solubility - Chapter 5 Aqueous Solubility equilibrium...

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Chapter 5: Aqueous Solubility equilibrium partitioning of a compound between its pure phase and water
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Air Water Octanol A gas is a gas is a gas T, P Fresh, salt, ground, pore T, salinity, cosolvents NOM, biological lipids, other solvents T, chemical composition Pure Phase (l) or (s) Ideal behavior P o L C sat w C sat o K H = P o L /C sat w K oa K H K ow = C sat o /C sat w K ow K oa = C sat o /P o L
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water covers 70% of the earth’s surface is in constant motion is an important vehicle for transporting chemicals through the environment Solubility is important in its own right will lead us to K ow and K aw
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Relationship between solubility and activity coefficient Consider an organic liquid dissolving in water: iL iL iL iL x RT + = γ μ μ ln * for the organic liquid phase iw iw iL iw x RT + = γ μ μ ln * for the organic chemical in the aqueous phase at equilibrium (maximum solubility): iL iL iw iw L i iw x RT x RT - = = - γ γ μ μ ln ln 0 RT RT RT x x sat iw iL iL sat iw γ γ ln ln ln - = At saturation!
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The relationship between solubility and activity coefficient is: RT RT RT x x sat iw iL iL sat iw γ γ ln ln ln - = Assume: x iL = 1 and γ iL = 1 RT G RT RT x sat E iw sat iw sat iw , ln ln - = - = γ Solubility = excess free energy of solubilization (comprised of enthalpy and entropy terms) over RT sat iw sat iw x γ 1 = sat iw w sat iw V C γ 1 = or for liquids The activity coefficient is the inverse of the mole fraction solubility
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Solids must account for the effect of “melting” of solid i.e. additional energy is needed to melt the solid before it can be solubilized: RT G sat iw sat iw i fus e s C L C / ) ( ) ( + = is iL i fus p p RT G * ln = is iL sat iw sat iw p p s C L C * ) ( ) ( = - - = 1 ) ( ln 0 0 T T R T S p p m m fus L s Recall Prausnitz: At any given temperature
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Phase change costs or Why bother with the hypothetical liquid?
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Melting point vs. boiling point Tm and Tb vs. MW y = 2.768x - 152.94 R 2 = 0.9524 y = 0.6573x + 13.002 R 2 = 0.3016 0 100 200 300 400 500 600 700 100 120 140 160 180 200 220 240 260 MW (g/mol) Tm or Tb (C) MW Tm Tb Naphthalene 128.2 80.6 217.9 Fluorene 166.2 113 295 Phenanthrene 178.2 99.5 340.2 Anthracene 178.2 217.5 342 Fluoranthene 202.3 110.8 Pyrene 202.3 156 Benz[a]anthracene 228.3 159.8 435 Benzo[a]pyrene 252.3 176.5 584
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Gases solubility commonly reported at 1 bar or 1 atm (1 atm = 1.013 bar) O 2 is an exception the phase change “advantage” of condensing the gas to a liquid are already incorporated. the solubility of the hypothetical superheated liquid (which you might get from an estimation technique) may be calculated as: i iL p iw sat iw p p C L C i * ) ( = Actual partial pressure of the gas in your system theoretical “partial” pressure of the gas at that T (i.e. > 1 atm)
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concentration dependance of γ In reality, γ at saturation γ at infinite dilution However, for compounds with γ > 100 assume: γ at saturation = γ at infinite dilution i.e. solute molecules do not interact, even at saturation
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Molecular picture of the dissolution process
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