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Chem 300 - Ch 25/#2 Today’s To Do List

Chem 300 - Ch 25/#2 Today’s To Do List. Binary Solid-Liquid Phase Diagrams Continued (not in text…) Colligative Properties. Stable Compound Formation. K/Na with incongruent MP & Unstable Compound Formation. Colligative Properties.

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Chem 300 - Ch 25/#2 Today’s To Do List

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  1. Chem 300 - Ch 25/#2 Today’s To Do List • Binary Solid-Liquid Phase Diagrams Continued (not in text…) • Colligative Properties

  2. Stable Compound Formation

  3. K/Na with incongruent MP & Unstable Compound Formation

  4. Colligative Properties • Depends upon only the number of (nonvolatile) solute particles • Independent of solute identity • From colligatus:“depending upon the collection” • Vapor pressure lowering • Boiling point elevation • Freezing point depression • Osmotic pressure

  5. Basis for Colligativity • Solvent chem potential (μ1) is reduced when solute is added: • μ*1 μ*1 + RT ln x1 (“1” is solvent) • Since x1 < 1  ln x1 < 0 • Thus μ1 (solution) < μ1 (pure solvent)

  6. Chemical Potential

  7. Vapor Pressure lowering

  8. Freezing Point Depression: ΔTfus = Kf m • Thermo Condition: • At fp: solid solvent in equilib with solvent that’s in soln • μsolid1(Tfus) = μsoln1(Tfus) • μsolid 1 = μ*1 + RT ln a1 = μliq1 + RT ln a1 • Rearranging: • ln a1 = (μsolid1 - μliq1)/RT

  9. ln a1 = (μsolid 1 - μliq1)/RT • Take derivative: • ( ln a1/  T)P, x1 =  [(μsolid 1 - μliq1)/RT]/ T • Recall Gibbs-Helmholtz equation: • [(μ/T)/  T]P, x1 = - H1/T2 • Substitute in above: • ( ln a1/  T)P, x1 = (Hliq1 – Hsol1)/RT2 = ΔfusH/RT2

  10. ( ln a1/  T)P, x1 = ΔfusH/RT2 • Integrate between T*fus and Tfus : • ln a1 = ƒ(ΔfusH/RT2)d T • Since it’s a dilute solution: • a1~ x1 = 1- x2 • ln (1 – x2) ~ - x2 • Substitute above: • - x2 = (ΔfusH/R)(1/T*fus – 1/Tfus)

  11. - x2 = (ΔfusH/R)(Tfus - T*fus)/T*fus Tfus • Solute lowers the freezing point: • Tfus < T*fus • Express in molality: • x2 = n2/(n1 + n2) = m/(1000/M1 + m) • But m << 1000/M1 • x2~M1m/1000 (substitute above for x2) • Note: T*fus~Tfus • (Tfus - T*fus)/T*fus Tfus~ (Tfus - T*fus)/T*2fus = - Δ T/T*2fus

  12. Substitute! • Δ Tfus = Kf m • Where Kf = M1 R(T*fus)2 /(1000ΔfusH) • Kf is function of solvent only • Similar expression obtained for bp elevation: Δ Tvap = Kb m • Where Kb = M1 R(T*vap)2 /(1000ΔvapH) • Compare terms

  13. Example Comparison • Calc. fp and bp change of 25.0 mass % soln of ethylene glycol (M1 = 62.1) in H2O. • m = nGly/kg H2O = (250/62.1)/(750/103) = 5.37 • Δ Tfus = Kf m = (1.86)(5.37) = 10.0 OC • Δ Tvap = Kb m = (0.52)(5.37) = 2.8 OC

  14. Osmotic Pressure

  15. Example • Calc. Osmotic pressure of previous example at 298 K. • Π = c2RT • c2 = 4.0 R = 0.0821 L-atm/mol-K • Π = c2RT = (4.0)(0.0821)(298) = 97 atm

  16. Debye-Hückel Model of Electrolyte Solutions • The Model: An electrically charged ion (q) immersed in a solvent of dielectric constant ε • Experimental Observations: • All salt (electrolyte) solutions are nonideal even at low concentrations • Equilibrium of any ionic solute is affected by conc. of all ions present.

  17. Next Time How to explain the experimental evidence: Debye-Huckel Model of electrolyte solutions

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