suggestion on note taking no lab tomorrow chem 1211 lab manual
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Suggestion on note taking
No lab tomorrow
CHEM 1211
Lab manual
Logarithm Review
ab = c, (a > 0, a ≠ 1) logac = b
Definition
If a = 10, it is called common logarithm
log c = log10c
If a = e = 2.718281828459045 ∙ ∙ ∙, it is called natural logarithm
ln c = logecKeys on your calculator
c > 0, b can be any real number
Properties of Logarithm
ln(xy) = ln(x) + ln(y)
ln(xm) = m ln(x)
Also see Appendix I B
x > 0, y > 0
Chapter 11
Liquids, Solids andIntermolecular Forces
continued
Vapor Pressure
Surface Molecules
Temperature: T Temperature: TWhat happens to P if T is increased?
phase equilibrium
Liquid Gasvaporization
condensation
Surface Molecules
Georgia, 760 torr = 1 atm
H2O100 °C
NormalBoiling Point
Tibet, 480 torr < 1 atm
H2O85 °C
NormalBoiling 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(Pvap) versus 1/T for
Water, Ethanol, and Diethyl Ether
1/T (K−1)
T is in K!
Linear relation: y = kx + C
y
xC: intercept
slope: k = tan θ
θ
Linear relation: y = kx + C
y
xθ
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 ∆Hvap: energy needed to convert one mole
of liquid to gas. Unit: J/mol or kJ/mol.
∆Hvap > 0
slope k < 0
1ln vapHP C
R T
y x
y = kx + C
1/T (K−1)
ln P
1/T (K−1)
ln P1
1/T1
1
2ln P2
1/T2
1ln vapHP C
R T
1
2 1 2
1 1ln vapHP
P R T T
Clausius-Clapeyron Equation
1ln vapHP C
R T
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: T1, T2, P1, P2, ∆Hvap
Four known, calculate the other.
1
2 1 2
1 1ln vapHP
P R T T
Clausius-ClapeyronequationR = 8.314 J · mol−1 · K−1
Units in ideal gas law
PV = nRT
P — atm, V — L, n — mol, T — K
Option 1
R = 0.082 atm · L · mol−1 · K−1
P — Pa, V — m3, n — mol, T — KOption 2
Chem 1211
Liquid potassium has a vapor pressure of 10.00 torr at 443 °C
and a vapor pressure of 400.0 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 420Section A: 1:00 pm, Section B: 9:00 am
1
2 1 2
1 1ln vapHP
P R T T
Clausius-Clapeyron Equation
1ln vapHP C
R T
slope k < 0
1ln vapHP C
R T
y x
Linear relation: y = kx + C
y
xθ
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 thisgraph, the order of slopes is
ka > kb > 0 > kc > kd
y
x
What is the order of heat of vaporization for these three substances?
|kwater| > |kethanol| > |kd.e.|
kwater < kethanol < kd.e.
( ) vapH water
R
( ) vapH ethanol
R
( . .) vapH d e
R< <
( ) vapH water
R
( ) vapH ethanol
R
( . .) vapH d e
R> >
( ) vapH water ( ) vapH ethanol ( . .) vapH d e> >
Stronger intermolecular attractions
↔ Higher boiling point and ΔHvap
(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 (SiO2)
Crystal
Noncrystal
Solid
Basis Crystal 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
CO2: 4 CO2 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. triclinic 2. monoclinic
3. orthorhombic
4. tetragonal5. rhombohedral (trigonal)
6. hexagonal7. cubic
The 14 Bravais lattices
7 crystal systems
a ≠ b ≠ cα ≠ β ≠ γ
a ≠ b ≠ c
α = β = γ = 90°
a = b ≠ cα = β = 90° ,γ = 120°
a = b = cα = β = γ = 90°
a = b ≠ cα = β = γ = 90°
a = b = c90° ≠ α = β = γ < 120°
γ
ab
ca
b
c
(Simple cubic)
Chem 1212: assume a lattice point is a single atom
• Size of the cell X-ray diffraction
Information of a cubic unit cell
The Wave Nature of LightThe 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
AB
C D
AB
C D E
F
Number of atoms in a unit cell = ¼ x 4 = 1
1 2 4
Number of Atoms in a Cubic Unit Cell
The body-centered cubic unit cell of a particular crystalline
form of iron is 0.28664 nm on each side. Calculate the density
(in g/cm3) of this form of iron.
d = 7.8753 g/cm3
Closest Packing
a a
aaa
a a
a a
aa
a a
a a a a a
a
a
b b b b
b b b b
b b b b
c c c c
c c c c
c c c c
· · · abab · · ·
· · · abab · · ·
Hexagonal unit cell
1. triclinic 2. monoclinic
3. orthorhombic
4. tetragonal5. rhombohedral (trigonal)
6. hexagonal7. cubic
The 14 Bravais lattices
7 crystal systems
a ≠ b ≠ cα ≠ β ≠ γ
a ≠ b ≠ c
α = β = γ = 90°
a = b ≠ cα = β = 90° ,γ = 120°
a = b = cα = β = γ = 90°
a = b ≠ cα = β = γ = 90°
a = b = c90° ≠ 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/cm3.
r8L
L
r
2r
r
L
d = 2.71 g/cm3
What about simple cubic?
Simple Cubic
r
L
L = 2r
What about body-centeredcubic?
Body centered cubic
D
Body diagonal D = 4r
L
D
L
L F
L
Body diagonal D = 4r
r3
4L
L
Pythagorean theorem
Titanium metal has a body-centered cubic unit cell. Thedensity of titanium is 4.50 g/cm3. Calculate the edge lengthof the unit cell and a value for the atomic radius of titaniumin pm.
L = 328 pm
Ti: 47.87 g/mol
r = 142 pm
Packing Efficiency
100-mL container
50 % 70 %
50 mL 70 mL
1 2 4
Packing Efficiency: fraction of volume occupied by atoms
74 %52 % 68 %
L = 2r r3
4L r8L
prove
Quiz next week during lab session
Calculate density from a unit cell.
Relationship between the length of a cell and theradius of an atom is given.