chem 300 - ch 25/#2 today’s to do list binary solid-liquid phase diagrams continued (not in...
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Chem 300 - Ch 25/#2 Today’s To Do List
• Binary Solid-Liquid Phase Diagrams Continued (not in text…)
• Colligative Properties
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Stable Compound Formation
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K/Na with incongruent MP & Unstable Compound Formation
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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
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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)
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Chemical Potential
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Vapor Pressure lowering
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Freezing Point Depression: ΔTfus = Kf m
Thermo Condition:• At fp: solid solvent in equilib with solvent
that’s in soln
• μsolid1(Tfus) = μsoln
1(Tfus)
• μsolid 1 = μ*
1 + RT ln a1 = μliq1 + RT ln a1
Rearranging:• ln a1 = (μsolid
1 - μliq1)/RT
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ln a1 = (μsolid 1 - μliq
1)/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 – Hsol
1)/RT2 = ΔfusH/RT2
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( 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)
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- 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*2
fus
= - Δ T/T*2fus
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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
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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
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Osmotic Pressure
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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
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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.
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Next Time
How to explain the experimental evidence:Debye-Huckel Model of electrolyte solutions