---

Description of the model used in "Acid-Base Solutions"

This simulation models 5 types of aqueous solutions:
  - Pure Water
  - Strong Acids
  - Weak Acids
  - Strong Bases
  - Weak Bases

Constants:
  W = concentration of water = 55.6 mol/L
  Kw = equilibrium constant of water = 1E-14

Variables:
  C = concentration of the acid or base in mol/L
  Ka = strength of acid
  Kb = strength of base

Generic symbols:
  A = the molecule that separates from hydrogen (H) when a weak or strong acid (HA) dissociates
  M = the metal ion that separates from hydroxide (OH-) and remains in solution after a strong base (MOH) dissociates
  B = a weak base molecule that can accept a hydrogen atom to form BH+

Concentration:

  The notation [X] indicates the concentration of molecule X.

  Pure Water:
  [H3O] = sqrt(Kw)
  [OH] = [H3O]
  [H2O] = W

  Strong Acids:
  [HA] = 0
  [A-] = C
  [H3O+] = C
  [OH-] = Kw / [H3O+]
  [H2O] = W - C

  Weak Acids:
  [HA] = C - [H3O+]
  [A-] = [H3O+]
  [H3O+] = ( -Ka + sqrt( Ka^2 + 4*Ka*C ) ) / 2 
  [OH-] = Kw / [H3O+]
  [H2O] = W - [A-]

  Strong Bases:
  [MOH] = 0
  [M+] = C
  [H3O+] = Kw / [OH-]
  [OH-] = C
  [H2O] = W

  Weak Bases:
  [B] = C - [BH+]
  [BH+] = ( -Kb + sqrt( Kb^2 + 4*Kb*C ) ) / 2 
  [H3O+] = Kw / [OH-]
  [OH-] = [BH+]
  [H2O] = W - [BH+]

pH:

  pH ranges from 0 to 14 in this simulation, and is computed as a function of [H3O+]:
  
  pH = -log10( [H30+] )

Conductivity:

  For the purposes of this simulation, conductivity is modeled as a number between 0 and 1 inclusive.
  This value has no units and determines the brightness of the light bulb.
  Conductivity is computed as a linear function of pH, as follows:

  pH_min = 0
  pH_max = 14
  C_open_circuit = 0
  C_max = 1
  C_neutral = conductivity of a neutral (pH=7) solution (a small constant > 0)
  if open circuit, conductivity = C_open_circuit
  else if pH < 7, conductivity = C_neutral + ( ( 1 - C_neutral ) * ( 7 - pH ) / ( 7 - pH_min ) )
  else if pH >= 7, conductivity = C_neutral + ( ( 1 - C_neutral ) * ( pH - 7 ) / ( pH_max - 7 ) )
  
---