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Born-Haber Cycle: ΔHhydration

• ΔHsolution,NaCl = ΔHhydration,NaCl(aq) – UNaCl

• ΔHhydration,NaCl(aq) = ΔHhydration,Na+(g) + ΔHhydration,Cl−(g)

Enthalpies of Hydration

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Sample Exercise 11.3 Use the appropriate enthalpy of hydration values in

Table 11.3 and ΔHsolution = 0.91 kJ/mol for NaF to calculate the lattice energy of NaF.

Vapor Pressure Pressure exerted by a gas in equilibrium with its liquid

Where are we going with this?

Colligative Properties – boiling

point elevation, freezing point

depression, osmosis

rate of evaporation = rate condensation

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The tendency for a liquid to evaporate

increases as -

1. the temperature rises

2. the surface area

increases

3. the intermolecular

forces decrease

Vapor Pressure • In general, vapor pressure of a solution is lower

than vapor pressure of pure solvent.

Rate of evaporation < rate of condensation

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Vapor Pressure of Solutions

Raoult’s Law:

vapor pressure of solution is proportional to mole fraction of solvent (non-volatile solute).

Psolution = XsolventPsolvent°

Vapor pressure lowering:

one of the colligative properties of solutions

Ideal Solutions:

solutions that obey Raoult’s Law.

Sample Exercise 11.4 The liquid used in automobile cooling systems is prepared by

dissolving ethylene glycol (HOCH2CH2OH, molar mass 62.07 g/mol) in water. What is the vapor pressure of a solution prepared by mixing 1.000 L of ethylene glycol (density 1.114 g/mL) with 1.000 L of water (density 1.000 g/mL) at 100.0°C? Assume that the mixture obeys Raoult’s law.

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Solutions of Volatile Components

• For mixtures containing more than one volatile component:

– Partial pressure of each volatile component contributes to total vapor pressure of solution.

– Ptotal = X1P1° + X2P2° + X3P3° …

– Where Xi = mole fraction of component i, and Pi° = equilibrium vapor pressure of pure volatile component at a given temperature.

Real vs Ideal Solutions Deviations from Raoult’s Law occur due to differences in

solute-solvent and solvent-solvent interactions (dashed lines = ideal behavior).

Negative deviations: Solute-solvent > solvent-solvent.

Positive deviations: Solute-solvent < solvent-solvent.

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Sample Exercise 11.7 Calculate the vapor pressure of a solution prepared by dissolving 13

g of n-heptane (C7H16) in 87 g of n-octane (C8H18) at 25°C. By what factor does the concentration of the more volatile component in the vapor exceed the concentration of this component in the liquid? The vapor pressures of n-octane and n-heptane at 25°C are 11 torr and 31 torr, respectively.

Vapor Pressure vs Temperature

Normal boiling point: the temperature at which the vapor pressure of a liquid equals 1 atm (760 mmHg).

(Increasing attractive forces.)

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Diethyl ether - dipole-dipole

interactions

Water - hydrogen

bonding (stronger)

Boiling Point “If you have a beaker of water open to the

atmosphere, the mass of the atmosphere is

pressing down on the surface. As heat is

added, more and more water evaporates,

pushing the molecules of the atmosphere

aside. If enough heat is added, a

temperature is eventually reached at which

the vapor pressure of the liquid equals the

atmospheric pressure, and the liquid boils.”

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Normal boiling point - the temperature at

which the vapor pressure of a liquid is equal to the

external atmospheric pressure of 1 atm.

Increasing the external atmospheric pressure

increases the boiling point

Decreasing the external atmospheric pressure

decreases the boiling point

Location Elevation (ft) Boiling Point H2O (oC)

San Francisco sea level 100.0 Salt Lake City 4400 95.6 Denver 5280 95.0 Mt. Everest 29,028 76.5

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Clausius-Clapeyron Equation Vapor Pressure vs Temperature

CTR

HP

1ln

vap

vap

Pre

ssu

re

Temperature

solid

liquid

gas

Plot of ln(P) vs 1/T yields straight line:

– Slope = −ΔHvap/R

– Intercept = constant

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Practice Exercise, p. 513

n-Pentane, C5H12, boils at 36 oC. What is its molar heat of vaporization in kJ/mol if its vapor pressure at 25 oC is 505 torr?