Properties of Liquids and Solids (Ch. 11)
Inter vs. Intramolecular Forces
Intra
≈
Inter
≈
strong forces within molecules (covalent or
ionic bonds) (related to chemical reactivity
of the substance)
weaker forces between molecules
(determine the bulk physical properties of a
substance)
Coulomb’s Law—electrostatic repulsion of like charges is proportional to the
amount of charge, and inversely proportional to the distance between them
Phases of Matter (Review)
fusion (melting)
freezing
sublimation
vaporization
(evaporation)
deposition
condensation
Types of Intermolecular Forces
• In pure substances:
– London forces (dispersion forces) -- very weak “instantaneous
induced dipole” forces between molecules
– H-bonding -- especially strong dipole-dipole forces for
compounds with H-F, H-O, or H-N bonds
– dipole-dipole forces -- between polar molecules (e.g. SO2, PF3)
• Forces within mixtures (in addition to the above):
– ion-dipole -- between ionic and polar substances
– ion-induced dipole -- between ionic and non-polar substances
– dipole-induced dipole -- between polar and non-polar
substances
Dipole-Dipole Forces
H-bonding
-- especially strong dipole-dipole forces in compounds
with H-F, H-O, or H-N bonds
London Forces
--very weak “instantaneous induced dipole” forces
between non-polar molecules
Sample Question
What is the predominant intermolecular force in each of the
following substances?
a)
Solid CO2
b)
Liquid CH3CH2OH
c)
Liquid SCl2
d)
MgCl2 dissolved in liquid SCl2
e)
CO2 dissolved in SCl2
Sample Question
What is the predominant intermolecular force in each of the
following substances?
a)
Solid CO2
London forces
b)
Liquid CH3CH2OH
H-bonding
c)
Liquid SCl2
dipole-dipole forces
d)
MgCl2 dissolved in liquid SCl2
e)
CO2 dissolved in SCl2
ion-dipole forces
dipole-induced dipole forces
Bulk Properties of Liquids and Solids
• (related to intermolecular forces)
–
–
–
–
phase changes
compressibility
viscosity– resistance of a liquid to flow
capillary action—the ability of a liquid to flow up a narrow tube
against gravity (cohesive versus adhesive forces)
– surface tension—the tendency of liquids to minimize their
surface area; the energy required to increase the surface area
by a unit amount
e.g. arrange the following in order of increasing boiling points:
NH3
PH3
CH4
SiH4
Answer:
CH4
(lowest)
<
SiH4
<
PH3
<
NH3
(highest)
Energy Changes during Changes of State
Molar Heat quantities (heat absorbed by 1 mole of substance)
–
–
–
–
fusion (DHfusion) -- melting of solid to liquid
sublimation (DHsublimation) -- solid to gas
vaporization (DHvaporization) -- evaporation of liquid to gas
(all of these are affected by intermolecular forces)
e.g. DHvaporization values:
H2O = 43.9 kJ/mole
SO2 = 24.3 kJ/mole
Heating and Cooling Curves
– Plots of temperature vs
amount of heat added (or
removed)
– Horizontal regions are found
during state changes (mp,
bp, etc)
Vaporization/Vapor Pressure
Vapor Pressure (pressure due to gas above surface of liquid)
– Determined by strength of intermolecular forces
– Related to surface tension
– Volatile vs. nonvolatile
boiling point -- temp at which vapor pressure = atmospheric
pressure
normal boiling point -- temp at which vapor pressure = 1 atm
•
Rate of Vaporization
– Increases with temp
– Increases with increased surface area
– Increases with weaker intermolecular forces
•
Heat of Vaporization (DHvap)
– Only slightly temperature-dependent
– Decreases with weaker intermolecular forces
– Not dependent on surface area
Clausius-Clapeyron Equation
Relationship between vapor pressure and temperature; vapor pressure
increases with temperature, but not linear.
ln Pvap =
2-point form:
ln
P1
P2
–DHvap
RT
=
+ ln b
(do not memorize)
–DHvap
1
R
T1
–
1
memorize!
T2
Changes of State
Dynamic Equilibrium
– Changes of state (e.g. evaporation/condensation) involve
process of dynamic equilibrium:
Liquid
Gas
at equilibrium:
forward rate = reverse rate (no net change with
time)
(e.g. rate of evaporation = rate of condensation)
Le Chatelier’s Principle
When a dynamic equilibrium is upset by a stress, the system
responds in a direction that tends to counteract the stress
and, if possible, restore equilibrium.
e.g. vaporization/condensation
Liquid
gas
If temp is raised (i.e. heat is added), the equilibrium
shifts forward (to the right), hence, vapor pressure
increases
Phase Diagrams
• Phase diagram -- pressure vs temperature plot that shows:
H2O
Three phase regions (solid, liquid,
gas)
dividing lines (curves) -- equilibrium
points between two phases
“triple point” -- T and P where all 3
phases coexist in equilibrium
“critical point” -- T and P upper limits
on the liquid-gas curve
– supercritical fluid -- state of matter beyond the critical points
(e.g. for H2O: critical T = 374 ºC and critical P = 218 atm)
Crystalline Solids
Crystal Lattice
A regular, repeating 3-dimensional pattern in which the particles of a
crystalline solid are arranged.
Depending on the type of substance, the lattice sites can be occupied by
atoms, molecules, or ions.
