Galvanic cells Knowledge-Based Study

Study notes

1. A galvanic cell (also called a voltaic cell) is an electrochemical system that converts chemical energy released by a spontaneous oxidation-reduction reaction into electrical energy.

   Fundamental Principles

   • Spontaneous Redox Reaction: The overall reaction has a negative Gibbs free energy change, meaning it occurs naturally without an external driving voltage.
   • Spatial Separation: Oxidation and reduction half-reactions are isolated into separate compartments, preventing direct electron transfer between reactants.
   • Electrical Work: Electrons released during oxidation are directed through an external conducting circuit, producing an electric current that can power external devices.

   A typical galvanic cell consists of two half-cells joined by an external circuit and an internal ionic conductor.

   Essential Components

   • Anode: The electrode where oxidation occurs. It serves as the negative terminal in a galvanic cell because electrons originate here and enter the external circuit.
   • Cathode: The electrode where reduction occurs. It serves as the positive terminal because electrons flow toward it from the external circuit.
   • External Circuit: A conductive wire connecting the electrodes, often equipped with a voltmeter or load, through which electrons flow from anode to cathode.
   • Salt Bridge: A tube containing an inert electrolyte solution that connects both half-cells. It maintains electrical neutrality by allowing anions to diffuse toward the anode compartment and cations toward the cathode compartment, preventing charge accumulation that would stop current flow.

   The Daniell cell, composed of zinc and copper half-cells, provides a standard model for analyzing galvanic processes.

   Half-Reactions

   • Anode (Oxidation): $\text{Zn}(s) \rightarrow \text{Zn}^{2+}(aq) + 2e^-$
   • Cathode (Reduction): $\text{Cu}^{2+}(aq) + 2e^- \rightarrow \text{Cu}(s)$
   • Overall Cell Reaction: $\text{Zn}(s) + \text{Cu}^{2+}(aq) \rightarrow \text{Zn}^{2+}(aq) + \text{Cu}(s)$

   Standard Cell Notation

   Chemists represent galvanic cells using shorthand line notation, conventionally written from anode (left) to cathode (right):

   $\text{Zn}(s) \mid \text{Zn}^{2+}(aq) \parallel \text{Cu}^{2+}(aq) \mid \text{Cu}(s)$

   A single vertical line represents a phase boundary, while a double vertical line represents the salt bridge or porous separator.

   The potential difference between the cathode and anode is known as the cell potential ($E_{\text{cell}}$) or electromotive force (EMF), measured in volts.

   Standard Cell Potential

   Under standard conditions (solute concentrations of 1 M, gas pressures of 1 atm, and a temperature of 298 K), the standard cell potential is determined from standard reduction potentials:

   $E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}$

   Criteria for Spontaneity

   • A positive standard cell potential ($E^\circ_{\text{cell}} > 0$) indicates a thermodynamically spontaneous reaction under standard conditions.
   • The relationship to standard Gibbs free energy is given by $\Delta G^\circ = -nFE^\circ_{\text{cell}}$, where n is the moles of electrons transferred and F is the Faraday constant.
   • Because $E^\circ_{\text{cell}}$ is positive for any functional galvanic cell, $\Delta G^\circ$ is necessarily negative.