chapter 2 - 1 chapter 2: atomic structure and interatomic bonding (updated) these notes have been...
TRANSCRIPT
Chapter 2 - 1
Chapter 2: Atomic Structure and Interatomic Bonding (updated)
These notes have been prepared by Jorge Seminario from the textbook material
Chapter 2 - 2
ISSUES TO ADDRESS...• What promotes bonding?
• What types of bonds are there?
• What properties are inferred from bonding?
Chapter 2-
– Atoms are made of protons, neutrons and electrons• me=0.00091094x10-27= 9.1094x10-31kg = 0.511MeV• mp = 1.6726 x 10-27 kg = 938.272 MeV
• mn = 1.6749 x 10-27 kg = 939.566 MeV = • mn = mp + 1.293 MeV
• proton & electron charge 1.6022 x 10-19 C• However p are +’ve and e are –’ve – Atomic number (Z) describes the number of protons
in the nucleus– Atomic mass (A) of an element is approximately
equal to the number of neutrons and protons the element has
• Remember elements have isotopes – elements can have different numbers of neutrons (e.g. 12C, 13C, 14C)
– Atomic weight is the weighted average of the element based on the relative amounts of its isotopes (e.g. 1 mol/carbon = 12.0107 g/mol, NOT 12 g/mol!)
Basic concepts
Chapter 2-
2.2 Fundamental Concept
Atomic Weight Weighted average of the atomic masses of an atom's
naturally occurring isotopes Atomic Mass Unit (amu)
Measure of atomic mass 1/12 the mass of C12 atom
Mole Quantity of a substance corresponding to 6.022X1023 atoms
or molecules 1 amu/ atom (or molecule) = 1g/mol
Chapter 2-
How many grams are there in one amu of a material?
The two major isotopes of carbon:
98.93% of 12C with an atomic weight of 12.00000 amu, and
1.07% of 13C with an atomic weight of 13.00335 amu.
Confirm that the average atomic weight of C is 12.011 amu.
Sum the product of the isotope atomic weight and the percent abundance.
(12 amu)*(.9893)+(13.00335 amu)*(.0107) = 12.011 amu
Examples
Chapter 2-
2.3 Electrons In AtomsBohr Atomic Model (old view)
Early outgrowth of quantum mechanics
Electrons revolve around nucleus in discrete orbitals
Electrons closer to nucleus travel faster then outer orbitals
Principal quantum number (n); 1st shell, n=1; 2nd shell, n=2; 3rd shell, n=3
Chapter 2-
Atomic Models
Wave-Mechanical Model
Electron exhibits both wave-like and particle-like characteristics
Position is now considered to be the probability of an electron being at various locations around the nucleus, forming an electron cloud
Chapter 2-
Atomic ModelsQuantum numbers
Principal quantum number n, represents a shell
K, L, M, N, O correspond to n=1, 2, 3, 4, 5....
Quantum number l, signifies the subshell Lowercase italics letter s, p, d, f; related to
the shape of the subshell
Quantum number ml , represents the
number of energy state s, p, d, f have 1, 3, 5, 7 states respectively
Quantum number ms, is the spin moment
Each electron is a spin moment (+1/2) and (-1/2)
Chapter 2-
Electron Configuration
Electron configuration represents the manner in which the states are occupied
Valence electrons Occupy the outermost
shell Available for bonding Tend to control chemical
properties Ex. Silicon (Si)
Chapter 2-
ExamplesGive the electron configurations for the following:C 1s2 2s2 2p2
Br 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p5
Mn+2
1s2 2s2 2p6 3s2 3p6 3d5
F-
1s2 2s2 2p6
Cr1s2 2s2 2p6 3s2 3p6 4s1 3d5
Chapter 2 - 15
Electronic Structure• Electrons have wave-like and particle-like (old view) properties. • We can better say that the wave-particle nature is the real thing;
individual wave and particle states are limiting cases; usually observed in measurements (collapse of the wave function)
• To better understand electronic structure, we assume– Electrons “reside” in orbitals.– Each orbital at discrete energy level is determined by quantum
numbers.c
Quantum # Designation n = principal (energy level-shell) K, L, M, N, O (1, 2, 3, etc.)
l = angular (orbitals) s, p, d, f (0, 1, 2, 3,…, n -1)
ml = magnetic 1, 3, 5, 7 (-l to +l)
ms = spin ½, -½
Chapter 2 - 16
Electron Configurations• Valence electrons – those in unfilled shells• Filled shells more stable• Valence electrons are most available for
bonding and tend to control the chemical properties
– example: C (atomic number = 6)
1s2 2s2 2p2
valence electrons
Chapter 2 - 17
Electronic Configurationsex: Fe - atomic # = 26
valence electrons
Adapted from Fig. 2.4, Callister & Rethwisch 3e.
