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Why is the Gibbs Free Energy of Formation of the Hydrogen Ion not zero?

You can enable some additional properties in OLI Studio and OLI Flowsheet: ESP. To do this in OLI Studio, see: How to Enable and View Optional Calculation Properties in OLI Studio. For OLI Flowsheet: ESP, see: How to enable the optional properties and calculations in OLI Flowsheet: ESP.

One of the most basic ideas in thermodynamics is that the Gibbs Energy of Formation of an element is zero at the reference state. In electrolyte chemistry, this is extended to the hydrogen ion (H+). Yet...

 

The Gibbs Free Energy of Formation for the H+ should be zero. Here we are calculating the value as 9956.79 J/mol. It is in various thermodynamic textbooks, so why is OLI calculating something different?

The difference in the standard state Gibbs Free Energy for species (e.g., H+) in the OLI report from what is usually reported in the literature (for H+ is zero by definition) is due to different concentration scales, i.e.,

 

where:

  • superscript m is the molal-based G0
  • superscript x is mole fraction-based G0

 

OLI reports the x-based value.

Thus, at 25 ℃ and 1 atm:

G0,m(H+) = 0, G0,x(H+) = 0 + RT * ln (55.50825) = 9956.8 [J/mol]

where:

  • R = 8.31446 J mol⁻¹ K⁻¹ (universal gas constant)
  • T = 298.15 K (temperature in Kelvin)
  • 55.50825 is the molar concentration of water in mol/L

 

Our 2002 paper has a description of the conversion. 

Citation: 

Peiming Wang, Andrzej Anderko, Robert D. Young, "A speciation-based model for mixed-solvent electrolyte systems," Fluid Phase Equilibria, Volume 203, Issues 1–2, 2002, Pages 141-176,
ISSN 0378-3812, https://doi.org/10.1016/S0378-3812(02)00178-4.

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