Cell potential Knowledge-Based Study

Study notes

1. In an electrochemical cell, a spontaneous redox reaction drives the movement of electrons through an external circuit. The force driving this movement is called the cell potential (also known as electromotive force, or EMF), designated as $E_{\text{cell}}$.

   Cell potential represents the difference in electric potential between the two half-cells (electrodes):

   • Units: Cell potential is measured in volts (V), where $1\text{ V} = 1\text{ J/C}$. One volt represents one joule of energy per coulomb of electrical charge transferred.
   • Direction of Flow: Electrons spontaneously flow from the electrode with a lower reduction potential (anode) to the electrode with a higher reduction potential (cathode).

   To compare different half-reactions, chemists measure cell potentials under standard thermodynamic conditions:

   • Solute concentrations of $1.0\text{ M}$
   • Gas pressures of $1.0\text{ bar}$ (or $1.0\text{ atm}$)
   • A specified temperature, typically $298\text{ K}$ ($25^\circ\text{C}$)

   Individual electrode potentials cannot be measured directly in isolation. Therefore, standard potentials are measured relative to a universal baseline known as the Standard Hydrogen Electrode (SHE), which is arbitrarily assigned a standard reduction potential of exactly $0.00\text{ V}$:

   $2\text{H}^+(aq) + 2e^- \rightarrow \text{H}_2(g) \quad E^\circ = 0.00\text{ V}$

   A more positive standard reduction potential ($E^\circ$) indicates a stronger tendency for the chemical species to gain electrons (act as an oxidizing agent).

   When both half-cell reactions are tabulated as standard reduction potentials, the standard cell potential ($E^\circ_{\text{cell}}$) is calculated using the following relationship:

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

   Key Principles to Remember:

   • Intensive Property: Standard reduction potential is an intensive property. Multiplying a half-reaction by a stoichiometric coefficient to balance electrons does not change the value of $E^\circ$.
   • Subtraction Handles the Direction: Because standard tables list reduction potentials for both half-reactions, subtracting $E^\circ_{\text{anode}}$ accounts for the fact that oxidation occurs at the anode. Do not change the sign of $E^\circ$ prior to applying this formula.

   The standard cell potential is directly related to the standard Gibbs free energy change ($\Delta G^\circ$) of the redox process by the following fundamental equation:

   $$\Delta G^\circ = -nFE^\circ_{\text{cell}}$$

   Here, $n$ is the number of moles of electrons transferred in the balanced redox equation, and $F$ is Faraday's constant (approximately $96{,}485\text{ C/mol}$).

   Spontaneity Criteria:

   • If $E^\circ_{\text{cell}} > 0$, then $\Delta G^\circ < 0$: The reaction is spontaneous under standard conditions, which is the operational basis of galvanic (voltaic) cells.
   • If $E^\circ_{\text{cell}} < 0$, then $\Delta G^\circ > 0$: The forward reaction is non-spontaneous under standard conditions and requires external electrical work to proceed (electrolytic cells).
   • If $E^\circ_{\text{cell}} = 0$, the cell has reached electrochemical equilibrium and can do no electrical work.