1s
2s2p
K-shell n = 1
L-shell n = 2
3s3p M-shell n = 3
3d
4s
4p4d
Energy
N-shell n = 4
1s2 2s2 2p6 3s2 3p6 3d 6 4s2
Chapter 2-
2.4 Periodic Table
Elements classified according to electron configuration Elements in a given column or group have similar valence electron
structures as well as chemical and physical properties Group 0 – inert gases, filled shells and stable Group VIIA – halogen Group IA and IIA - alkali and alkaline earth metals Groups IIIB and IIB – transition metals Groups IIIA, IVA and VA – characteristics between the metals and
nonmetals
Chapter 2 - 20
Atomic Bonding
• Valence electrons determine all of the following properties
1) Chemical
2) Electrical
3) Thermal
4) Optical
5) Deteriorative
6) etc.
Chapter 2-
2.5 Bonding Forces and Energies
FN = FA + FR
EN = EA + ER
When 0 = FA + FR, equilibrium exists. The centers of the atoms will remain separated by the
equilibrium spacing ro.
This spacing also corresponds to the
minimum of the potential energy
curve. The energy that would be
required to separate two
atoms to an infinite separation is Eo
Figure 2.8
Chapter 2-
2.5 Bonding Forces and Energies
• A number of material properties depend on Eo, the curve shape, and bonding type– Material with large Eo typically have higher melting
points
– Mechanical stiffness is dependent on the shape of its force vs. interatomic separation curve
– A material’s linear coefficient of thermal expansion is related to the shapeof its Eo vs. ro curve
Chapter 2-
Bonding in Solids
• 2.5 Bonding forces and energies
– Far apart: atoms don’t know about each other– As they approach one another, exert force on one another
• Forces are– Attractive (FA) – slowly changing with distance
– Repulsive (FR) – typically short-range
– Net force is the sum of these
FN = FA + FR
– At some point the net force is zero; at that position a state of equilibrium exists
Chapter 2-
Bonding in Solids• Bonding forces and energies
– We are more accustomed to thinking in terms of potential energy instead of forces – in that case
RAN
r
R
r
AN
EEE
drFdrFE
• The point where the forces are zero also corresponds to the minimum potential energy for the two atoms (i.e. the trough in Figure 2.8), which makes sense because dE/dr = F =0 at a minimum.
• The interatomic separation at that point (ro) corresponds to the potential energy at that minimum (Eo, it is also the bonding energy)• The physical interpretation is that it is the energy needed to separate the
atoms infinitely far apart
FdrESetting our ZERO ENERGY reference at infinite
Chapter 2-
ExamplesCalculate the force of attraction between ions X+ and an Y-, the centers of which are separated by a distance of 2.01 nm.
&
Chapter 2-
• Types of chemical bonds found in solids– Ionic
– Covalent
– Metallic
• As you might imagine, the type of bonding influences properties – why?
• Bonding involves the valence electrons!!!
2.6 Primary Interatomic Bonds
Chapter 2-
2.6 Primary Interatomic Bonds• Ionic Bonding
– Compounds composed of metallic and nonmetallic elements
– Coulombic Attractive Forces: positive and negative ions, by virtue of their net electrical charge, attract one another
• EA = -A/r• ER = -B/rn
– Bonding is nondirectional: the magnitude of the bond is equal in all directions around an ion
– Properties: generally large bonding energies (600-1500 kJ/mol) and thus high melting temperatures, hard, brittle, and electrically and thermally insulative
A, B, and n are constants
Na+ Cl-Coulombic bonding Force
Chapter 2-
2.6 Primary Interatomic Bonds
• Ionic bonding– Prototype example – sodium chloride (NaCl)
• Sodium gives up one its electrons to chlorine – sodium becomes positively charged, chlorine becomes negatively charged
– The attraction energy is electrostatic in nature in ionic solids (opposite charges attract)
– The attractive component of the potential energy (for 2 point charges) is given by
r
eZeZE
oA
1
421
– The repulsive term is given by
128~ , nr
BE
nR
Chapter 2-
IONIC BONDING– Ionic bonding is non-directional – magnitude of the bond is equal in
all directions around the ion
– Many ceramics have an ionic bonding characteristic
– Bonding energies typically in the range of 600 – 1500 kJ/mol
– Often hard, brittle materials, and generally insulators
Chapter 2 - 32
Ionic bond: metal + nonmetal
donates accepts electrons electrons
Dissimilar electronegativities
ex: MgOMg 1s2 2s2 2p6 3s2 O 1s2 2s2 2p4
[Ne] 3s2
Mg2+ 1s2 2s2 2p6 O2- 1s2 2s2 2p6 [Ne] [Ne]
Chapter 2 - 33
• Occurs between + and - ions.
• Requires electron transfer.• Large difference in electronegativity required.• Example: NaCl
Ionic Bonding
Na (metal) unstable
Cl (nonmetal) unstable
electron
+ - Coulombic Attraction
Na (cation) stable
Cl (anion) stable
Chapter 2 - 34
Ionic Bonding
• Energy – minimum energy most stable– Energy balance of attractive and repulsive terms
Attractive energy EA
Net energy EN
Repulsive energy ER
Interatomic separation r
rA
nrBEN = EA + ER =
Adapted from Fig. 2.8(b), Callister & Rethwisch 3e.
