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

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

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

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)

Chemical Potential

Vapor Pressure lowering

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

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

( 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)

- 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

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

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

Osmotic Pressure

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

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.

Next Time

How to explain the experimental evidence:Debye-Huckel Model of electrolyte solutions