The quiz next week will be given during your recitation.

It will cover material starting with section10.7.

First Midquarter ExamMonday, Jan 29

6:30-7:48 pmRooms TBA

Chaps 10, 11, 13

Dr. Zellmer’s web site has very useful informationon BP data and the use of Excel for Exps. 13 and 17.

11.5 Vapor Pressure• Explaining Vapor Pressure on the Molecular Level, Volatility, • Vapor Pressure, and Temperature; • Vapor Pressure and Boiling Point

11.6 Phase Diagrams• The Phase Diagrams of H2O and CO2

11.7 Structures of Solids• Unit Cells• The Crystal Structure of Sodium Chloride• Close Packing of Spheres

11.8 Bonding in Solids• Molecular Solids• Covalent-Network Solids• Ionic Solids• Metallic Solids

Chapter 13 Properties of Solutions13.1 The Solution Process

• Energy Changes and Solution Formation• Solution Formation, Spontaneity, and Disorder• Solution Formation and Chemical Reactions

(Add slide of C-C eq and plot.)

But, recall, we always prefer straight lines!

ln PH

R TCvap

vap

1

← Temp. increases

O r w ith P the vapor pressu re a t T and P the vapor pressu re a t T

PH

R TC and P

H

R TC

sub trac t to g ive

P PH

R T T

or

P

P

H

R T T

vap vap

vap

vap

,

ln ln

ln ln

ln

1 1 2 2

22

11

2 12 1

2

1 2 1

1 1

1 1

1 1

Using the Clausius-Clapeyron Equation:

Tabulate P in atm and T in K; Calculate lnP and 1/TPlot lnP vs 1/T

The slope is = - ΔHvap /R

The slope!

Phase Diagrams

The Critical Point:

11.55 The normal melting and boiling points of xenon are -112 oC and -107 oC, respectively. Its triple point is at-121 oC and 282 torr, and its critical point is a 16.6 oCand 57.6 atm.

(a) Sketch the phase diagram of Xe, showing the fourpoints given above and indicating the area in which each phase is stable.

(b) Which is more dense, solid or liquid Xe?

(c) If Xe gas is cooled under an external pressure of 100 torr, will it undergo condensation or deposition?

Example Question on Phase Diagrams

11.7 Structures of Solids• Unit Cells• The Crystal Structure of NaCl• Close Packing of Spheres

11.8 Bonding in Solids• Molecular Solids• Covalent-Network Solids• Ionic Solids• Metallic Solids

Sulfur Crystals

Millerite Crystals (a nickel ore)

Some interesting web sites:

Ice and Snow Crystals at Cal Tech web site

See the Carmen site for excellentdiscussion of your XRD Experiment (X-Ray Diffraction experiment)

Univ. of PA discussion of XRD

Youngstown State Univ. XRD Lab

Research Experiences to Enhance Learning (Ohio REEL)

Solids

• We can think of solids as falling into two groups:

– Crystalline—particles are in highly ordered arrangement.

Solids

– Amorphous—no particular order in the arrangement of particles.

These are the ones we’ll beinterested in.

↓

These are the ones we’llbe interested in.

Bravais Lattice Type = P (primitive)

Bravais Lattice Type = I (body centered)

Bravais Lattice Type = F (face centered)

Crystallographic ‘Planes’and Miller Indices

A plane that intercepts the a-axis at a/h,the b-axis at b/k, and the c-axis at c/l is known as an hkl plane, where hkl are the Miller indices.

Alternatively, you can get the Miller indices bycounting the number of times the plane crosseseach axis within a unit cell for each direction.

sin2

and c, b a systems cubicfor that Note

222

lkh

adhkl

Now back to some discussions of unit cells.

The ‘NaCl’ Structure

An alternate view of the NaCl Structure

The quiz next week will be given during your recitation.

It will cover material starting with section10.7.

First Midquarter ExamMonday, Jan 29

6:30-7:48 pmRooms TBA

Chaps 10, 11, 13

Dr. Zellmer’s web site has very useful informationon BP data and the use of Excel for Exps. 13 and 17.

