{V}
  • Half-reaction roles as written in transcript’s equation
    • Sm3+\text{Sm}^{3+} is reduced.
    • Rh\text{Rh} (within RhCl63−\text{RhCl}_{6}^{3-} framework) is oxidized.
  • EMF calculation: Ecell∘=(−2.41  V)−(+0.44  V)=−2.85  VE_{\text{cell}}^{\circ} = (-2.41\;\text{V}) - (+0.44\;\text{V}) = -2.85\;\text{V}
    • Negative EMF → electrolytic under stated orientation.
    • Reversing the reaction (making it galvanic) would give +2.85  V+2.85\;\text{V} and proceed spontaneously in the opposite direction.

Practical & Conceptual Notes

  • Lead–acid and nickel–cadmium batteries (mentioned) employ the same sign conventions—tables usually list reduction potentials, even when oxidation half-reactions are discussed.
  • In calculations of ΔG\Delta G for electrochemical cells: ΔG∘=−nFEcell∘\Delta G^{\circ} = -nF E_{\text{cell}}^{\circ}
    • nn = moles of electrons transferred
    • FF = Faraday constant ≈96,485  C mol−1\approx 96,485\;\text{C\,mol}^{-1}
  • Ethical / safety implication: Knowing EMF and directionality guides safe battery charging/discharging and electrolysis operations.
  • Philosophical note: The arbitrary zero point (SHE) illustrates convention-driven measurement systems—absolute potentials aren’t measurable, only differences.