9.1: Electrochemical Systems

Electrochemical systems provide a fascinating insight into the dynamic interplay of charged species within various phases. One notable example is the interaction between a membrane permeable to K⁺ ions but not to Cl⁻ ions, separating an aqueous KCl solution from pure water. As K⁺ ions diffuse through the membrane, they generate net charges on each phase, leading to a potential difference between them.

Similarly, when a piece of Zn is immersed in an aqueous ZnSO₄ solution, the Zn metal, composed of Zn²⁺ ions and mobile valence electrons, undergoes a dynamic equilibrium where the rates of Zn²⁺ leaving and entering the metal become equal. This results in a net negative charge on the Zn, creating a potential difference (ΔΦ) between the metal and the solution.

The charge associated with Zn²⁺ ions crossing 1 cm² of the metal–solution interface in 1 s, known as the exchange current, is 2 × 10⁻⁵ C. Utilizing the charge on one proton (e = 1.60218 x 10⁻¹⁹ C) and the Avogadro constant (N_A = 6.02214 x 10²³ mol⁻¹), the Faraday constant (F) is determined; F = N_Ae = 96485 C/mol.

The charge on a particle of species i is z_ie, where z_i is the charge number. Therefore, the charge per mole of species i is z_iF, and the charge on n_i moles of i is Q_i = z_iFn_i.

The magnitude and sign of ΔΦ depend on several factors, including temperature, pressure, the nature of the metal, the solvent, and the concentrations of metal ions in the solution.

An example involving Cu and Zn demonstrates that even though solid ions don't diffuse significantly, electrons can move freely between metals, leading to a net charge on each metal at equilibrium. This phenomenon, discovered by Galvani and Volta in the 1790s, has practical applications, such as in thermocouples that utilize the temperature-dependent interphase potential difference to measure temperature.

Electrochemical systems involve a difference in electric potential between two or more phases at equilibrium, where no net chemical transfer occurs, and the potential difference reflects only the electric potential; otherwise, both electric and chemical potentials influence the system. Besides charge transfer, factors like water molecule orientation, electron distribution, and ion distribution contribute to ΔΦ. The potential difference can even arise without charge transfer, as seen in a two-phase system of immiscible liquids. While measuring ΔΦ directly between phases in contact is challenging due to the creation of new interfaces, statistical-mechanical models offer a means to calculate ΔΦ if the distribution of charges and dipoles in the interphase region is known.