Specific heat of metals and standard electrode potentials

Abstract

Traditional thermodynamic considerations show that the standard electrode potentials, E0, of metal/metal ion electrodes are linearly related to the Fermi energies of the metal electrons, μ. Expressing E0 in volts, μ in volts/ion, and accounting for the dielectric screening of the solution, the expected slope of the straight line equals 1. Having evaluated μ from the electronic contributions of the specific heats of 11 sp metals in terms of Sommerfeld’s theory, we found a linear relationship between μ and E0. The slope of that line depends on the relative permittivity of water at the metal surface, ɛin. Taking ɛin = 6, in accordance with the general practice in electrochemistry, the expected slope was obtained without any parameter fitting. The intercept of the straight line can be interpreted as the absolute standard potential of the hydrogen electrode finding EH+/H20abs=3.86±0.13V. The calculations being based on equilibrium thermodynamics are independent of any actual mechanism.