Miller Indices in 3D

In a 3D system there are three Miller Indices, h, k and l. In a 3D system there are three Miller Indices, h, k and l. The values of h, k and l are integers whose values are The values of h, k and l are integers whose values are determined as follows:determined as follows:

h = 1/(x-intercept)h = 1/(x-intercept) h = a/(1a) = 1h = a/(1a) = 1k = 1/(y-intercept)k = 1/(y-intercept) k = b/(1b) = 1k = b/(1b) = 1l = 1/(z-intercept)l = 1/(z-intercept) l = c/(l = c/() = 0) = 0

110 plane110 plane

The distance between planes is The distance between planes is given by the following formula given by the following formula (for an orthorhombic lattice):(for an orthorhombic lattice):

1/d1/d22 = h = h22//aa22 + k + k22//bb22 + + ll22//cc22

For a cubic lattice this reduces For a cubic lattice this reduces to:to:

1/d1/d22 = (h = (h22 + k + k22 + l + l22)/)/aa22

Plane that goes through the origin

The next plane is the one used to calculate hkl

X-Ray Powder Pattern

2020 2020 3030 4040 5050 6060

2-Theta (Degrees)2-Theta (Degrees)

There are many different planes of atoms in a crystal. In an X-ray powder diffraction pattern we see many peaks, each one corresponding to scattering from different planes of atoms. The numbers in the above diagram are called Miller Indices, they identify different planes of atoms

in the crystal.

20 30 40 50 60 702Theta

0

50

100

150

200

250

300

350

Int.

X-Ray Powder Diffraction Pattern (Lead Sulfide, PbS)

Each peak corresponds to scattering from a different set of lattice planes. Two planes are

shown above for PbS, which has the same structure as NaCl.

020 planes

220 planes

Hexagonalclosepacking(ABABAB…)

Cubicclosepacking(ABCABC..)

fact

Cubic and Hexagonal Close Packing

Hexagonal Close Packing Hexagonal Close Packing (ABAB…)(ABAB…)

AABBAABB Stacking Stacking

AABBCCAABBCC Stacking Stacking

Cubic Close Packing Cubic Close Packing (ABCABC…)(ABCABC…)

Coordination Environment (Close Packed Structures)

Hexagonal Close Packing

Each atom has 12 nearest neighbors in both structures

A

B

B

B

A

C

Cubic Close Packing

HCP Unit Cell (ABAB…)

Hexagonal close packed structures adopt a hexagonal unit cell, as shown above. For every lattice point there are two atoms displaced from the lattice point by the following vectors:

Atom 1: 1/3a + 2/3b + 1/4cAtom 2: 2/3a + 1/3b + 3/4c

(a) (b) (c)

CCP Unit Cell (ABCABC…)

Cubic close packed structures adopt a face centered cubic (fcc) unit cell. The layers stack perpendicular to the body diagonal of the unit cell.

(a) (b)

A

B

C

A

A

BC

A

11.7 Structures of Solids• Unit Cells• The Crystal Structure of NaCl• Close Packing of Spheres

11.8 Bonding in Solids• Molecular Solids• Covalent-Network Solids• Ionic Solids• Metallic Solids

Know this table in detail. You will see questionsbased on these characteristics.

Contrast the MPs and BPs of some materials which are Molecular Solids:

C6H6 C6H5-CH3 C6H5-OH

MP 5 -95 43

BP 80 111 182

MP of benzene vs that of toluene: Benzeneis highly symmetric and planar. Toluene isless symmetric and cannot pack as tightly,leading to a lower MP.

Another example of Molecular Solids.

11.59 Aluminum metal crystallizes in a cubic close-packedstructure (face-centered cubic cell).

(a) How many aluminum atoms are in a unit cell?

(b) What is the coordination number of each aluminum atom?

(c) Assume that the aluminum atoms can be represented as spheres. If each Al atom has a radius of 1.43 Å, what is the length of a side (usually called a )of the unit cell?

(d) Calculate the density of Al metal.

11.63 An element crystallizes in a body-centeredcubic lattice (bcc). The edge of the unit cell is 2.86 Ǻ,and the density is 7.92 g/cm3.

a) calculate the atomic weight of the element.

b) assuming the molecules are in contact along the body diagonal, what is the radius of the element?

Use this graph to answerthese questions. Note that 3.0 on the 1/T-axis is equal to 3.0 x 10-3 K-1, where T = 333 K

a) What is the normal boiling point of the liquid?

b) Calculate the heat of vaporization of the

liquid.

Pop Quiz No. 1