Application of the Gouy-Chapman equation in metal speciation modelling

While expanding a speciation model to include adsorption of trace elements in marine aquatic systems, we encountered a confusing presentation of the Gouy-Chapman (G-C) equation which is used to quantify ion sorption on charged particles. The G-C equation relates particle surface charge (σ in C m^-2) and surface potential (ψ in V) as: σ = [8×n(o)×ε(r)×ε(o)×kT]1/2 sinh[Zeπ2kT] where n(o) is the concentration of ions (m^-3), ε(r) is the dimensionless dielectric constant of the surrounding medium, ε(o) is the permittivity of vacuum, kT is the Boltzmann constant times the absolute temperature, z is the ion valence, and e is the charge of an electron (C). For an aqueous medium of ionic strength I (M) containing uniunivalent electrolytes at 25°C, σ = 0.1174 I^1/2 sinh(19.46ψ). The square root argument of the G-C equation has alternatively been reported as [(2/π)×n(o)×ε(r)×kT], making it unclear how the factor of 0.1174 is obtained. We have reconciled these different expressions in order to assist others in applying the G-C equation in speciation models including electrostatic adsorption.