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States of Matter: Liquids and Solids

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Chapter 11. 7. A Question of Energy ... Chapter 11. 9 ... Chapter 11. 17. What Is a Unit Cell? ... – PowerPoint PPT presentation

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Title: States of Matter: Liquids and Solids


1
States of Matter Liquids and Solids
  • Chapter 11

2
Changes of State
Phase Transition Name Solid Liquid Melting/Fus
ion Solid Gas Sublimation Liquid
Solid Freezing Liquid Gas Vaporization Gas
Liquid Condensation Gas Solid Condensation
3
Vapor Pressure and ??vap
  • The heat involved in vaporizing a liquid is the
    enthalpy of vaporization.

?Hvap
log (Pvap) - (1/T) C
2.303R
Pvap is the vapor pressure ?Hvap is the heat of
vaporization C is a constant
4
Determining ??vap
  • A Plot of the vapor pressure vs. 1/T yields ??vap

Pvap
Ether
H2O
1/T
5
Determining ??vap
  • A Plot of the vapor pressure vs. 1/T yields ??vap

Pvap
Ether
H2O
1/T
?Hvap
Pvap1
log ( - )
1 T2
1 T1
Pvap2
2.303R
6
Heat of Fusion
  • The heat necessary to melt one mole of a solid.
  • ?Hfus

7
A Question of Energy
  • What parameters do you need to calculate the
    energy necessary to raise the temperature of
    water from -20 oC to 120 oC?
  • g H2O, Cwater, Cice, Csteam, b.p. of water, m.p.
    of water, ?Hfus, ?Hvap

8
Boiling Point
  • The boiling point is the point at which the vapor
    pressure equals the pressure exerted on the
    liquid.
  • Pvap Psys

9
Vapor Pressure Example
  • Chloroform, CHCl3, a volatile liquid, was once
    used as an anesthetic but has been replaced by
    safer compounds. It boils at 61.7oC and has a
    heat of vaporization of 31.4 kJ/mol. What is its
    vapor pressure at 25.0oC?

10
Vapor Pressure of CHCl3 at 25 oC
  • At the normal boiling point, the vapor pressure
    of a liquid is 760.0 mmHg. Use the
    Clausius-Clapeyron equation to find P2 when P1
    760.0 mmHg, T1 334.8 K, and T2 298.1 K.

11
Vapor pressure of CHCl3 at 25.0oC?
  • P1 760.0 mmHg, T1 334.8 K, T2 298.1 K

??vap 31.4 kJ/mol
??vap
(T2 - T1)
P2
_____
______
___
Log

x
P1
2.303 R
T2T1
12
Vapor Pressure of CHCl3 at 25 oC
  • P1 760.0 mmHg, T1 334.8 K, T2 298.1 K

??vap 31.4 kJ/mol
??vap
(T2 - T1)
P2
_____
______
___
Log

x
P1
2.303 R
T2T1
31.4 x 103 J/mol
(298.1 - 334.8 K)
________________
_______________

x
(298.1K)(334.8 K)
(2.303)8.31 J/(K.mol)
13
Vapor Pressure of CHCl3 at 25 oC
P2
__
Log
-0.6033
P1
log P2 log P1 - 0.6033 log (760.0) - 0.6033
2.27751
P2 antilog (2.27751) 189.4 189 mmHg
14
Phase Diagrams
  • A plot of temperature vs. pressure has discrete
    phase regions.

liquid
Critical Point
solid
P
Triple Point
gas
T
15
Intermolecular Forces
  • Dipole-Dipole Forces
  • Electrostatic interactions between polarized
    molecules
  • Hydrogen Bonding
  • Same as Dipole-Dipole, but involve H?-O?-
  • London-Dispersion Forces
  • Interactions of instantaneous dipoles
  • Metallic Bonding

16
Two Types of Solids
  • Crystals are . . .
  • well-defined arrangements of atoms, ions, or
    molecules.
  • Amorphous Solids are . . .
  • solids with no long-range molecular order.

17
What Is a Unit Cell?
  • The smallest repeating unit that contains the
    characteristics of the crystal as a whole.

18
Crystal Lattice
  • The 3-D array of points which represents an
    identical environment within the crystal.

19
3 Kinds of Cubic Unit Cells
  • Primitive Cubic
  • Body-centered Cubic
  • Face-centered Cubic

20
Fraction of an Atom at Various Positions in the
Unit Cell
Position
Fraction
Center Face Edge Corner
1 1/2 1/4 1/8
21
Example
  • Find the density (g/cm3) for ??Fe.
  • BCC (Body-centered Cubic)
  • a 2.86
  • Fe 55.85 g/mole
  • N 6.02 x 1023 atoms/mole

