Δ μ i = ΔH i – TΔS i

1. - - 0 Δμi = ΔHi – TΔSi 0 0 (open systems under external field) distribution coefficient ext -Δμi - Δμi 0 = exp K RT q A---B A + B = int ext dG -S dT + V dP + Σ(µi +µi )dni * * Fundamentals of Distribution Separations (II) (08/26/13) 1. Principles of distribution equilibria 2. Intermolecular interactions

2. Dissociation of H2O = 200 kcal/mol (H2O 2 H + O) Vaporization energy of H2O = 9.7 kcal/mol (H2Ol H2Og ) Intermolecular Interactions Intermolecular interactions: Intermolecular interactions are weaker than intramolecular interactions, but It is determining solubility, boiling points, vapor pressure, melting points…. These properties are of importance in determining the behavior of compound in chromatography and other separation methods A useful general principle in separation is like dissolves like. In other words, a molecule will interaction most strongly with the phase or solvent that is most similar to it in its chemical characters. Question: glucose (1) Hexane (1) naphthalene (2) Water (2)

3. Intermolecular Interactions The intermolecular interactions can either be attactive or repulsive in nature. r i j Etotal = A/r12 – ΣB/rz Where: E total = net total energy of interactions A = constant describing repulsive forces between i and j B = constant describing attractive forces between i and j z = constant for a given type of attractive force Lennard-Jones potential: z=6 1. Dipole-dipole interaction van der Waals forces 2. Induction interaction 3. Dispersion interaction (London forces) 4. Hydrogen bond Electrostatic interaction (Coulombic) (hard interactions) 5. Lewis acid-base interactions Electron transfer (sharing electron) (soft interactions)

4. 1. Dipole-dipole interaction + - - - + + + - j i j i 2 2 µi µj ED = - 3 (4 π ε0)2 kTr6 µj = dipole moments of i and j µi, T = Temperature k = Boltzmann’s constant Note: Temperature dependent

5. 2. Induction interaction - - - + + + j i j i 2 µi αj EI = - (4 π ε0)2 r6 = dipole moments of i µi αj = polarizability of j Note: independent of temperature

6. αi αj 3 hν two atoms EL = - 4 (4 π ε0)2 r6 αi, αj = polarizability of i and j r = distance h = Plank’s constant ν = Frequency of light required for ionization of each species ε0 = dielectric permittivity of the medium - EL = -CL Vi (αi)v (αi)v two molecules (αi)v (αi)v = polarizability of i and j per unit volume CL: Dispersion constant (uniform for most compounds) Vi = Molar volume of i (MW/density) 3. Dispersion interactions (London Force) + - + - - + i i j j i j

7. 4. Hydrogen bonds Non-covalent bond forms between a molecule with a proton donor group And proton acceptor group. (a) Common proton donors are –OH, -NH, and –SH (b) Common proton acceptor are –O-, =N-, -F, -S-, -Cl, C=C….. (c) E ~ 1/r6 (d) Hydrogen bond is one example of a more general class of Lewis acid-base interactions. A + :B A:B

8. 5. Lewis acid-base interactions (A) Electrostatic interaction (Coulombic) (hard interactions) j i • Coulombic interaction - + QiQj EAB = 4 π ε0 r (2) Interactions with polar and non-ionic compounds (ED) j i 2 2 Qi µj + ED = - 6 (4 π ε0)2 kTr4 polar (3) Interactions with non-polar compounds (EL) j 2 2 i Qi αj EL = - + 2 (4 π ε0)2 r4 (B) Electron transfer (sharing electron) non-polar (soft interactions)

9. 5. Lewis acid-base interactions EAB = - [EA* EB + CA* CB],Approximation for A-B interaction Where: EA* EB = Measures of acid (A) and base (B)’s ability to undergo hard acid-base interaction CA* CB = Measures of acid (A) and base (B)’s ability to undergo soft acid-base interaction The values of EA, EB, CA, CB: Rel. Basicity EB CB Rel. Acidity Ammonia 1.3 0.3 Ketones 0.7 0.1 1’ Amines 1.2 0.6 2’ Amines 0,9 0,9 3’ Amines 0,6 1.2 Esters 0.6 0.4 Sulfides 0.0 0.8 EA CA HF 17.0 0.0 Alcohols 3.6 0.8 Phenols 4.7 1.7 SO2 1.1 7.2 Iodine 1.0 10.0 Strong interactions: hard-hard interactions, and soft-soft interactions Weak interactions: hard-soft interactions.

10. - - 0 Δμi = ΔHi – TΔSi 0 0 i dissolved in j Solubility: ΔG= ΔH– TΔS ΔH = Δμ – TΔS = RT ln (Ci) 0 ΔG= Δμ + RT ln (Ci) 0 ext -Δμi - Δμi 0 At soluble equilibrium: ΔG= Δμ + RT ln (Ci) = 0 Ci = exp K RT -Δμ 0 q = exp A---B A + B RT Distribution equilibria and Solubility distribution coefficient 0 ΔH = EL +EI + ED + EAB

11. - - 0 Δμi = ΔHi – TΔSi 0 0 Possible interactions Relative strength Type of Compounds EL, EI, ED, EAB Acid-base compounds Strong Non Acid-base Permanent dipole moment Polar compounds EL, EI, ED q A---B A + B Non-Polar compounds EL Weak Distribution equilibrium and Solubility ΔH = EL +EI + ED + EAB For all of the above interactions are present in one compounds EL < EI < ED < EAB

12. Quantitative Approach for the Strength of Molecular Interactions A more quantitative approach in estimating the strength of molecular interactions is to use various scales that decribe molecular polarity. • Polarizability • Dipole Moments • Solubility parameters • Polarizability • The polarizability (α)of a compound is a measure of how easily the electron clouds of a compound may be distorted • The value of α for any atom or molecules can be calculated fromspectroscopica properties, such as its refractive index. (αi)v = [3 π N/4][(n2-1)/(n2+2)] Where, (αi)v = polarizability of the compound per unit volume N = Avogadro’s number n = refractive index of the compounds

13. - EL = - CL Vi (αi)v (αi)v two molecules - Vi = Molar volume of i (MW/density) Dispersion interaction (London forces) Where: (αi)v (αi)v = polarizability of i and j per unit volume CL: Dispersion constant (uniform for most compounds) Note: it is useful in predicting boiling points and solubility of non-polar compounds, such as saturated aliphatics. MW (g/mol) Density (g/mL) Refractive Index Boiling Points (oC) Compound Ethane 30.07 0.572 1.0377 -88.6 Octane 114.23 0.7025 1.3974 125.7