X-ray Diffraction–a technique for determining crystal lattice and molecular
structures
Bragg Equation
basic mathematical tool of x-ray diffraction
nl = 2dsin q
Crystal Lattice Types
unit cell -- simplest geometrical unit that defines the crystal
lattice
Common types of crystal lattices:
Simple cubic
--Particle at 8 corners of a cube
--Total of one particle per unit cell
Face-centered cubic (e.g. NaCl)
--Simple cubic plus particle of each face-center of the
cube
--Total of 4 particles per unit cell
Body-centered cubic
--Simple cubic plus particle at center of cube
--Total of 2 particles per unit cell
Simple Cubic Lattice
-- particle at 8 corners of a cube
-- total of one particle per unit cell
Face-Centered Cubic Lattice
(e.g. NaCl)
-- simple cubic plus particle at center of each face of the cube
-- total of 4 particles per unit cell
Body-Centered Cubic Lattice
-- simple cubic plus particle at center of cube
-- total of 2 particles per unit cell
Sample Problem
•
Gold forms face-centered cubic crystals in which the
edge dimension of the unit cell is 408 pm.
a)
Determine the atomic radius of gold (in pm). Use a rough
sketch of the face of a unit cell to illustrate your method.
b)
Determine the specific gravity of gold.
Sample Problem
•
Gold forms face-centered cubic crystals in which the
edge dimension of the unit cell is 408 ppm.
a)
Determine the atomic radius of gold (in pm). Use a rough
sketch of the face of a unit cell to illustrate your method.
Answer: 144 pm
b) Determine the specific gravity of gold.
Answer: 19.3
Closest-Packed Structures
• Common for metals
Common types of closest-packing:
hexagonal closest packing (hcp)
--hexagonal unit cell, not cubic
--Layers have ABAB pattern
Cubic closest packing (ccp)
--same as face-centered cubic! (fcc)
--Layers have ABCABC pattern
Hexagonal Closest Packing
--hexagonal unit cell
--layers are ABAB…
Top view:
Side view:
Unit cell:
Cubic Closest Packing
--same as fcc
--pattern is ABCABC…
Types of Crystals
Held together by
London forces, dipoledipole, dipole-induced
dipole, and/or H-bond
Held together by
electrostatic
attractions
amorphous solids -- non-crystalline, glassy substances
Bonding in Solids -- Band Theory
An energy “band” is composed of a very large number of
closely spaced energy levels that are formed by combining
similar atomic orbitals of atoms throughout the substances.
• Metals and metalloids have a
“ conduction band”
– Set of highly delocalized, partially filled, MO’s that extend over
the entire solid lattice structure
“band gap”
– Energy difference between filled “valence band” and the
conduction band
Energy Bands in Solid Li
Band Gaps in Solids
empty
empty
empty
full
full
full
Doping; adding trace impurities that bridge the band gap and allow some
conductivity
n-type: impurities have extra valence electrons
p-type; impurities have fewer valence electrons
Sample Problems
The heat of fusion of benzene (C6H6, 78.1 g/mole) is 9.92
kJ/mole. A 10.0 g cube of solid benzene at its melting point
is placed in 25.0 g of water at 30.0 °C. Calculate the
temperature of the water after all of the benzene has
melted. (The specific heat of water is 4.184 J/g °C.)
CO2 gas can be prepared by the following reaction:
CaCO3(s) + 2 HCl(aq) --> CaCl2(aq) + H2O(l) + CO2(g)
What volume of dry CO2 (in mL) at 20 °C and 745 torr can be
prepared from a mixture of 12.3 g CaCO3 (100.1 g/mole) and
185 mL of 0.25 M HCl?
Sample Problems
The heat of fusion of benzene (C6H6, 78.1 g/mole) is 9.92
kJ/mole. A 10.0 g cube of solid benzene at its melting point
is placed in 25.0 g of water at 30.0 °C. Calculate the
temperature of the water after all of the benzene has
melted. (The specific heat of water is 4.184 J/g °C.)
Answer: 17.9 °C
CO2 gas can be prepared by the following reaction:
CaCO3(s) + 2 HCl(aq) --> CaCl2(aq) + H2O(l) + CO2(g)
What volume of dry CO2 (in mL) at 20 °C and 745 torr can be
prepared from a mixture of 12.3 g CaCO3 (100.1 g/mole) and
185 mL of 0.250 M HCl?
Answer: 567 mL
More Sample Problems
Titanium(IV) bromide, TiBr4, forms soft orange crystals that
melt at 39 °C to give a liquid that does not conduct
electricity. The liquid boils at 230 °C. What is the most
likely crystal type for TiBr4?
Of the following substances
PH3
CH4
H2O
CO2
SO2
a)
What is the predominant intermolecular force in each
substance?
b)
c)
d)
e)
Which has the lowest heat of vaporization?
Which is the best example of H-bonding?
Which is often used as a supercritical fluid?
Which should be the best solvent for NH4Cl?
More Sample Problems
Titanium(IV) bromide, TiBr4, forms soft orange crystals that
melt at 39 °C to give a liquid that does not conduct
electricity. The liquid boils at 230 °C. What is the most
likely crystal type for TiBr4?
Answer: molecular
Of the following substances
PH3
CH4
H2O
a)
CO2
SO2
What is the predominant intermolecular force in each
substance?
Answer: PH3 dipole-dipole, CH4 London, H2O H-bonding, CO2 London, SO2 dipole-dipole
b)
c)
d)
e)
Which has the lowest heat of vaporization? CH4
Which is the best example of H-bonding? H2O
Which is often used as a supercritical fluid? CO2
Which should be the best solvent for NH4Cl? H2O