Computing pH

This page follows Chapter 11 of Bethke (2007).

The geochemistry module can be used to provide values for pH assuming equilibrium. Recall that $var element = document.getElementById("moose-equation-8f68ae94-aaab-4f51-a721-6e2ab2c57b41");katex.render("\\mathrm{pH} = -\\log_{10}a_{\\mathrm{H}^{+}} \\ ,", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ where $var element = document.getElementById("moose-equation-13197e94-67cf-4530-a694-2c18b7a55204");katex.render("a", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ denotes activity.

An example of such a calculation involves the mineral hematite. Hematite's equilibrium reaction is $var element = document.getElementById("moose-equation-1c3a806e-4b53-4e54-a0da-2989e7affe6e");katex.render("\\mathrm{hematite} \\rightleftharpoons 2\\mathrm{H}_{2}\\mathrm{O} - 4\\mathrm{H}^{+} + 2\\mathrm{Fe}^{2+} + \\frac{1}{2}\\mathrm{O}_{2}\\mathrm{(aq)} \\ ,", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ has an equilibrium constant $var element = document.getElementById("moose-equation-485bf945-76a8-4355-b2c5-e248215c5e50");katex.render("\\log_{10}K = -16.93", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ at 25 $var element = document.getElementById("moose-equation-82259f85-c934-4b10-8004-376a4e67856c");katex.render("^{\\circ}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ C. Assuming a water activity of 1, and $var element = document.getElementById("moose-equation-cd6daa44-501c-4350-a388-d84b4980812f");katex.render("a_{\\mathrm{Fe}^{2+}} = 10^{-10}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , equilibrium reads $(1)var element = document.getElementById("moose-equation-19508ca3-bc52-4958-8b1e-7be409e5fe41");katex.render(" \\log_{10}a_{\\mathrm{O}_{2}\\mathrm{(aq)}} = 6.14 - 8\\mathrm{pH} \\ .", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

To perform this calculation using the geochemistry module, a GeochemicalModelDefinition object must be created with the desired mineral species:

[UserObjects]
  [definition]
    type = GeochemicalModelDefinition
    database_file = "../../../database/moose_geochemdb.json"
    basis_species = "H2O Fe++ H+ O2(aq)"
    equilibrium_minerals = "Hematite"
    piecewise_linear_interpolation = true # to get exact logK at 25degC with no best-fit interpolation
  []
[]

Then a GeochemicalModelInterrogator must be created which specifies the desired swaps and the interrogation = activity instruction:

[GeochemicalModelInterrogator]
  model_definition = definition
  equilibrium_species = Hematite
  activity_species = 'H2O Fe++'
  activity_values = '1 1E-10'
  interrogation = activity
[]

The output yields the desired information:


(A_H+)^-4 (A_O2(aq))^0.5 = 10^3.068

This is the square-root of Eq. (1).

References

Craig M. Bethke. Geochemical and Biogeochemical Reaction Modeling. Cambridge University Press, 2 edition, 2007. doi:10.1017/CBO9780511619670.

@book{bethke_2007,
    author = "Bethke, Craig M.",
    place = "Cambridge",
    edition = "2",
    title = "Geochemical and Biogeochemical Reaction Modeling",
    DOI = "10.1017/CBO9780511619670",
    publisher = "Cambridge University Press",
    year = "2007"
}

(modules/geochemistry/test/tests/interrogate_reactions/hematite.i)

# Compute pH values for an equilibrium reaction involving the mineral hematite
[GeochemicalModelInterrogator]
  model_definition = definition
  equilibrium_species = Hematite
  activity_species = 'H2O Fe++'
  activity_values = '1 1E-10'
  interrogation = activity
[]

[UserObjects]
  [definition]
    type = GeochemicalModelDefinition
    database_file = "../../../database/moose_geochemdb.json"
    basis_species = "H2O Fe++ H+ O2(aq)"
    equilibrium_minerals = "Hematite"
    piecewise_linear_interpolation = true # to get exact logK at 25degC with no best-fit interpolation
  []
[]

(modules/geochemistry/test/tests/interrogate_reactions/hematite.i)

# Compute pH values for an equilibrium reaction involving the mineral hematite
[GeochemicalModelInterrogator]
  model_definition = definition
  equilibrium_species = Hematite
  activity_species = 'H2O Fe++'
  activity_values = '1 1E-10'
  interrogation = activity
[]

[UserObjects]
  [definition]
    type = GeochemicalModelDefinition
    database_file = "../../../database/moose_geochemdb.json"
    basis_species = "H2O Fe++ H+ O2(aq)"
    equilibrium_minerals = "Hematite"
    piecewise_linear_interpolation = true # to get exact logK at 25degC with no best-fit interpolation
  []
[]

References