10.2 Voltaic (Galvanic) Cells & Standard Reduction Potentials

10.2 Voltaic (Galvanic) Cells & Standard Reduction Potentials

Quick Summary: Voltaic (galvanic) cells convert the chemical energy of thermodynamically spontaneous redox reactions ($\Delta G^\circ < 0, E^\circ_{\text{cell}} > 0$) into electrical work by physically separating half-reactions into discrete compartments. Electrons released at the anode flow through an external circuit to the cathode, while a salt bridge maintains electroneutrality by allowing ion migration between compartments. Cell potential is determined by standard reduction potentials measured against the Standard Hydrogen Electrode (SHE).

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1. Voltaic Cell Architecture & Fundamental Operation

In a direct redox reaction, such as dipping solid zinc into aqueous copper(II) sulfate, electrons transfer directly from zinc atoms to copper ions. This releases Gibbs free energy ($\Delta G^\circ = -nFE^\circ = -(2)(96{,}485\text{ C/mol})(1.10\text{ V}) \approx -212\text{ kJ}$ per mole of Zn) purely as thermal energy.

A voltaic (galvanic) cell captures this free energy as electrical work by physically separating the oxidation and reduction half-reactions into two separate containers called half-cells. Electrons must traverse an external circuit (wire) to complete the reaction.

Cell Components and Polarity

Every voltaic cell contains two functional electrodes:

Electrons always flow spontaneously through the external circuit from anode to cathode (from negative to positive terminal).

Voltaic Cell Architecture Schematic

                  External Circuit (Electrons: e⁻ →)
             [V / Load] ---------------------------
            /                                      \
    [-] Anode (Zn)                             [+] Cathode (Cu)
     Oxidation:                                 Reduction:
     Zn → Zn²⁺ + 2e⁻                           Cu²⁺ + 2e⁻ → Cu
          |                                          |
     [Zn²⁺ Solution] <== [ Salt Bridge ] ==> [Cu²⁺ Solution]
                       (Anions ← | → Cations)

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2. The Salt Bridge & Electrolytic Neutrality

As zinc oxidizes at the anode, positive $\text{Zn}^{2+}$ ions accumulate in the anode half-cell. Simultaneously, copper ions reduce at the cathode, depleting positive charge and leaving excess $\text{SO}_4^{2-}$ counterions. Without intervention, this charge separation (polarization) establishes an opposing electric field that halts electron flow almost immediately.

A salt bridge—a U-tube filled with an inert electrolyte gel like $\text{KNO}_3$ or $\text{KCl}$—completes the circuit and sustains current:

• Anions (e.g., $\text{NO}_3^-$) migrate into the anode compartment to balance accumulating cations.
• Cations (e.g., $\text{K}^+$) migrate into the cathode compartment to replace consumed cations.
• Electrons never enter the salt bridge; charge transfer through the liquid phase occurs exclusively via migrating ions.

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3. Standard Cell Notation (Line Notation)

Electrochemists summarize cell configurations using a conventional shorthand called line notation: $\text{Anode (s)} \mid \text{Anodic Electrolyte (aq)} \parallel \text{Cathodic Electrolyte (aq)} \mid \text{Cathode (s)}$

Key conventions include:

1. The oxidation half-cell (anode) is written on the far left; the reduction half-cell (cathode) is written on the far right.
2. A single vertical line ($\mid$) denotes a phase boundary (e.g., between solid electrode and liquid solution).
3. A double vertical line ($\parallel$) designates the salt bridge or porous separator.
4. Molar concentrations and gas partial pressures are indicated in parentheses.
5. When a half-reaction involves only aqueous ions or gases, an inert conductor like platinum ($\text{Pt}$) or graphite is utilized: $\text{Pt}(s) \mid \text{Fe}^{2+}(1.0\text{ M}), \text{Fe}^{3+}(1.0\text{ M}) \parallel \text{Ag}^+(1.0\text{ M}) \mid \text{Ag}(s)$

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4. Standard Reduction Potentials ($E^\circ_{\text{red}}$) & The SHE

Cell potential ($E_{\text{cell}}$), also known as electromotive force (emf), is measured in volts ($\text{V} = \text{J/C}$). Because single half-cell potentials cannot be measured in isolation, all standard potentials are determined relative to the Standard Hydrogen Electrode (SHE), assigned an arbitrary potential of zero volts: $2\text{H}^+(aq, 1.0\text{ M}) + 2e^- \to \text{H}_2(g, 1.0\text{ atm}) \quad E^\circ = 0.000\text{ V}$

Standard Reduction Potentials Reference Table (at 298.15 K)

Interpreting Potential Strengths

• The species with the most positive $E^\circ$ has the greatest affinity for electrons; it is reduced most readily and acts as the strongest oxidizing agent (e.g., $\text{F}_2$).
• The species with the most negative $E^\circ$ is the most difficult to reduce. Its reverse oxidation product is the strongest reducing agent (e.g., $\text{Li}$).

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5. Calculating Standard Cell Potentials & Predicting Spontaneity

Standard cell potential is computed using: $E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}$

Both values are taken directly from the reduction table without inverting signs. Because electrical potential is an intensive property, never multiply $E^\circ$ by stoichiometric coefficients.

Spontaneity Criteria

• $E^\circ_{\text{cell}} > 0$: The reaction is thermodynamically spontaneous under standard conditions.
• $E^\circ_{\text{cell}} < 0$: The forward reaction is nonspontaneous; the reverse reaction is favored.

Worked Calculation

Problem: Calculate $E^\circ_{\text{cell}}$ for a cell operating with nickel and silver electrodes: $\text{Ni}(s) + 2\text{Ag}^+(aq) \to \text{Ni}^{2+}(aq) + 2\text{Ag}(s)$

1. Identify half-reactions:
   • Cathode (reduction): $\text{Ag}^+ + e^- \to \text{Ag} \quad E^\circ = +0.80\text{ V}$
   • Anode (oxidation): $\text{Ni} \to \text{Ni}^{2+} + 2e^- \quad E^\circ = -0.26\text{ V}$
2. Calculate potential: $E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} = (+0.80\text{ V}) - (-0.26\text{ V}) = +1.06\text{ V}$ Since $E^\circ_{\text{cell}} > 0$, the reaction is spontaneous as written.