Diprotic Acid

breed [acids acid]           ;; acid molecules (yellow)
breed [hydroxides hydroxide] ;; base molecules (red)
breed [hydroniums hydronium]  ;; hydronium ions (green)
breed [waters water]         ;; water molecules (blue)
breed [con-bases con-base]   ;;first conjugate base molecules (magenta)
breed [con-base2s con-base2] ;;second conjugate base molecules (cyan)

globals
  [
   pH pOH                                         ;;variables for calculating pH
   mmolH mmolOH mmolA mmolA2 mmolHA               ;;variables for calculating amount of molecules
   Hconc OHconc Aconc HAconc A2conc volume        ;;variables for calculating concentrations
  ]

turtles-own [partner]                                  ;;variable to control reactions

to setup
  clear-all
  set-default-shape waters "water"
  set-default-shape hydroniums "hydronium"
  set-default-shape hydroxides "hydroxide"
  set-default-shape acids "acid"
  set-default-shape con-bases "conbase"
  set-default-shape con-base2s "conbase2"
  ;;creates variable amount of acid
  create-acids starting-acid
  ;;initializes the amount of dissociated acid
  ask acids
    [
     if ((random 100) > (99 - Ka1))
      [
       hatch-hydroniums 1 [fd 3]
       set breed con-bases
      ]
    ]
  ;;initializes the amount of dissociated conjugate base
  ask con-bases
    [
     if ((random 100) > (99 - Ka2))
      [
       hatch-hydroniums 1 [fd 3]
       set breed con-base2s
      ]
    ]
  if see-starting-water?
    [ create-waters (100 - (count hydroniums)) ]
  calculate-ions    ;;used to calculate pH
  set-colors    ;;assigns colors
  set mmolOH 0
  ;; calculates overall number of molecules (total volume)
  set volume count turtles
  ;;randomizes position and headings
  ask turtles [setxy random-xcor random-ycor]
  reset-ticks
  plot-molecules
  plot-ph
end 

to go ;;main turtle procedure
  collide
  set-colors
  ask turtles [fd 1]
  calculate-ions
  tick
  if (ticks > 30) [plot-pH plot-molecules]
end 

to collide ;;turtle procedure - tells molecules how to find other molecules
  ;; hydroxide molecules will react with all proton donor molecules in the model
  if (count hydroxides > 0)
    [
     ask hydroxides
       [
        if any? hydroniums-here [set partner one-of hydroniums-here react-bases]
        if any? acids-here [set partner one-of acids-here react-bases]
        if any? con-bases-here [set partner one-of con-bases-here react-bases]
       ]
    ]

  ;; acid molecules always have a chance to dissociate to hydroniums depending on their
  if (count acids > 0)
    [
     ask acids
       [
        if ((random 100) > (99 - Ka1))
          [if any? waters-here [set partner one-of waters-here react-acids]]
       ]
    ]

  ;; conjugate base molecules always have a chance to dissociate to hydroniums depending on their Ka
  if count con-bases > 0
    [
      ask con-bases
        [
         if ((random 100) > (99 - Ka2))
           [if any? waters-here [set partner one-of waters-here react-bases]]
        ]
    ]

  ;; hydroniums molecules always have a chance to recombine with conjugate base to form acid
  if count hydroniums > 0
    [
     ask hydroniums
          [
           if ((random 100) > Ka1)
             [if any? con-bases-here [set partner one-of con-bases-here react-acids]]
          ]
    ]

  ;; hydroniums molecules can also recombine with the second conjugate base to form conjugate base
  if count hydroniums > 0
    [
     ask hydroniums
            [
             if ((random 100) > Ka2)
               [if any? con-base2s-here [ set partner one-of con-base2s-here react-acids ]]
            ]
    ]
end 

to set-colors ;;turtle procedure to assign graphics
  ask waters [set color blue]
  ask hydroniums [set color green]
  ask acids [set color yellow]
  ask con-bases [set color magenta]
  ask con-base2s [set color cyan]
  ask hydroxides [set color red]
end 

to react-bases ;;turtle procedure that tells base molecules how to react

;; all hydroxide molecules will instantly react with hydroniums molecules
  if [breed] of partner = hydroniums
    [set breed waters
     ask partner [ set breed waters ]]

;; hydroxide molecules have a high probability of reacting with acid molecules
  if [breed] of partner = acids
    [if ((random 100) > (99 - Ka1)) [set breed waters
                                     ask partner [set breed con-bases]]]

;; hydroxide molecules have a low probablity of reacting with conjugate base
  if [breed] of partner = con-bases
    [if ((random 100) > (99 - Ka2)) [set breed waters
                                     ask partner [set breed con-base2s]]]

;; conjugate base molecules react with water to form hydroniums and con-base2
  if [breed] of partner = waters
    [set breed con-base2s
     ask partner [set breed hydroniums]]
end 

to react-acids ;;turtle procedure that tells acid turtles how to react

;;acid molecules react with water to form hydroniums and con-base
if [breed] of partner = waters
  [set breed con-bases
   ask partner [set breed hydroniums]]

;;hydroniums molecules react with con-base to form acid and water
if [breed] of partner = con-bases
  [set breed waters
   rt random 360 fd 2
   ask partner [set breed acids]]

;;hydroniums molecules react with con-base2 to form con-base and water
if [breed] of partner = con-base2s
  [set breed waters rt random 360 fd 2
   ask partner [set breed con-bases]]
end 


;; calculates variables for determining the pH

to calculate-ions
  set mmolH count hydroniums
  set mmolOH count hydroxides
  set mmolA count con-bases
  set mmolHA count acids
  set mmolA2 count con-base2s
  set volume count turtles
  set Hconc (mmolH / volume)
  set OHconc (mmolOH / volume)
  set Aconc (mmolA / volume)
  set A2conc (mmolA2 / volume)
  set HAconc (mmolHA / volume)
  calculate-pH
end 


;; calculates the pH from the amount of the various ions in solution;
;; note that for simplicity the calculations don't take the true molar
;; concentration of water into account; instead we simply divide by
;; a factor of 1000 to bring the numbers into a reasonable range.
;; Above the endpoint, the pH is calculated as a strong acid.

to calculate-pH
  let concH 0
  let concOH 0
  set concH (count hydroniums / volume)
  set concOH (count hydroxides / volume)
  ifelse (concH = concOH)
    [ set pH 7 ]
    [ ifelse (concH > concOH)
      [ set pH (- log (concH / 1000) 10) ]
      [ set pOH (- log (concOH / 1000) 10)
        set pH 14 - pOH ] ]
end 

;; adds more base to the system

to add-base
  create-hydroxides base-added
    [
     fd 1
    ]
  set-colors
end 

;; plotting procedures

to record-pH
  set-current-plot "Titration Curve"
  set-plot-pen-interval base-added
  ; before next plotting, move along x-axis by magnitude of amount added
  plot pH
end 

to plot-pH
  set-current-plot "pH Curve"
  plot pH
end 

to plot-molecules
  set-current-plot "Molecule Counts"
  set-current-plot-pen "con-base"
  plot count con-bases
  set-current-plot-pen "acid"
  plot count acids
  set-current-plot-pen "hydroxide"
  plot count hydroxides
  set-current-plot-pen "hydronium"
  plot count hydroniums
  set-current-plot-pen "water"
  plot count waters
end 


; Copyright 2005 Uri Wilensky.
; See Info tab for full copyright and license.