Suggestion on note taking No lab tomorrow CHEM 1211 Lab manual

Logarithm Review a b = c, (a > 0, a ≠ 1)log a c = b Definition If a = 10, it is called common logarithm log c = log 10 c If a = e = ∙ ∙ ∙, it is called natural logarithm ln c = log e c Keys on your calculator c > 0, b can be any real number

Properties of Logarithm ln(xy) = ln(x) + ln(y) ln(x m ) = m ln(x) Also see Appendix I B x > 0, y > 0

Chapter 11 Liquids, Solids and Intermolecular Forces continued

Vapor Pressure

Surface Molecules

Temperature: T What happens to P if T is increased? phase equilibrium Liquid Gas vaporization condensation

Surface Molecules

Georgia, 760 torr = 1 atm H2OH2O 100 °C Normal Boiling Point

Tibet, 480 torr < 1 atm H2OH2O 85 °C Normal Boiling Point

How are the vapor pressure P and temperature T related exactly?

(a) The Vapor Pressure of Water, Ethanol, and Diethyl Ether as a Function of Temperature. (b) Plots of In(P vap ) versus 1/T for Water, Ethanol, and Diethyl Ether 1/T (K −1 ) T is in K!

Linear relation: y = kx + C y x C: intercept slope: k = tan θ θ

Linear relation: y = kx + C y x θ k > 0 θ k < 0 slope: k = tan θ

ln P = k(1/T) + C Linear relation: y = kx + C 1/T (K −1 ) What is the value of k?

Heat of vaporization ∆H vap : energy needed to convert one mole of liquid to gas. Unit: J/mol or kJ/mol. ∆H vap > 0

slope k < 0 y x y = kx + C

1/T (K −1 )

ln P 1/T (K −1 ) ln P 1 1/T ln P 2 1/T 2

Clausius-Clapeyron Equation

The vapor pressure of water at 25 °C is 23.8 torr, and the heat of vaporization of water is 43.9 kJ/mol. Calculate the vapor pressure of water at 50 °C. Five: T 1, T 2, P 1, P 2, ∆H vap Four known, calculate the other.

Clausius-Clapeyron equation R = J · mol −1 · K −1 Units in ideal gas law PV = nRT P — atm, V — L, n — mol, T — K Option 1 R = atm · L · mol −1 · K −1 P — Pa, V — m 3, n — mol, T — K Option 2 Chem 1211

Liquid potassium has a vapor pressure of torr at 443 °C and a vapor pressure of torr at 708 °C. Use these data to calculate (a) The heat of vaporization of liquid potassium; (b) The normal boiling point of potassium; (c) The vapor pressure of liquid potassium at 100. °C. ( Please try to work on this question by yourself. Will review next week)

Plan for this week’s lab Lab syllabus, then sign agreement Calculations on C-C question Demo on vapor pressure Quiz on C-C question Thursday, IC 420 Section A: 1:00 pm, Section B: 9:00 am

Clausius-Clapeyron Equation

slope k < 0 y x

Linear relation: y = kx + C y x θ k > 0 θ k < 0 slope: k = tan θ

a b c d Lines tilt to the right have positive slopes (a and b), left negative (c and d). Steeper line has greater absolute value of slope. In this graph, the order of slopes is k a > k b > 0 > k c > k d y x

What is the order of heat of vaporization for these three substances?

|k water | > |k ethanol | > |k d.e. | k water < k ethanol < k d.e. <<>> >>

Stronger intermolecular attractions ↔ Higher boiling point and ΔH vap (Chem 1211)

H―O―H ¨ ¨ ¨ H―C― ― ― H H C―O―H ― ― H H ¨ ¨ H―C― ― ― H H C―O― ― ― H H ¨ ― ― H H C―C―H ― ― H H Water: Ethanol: Diethyl Ether:

Solids

Glass (SiO 2 )

Crystal Noncrystal Solid

BasisCrystal structure

The basis may be a single atom or molecule, or a small group of atoms, molecules, or ions. NaCl:1 Na + ion and 1 Cl − ion Cu:1 Cu atom Zn:2 Zn atoms Diamond:2 C atoms CO 2 :4 CO 2 molecules

= Use a point to represent the basis:

Lattice Lattice point:

Unit cell: 2-D, at least a parallelogram Unit cell is the building block of the crystal

How many kinds of 2-D unit cells can we have?

     

                         

Extend the concept of unit cell to 3-D, the real crystals.

: 3-D, at least a parallelepiped

How many kinds of 3-D unit cells can we have?

1. triclinic2. monoclinic 3. orthorhombic 4. tetragonal 5. rhombohedral (trigonal) 6. hexagonal 7. cubic The 14 Bravais lattices 7 crystal systems a ≠ b ≠ c α ≠ β ≠ γ a ≠ b ≠ c α = β = γ = 90° a = b ≠ c α = β = 90°,γ = 120° a = b = c α = β = γ = 90° a = b ≠ c α = β = γ = 90° a = b = c 90° ≠ α = β = γ < 120° γ a b c a b c

(Simple cubic) Chem 1212: assume a lattice point is a single atom

Size of the cellX-ray diffraction Information of a cubic unit cell

The Wave Nature of Light

Number of atoms in a cell Size of the cell Size of the atoms Soon X-ray diffraction Now Information of a cubic unit cell

A B CD

A B CD E F Number of atoms in a unit cell = ¼ x 4 = 1

124 Number of Atoms in a Cubic Unit Cell

The body-centered cubic unit cell of a particular crystalline form of iron is nm on each side. Calculate the density (in g/cm 3 ) of this form of iron. d = g/cm 3

Closest Packing

aa aaa aa aa aa aa aa aaa a a bbbb bbbb bbbb c ccc c ccc c ccc

· · · abab · · ·

Hexagonal unit cell

1. triclinic2. monoclinic 3. orthorhombic 4. tetragonal 5. rhombohedral (trigonal) 6. hexagonal 7. cubic The 14 Bravais lattices 7 crystal systems a ≠ b ≠ c α ≠ β ≠ γ a ≠ b ≠ c α = β = γ = 90° a = b ≠ c α = β = 90°,γ = 120° a = b = c α = β = γ = 90° a = b ≠ c α = β = γ = 90° a = b = c 90° ≠ α = β = γ < 120° γ

· · · abcabc · · ·

abcabc = Cubic Closest Packing

Number of atoms in a cell Size of the cell Size of the atoms Soon X-ray diffraction Now Information of a unit cell Now!

Example 11.7 Al crystallizes with a face-centered cubic unit cell. The radius of an Al atom is 143 pm. Calculate the density of solid Al in g/cm 3. L r 2r r L d = 2.71 g/cm 3

What about simple cubic?

Simple Cubic r L L = 2r

What about body-centered cubic?

Body centered cubic

D Body diagonal D = 4r L

D L L F L L Pythagorean theorem 

Titanium metal has a body-centered cubic unit cell. The density of titanium is 4.50 g/cm 3. Calculate the edge length of the unit cell and a value for the atomic radius of titanium in pm. L = 328 pm Ti: g/mol r = 142 pm

Packing Efficiency

100-mL container 50 %70 % 50 mL70 mL

124 Packing Efficiency: fraction of volume occupied by atoms 74 % 52 % 68 % L = 2r prove

Quiz next week during lab session Calculate density from a unit cell. Relationship between the length of a cell and the radius of an atom is given.