A
22
Example
  • Find the density (g/cm3) for ??Fe.
  • Solution
  • Volume of Unit Cell (2.86 A )3 x (1 cm/108 A
    )3
  • 2.34 x 10-23 cm3

23
Example
  • Find the density (g/cm3) for ??Fe.
  • Solution

Volume of Unit Cell (2.86 )3 x (1 cm/108
)3 2.34 x 10-23 cm3 mass/unit cell
55.85g/mole x 2 atoms 6.02 x
1023 atoms/mole 1.86 x 10-22 g
A
A
24
Example
  • Find the density (g/cm3) for ??Fe.
  • Solution

Volume of Unit Cell (2.86 )3 x (1 cm/108
)3 2.34 x 10-23 cm3 mass/unit cell
55.85g/mole x 2 atoms 6.02 x
1023 atoms/mole 1.86 x 10-22 g Density
Mass/Volume 7.93 g/cm3
A
A
25
Atomic Mass of Iron
  • Metallic iron has a body-centered cubic lattice
    with all atoms at lattice points and a unit cell
    whose edge length is 2.866 A. The density of
    iron is 7.87 g/cm3. What is the mass of an iron
    atom? Compare this value with the value you
    obtain from the molar mass.

26
Atomic Mass of Iron
  • Calculate the volume of the unit cell, change
    density to g/m3, and then convert volume to mass,
    using density
  • Volume (2.866 x 10-10m3) 2.354 x 20-29m3

27
Atomic Mass of Iron
  • Calculate the volume of the unit cell, change
    density to g/m3, and then convert volume to mass,
    using density
  • Volume (2.866 x 10-10m3) 2.354 x 20-29m3

3
7.87 g
102cm
x
7.87 x 106 g/m3
cm3
m
28
Atomic Mass of Iron
  • Calculate the volume of the unit cell, change
    density to g/m3, and then convert volume to mass,
    using density
  • Volume (2.866 x 10-10m3) 2.354 x 20-29m3

3
7.87 g
102cm
x
7.87 x 106 g/m3
cm3
m
Mass of one cell
(7.87 x 106 g/m3) x (2.354 x 10-29 m 3)
1.8526 x 10-22 g
29
Atomic Mass of Iron
  • Because Fe is a body-centered cubic cell, there
    are two Fe atoms in the cell, and . .
    . Mass of one Fe atom (1.8526 x 10-22g)
    x 2 9.263 x 10-23 g

30
Atomic Mass of Iron
  • Because Fe is a body-centered cubic cell, there
    are two Fe atoms in the cell, and . .
    . Mass of one Fe atom (1.8526 x 10-22g)
    x 2 9.263 x 10-23 g

Using the molar mass to calculate the mass of
one Fe atom, you find the agreement is good
55.85 g Fe
1 mol Fe
x

1 mol Fe
6.022 x 1023 Fe atoms
9.274 x 10-23 g/Fe atom
31
Close Packing of Spheres
  • Ions and molecules can be viewed as spheres.
  • Efficient packing maximizes attractive forces.

32
2 Types of Closest Packing
  • Hexagonal Closest Packed (HCP)
  • ABAB
  • Hexagonal
  • Cubic Closest Packed (CCP)
  • ABCABC
  • Face-centered Cubic

33
Coordination Number (CN)
  • The number of particles immediately surrounding
    a particle in the crystal structure.
  • CN Number of nearest numbers

34
Lattice Defects
  • Disorder During Packing
  • Point Defects
  • Missing particles form Schottky defects
  • May still maintain electrostatic neutrality
  • Frenkel Defects
  • Particles in the wrong position

35
A Question of Distance
  • How can we rationalize the different distances in
    each of the following cases?

Solid Atomic Distance Molecule Distance
P4 S8 Cl2
2.20 2.06 1.99
3.8 3.7 3.6
36
Molecular Solids
  • Intermolecular Forces
  • Dispersion forces, dipole-dipole forces,
    H-bonding
  • Properties
  • Soft, low melting point, poor thermal and
    electrical conductivity
  • Examples
  • H2O, CO2

37
Covalent/Network Solids
  • Covalent bonds
  • Properties
  • Very hard, very high melting point, poor thermal
    and electrical conductivity
  • Examples
  • C(diamond), SiO2(quartz)

38
Ionic Solids
  • Electrostatic attractions
  • Highly dependent on the charge of the ions
  • Properties
  • Hard brittle, high melting point, poor thermal
    and electrical conductivity
  • Examples
  • NaCl, CaCO3

39
X-ray Diffraction
  • X-rays will be diffracted by an array of atoms in
    an ordered solid. The diffraction is due to
    scattering of X-rays by the atoms.

40
X-ray Diffraction
  • X-rays will be diffracted by an array of atoms in
    an ordered solid. The diffraction is due to
    scattering of X-rays by the atoms.

Bragg Equation
n? 2dsin?
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