Chapter 2 - 35
• Predominant bonding in Ceramics
Adapted from Fig. 2.7, Callister & Rethwisch 3e. (Fig. 2.7 is adapted from Linus Pauling, The Nature of the Chemical Bond, 3rd edition, Copyright 1939 and 1940, 3rd edition. Copyright 1960 by Cornell University.
Examples: Ionic Bonding
Give up electrons Acquire electrons
NaClMgO
CaF2CsCl
Chapter 2-
2.6 Primary Interatomic Bonds• Covalent Bonding
– Stable electron configurations are assumed by the sharing of electrons between adjacent atoms
– Bonding is directional: between specific atoms and may exist only in the direction between one atom and another that participates in electron sharing
– Number of covalent bonds for a particular molecule is determined by the number of valence electrons
– Bond strength ranges from strong to weak
• Rarely are compounds purely ionic or covalent but are a percentage of both.
Sharing 4 electrons
Sharing 2 electrons
%ionic character = {1 – exp[-(0.25)(XA-XB)2]} x 100
XA and XB are electronegatives
Chapter 2-
Covalent bonding
– Sharing of electrons between adjacent atoms
– Most nonmetallic elements and molecules containing dissimilar elements have covalent bonds
– Polymers!
– Bonding is highly directional!
– Number of covalent bonds possible is guessed by the number of valence electrons
• Typically is 8 – N, where N is the number of valence electrons
• Carbon has 4 valence e’s – 4 bonds (ok!)
Chapter 2-11
• Molecules with nonmetals• Molecules with metals and nonmetals• Elemental solids (RHS of Periodic Table)• Compound solids (about column IVA)
He -
Ne -
Ar -
Kr -
Xe -
Rn -
F 4.0
Cl 3.0
Br 2.8
I 2.5
At 2.2
Li 1.0
Na 0.9
K 0.8
Rb 0.8
Cs 0.7
Fr 0.7
H 2.1
Be 1.5
Mg 1.2
Ca 1.0
Sr 1.0
Ba 0.9
Ra 0.9
Ti 1.5
Cr 1.6
Fe 1.8
Ni 1.8
Zn 1.8
As 2.0
SiC
C(diamond)
H2O
C 2.5
H2
Cl2
F2
Si 1.8
Ga 1.6
GaAs
Ge 1.8
O 2.0
colu
mn IVA
Sn 1.8Pb 1.8
Adapted from Fig. 2.7, Callister 6e. (Fig. 2.7 isadapted from Linus Pauling, The Nature of the Chemical Bond, 3rd edition, Copyright 1939 and 1940, 3rd edition. Copyright 1960 by Cornell University.
EXAMPLES: COVALENT BONDING
Chapter 2 - 39
C: has 4 valence e-, needs 4 more
H: has 1 valence e-, needs 1 more
Electronegativities are comparable.
Adapted from Fig. 2.10, Callister & Rethwisch 3e.
Covalent Bonding• similar electronegativity share electrons• bonds determined by valence – s & p orbitals
dominate bonding
• Example: CH4 shared electrons from carbon atom
shared electrons from hydrogen atoms
H
H
H
H
C
CH4
Chapter 2-
Bonding in Solids
• Many materials have bonding that is both ionic and covalent in nature (very few materials actually exhibit pure ionic or covalent bonding)
• Easy (empirical) way to estimate % of ionic bonding character:
XA, XB are the electronegativities of atoms A and B involved
Notice: this is a very very very empirical formula
100x))(25.0(exp1character ionic % 2BA XX
Chapter 2 - 41
Primary Bonding
• Ionic-Covalent Mixed Bonding
% ionic character =
where XA & XB are Pauling electronegativities
%)100( x
1 e
(XA XB )2
4
ionic 70.2% (100%) x e1 characterionic % 4)3.15.3(
2
Ex: MgO XMg = 1.3XO = 3.5
Chapter 2-
2.6 Primary Interatomic Bonds• Metallic Bonding
– Found in metals and their alloys– 1 to 3 valence electrons that form a
“sea of electrons” or an “electron cloud” because they are more or less free to drift through the entire metal
– Nonvalence electrons and atomic nuclei form ion cores
– Bonding energies range from weak to strong
– Good conductor of both electricity and heat
– Most metals and their alloys fail in a ductile manner
Ion Cores
Sea of Valence Electrons
+
+
+
+
+
+
+
+
+
- -
- -
Chapter 2-12
• Arises from a sea of donated valence electrons (1, 2, or 3 from each atom).
• Primary bond for metals and their alloys
+ + +
+ + +
+ + +Adapted from Fig. 2.11, Callister 6e.
METALLIC BONDING
Chapter 2-
Bonding in Solids
• Metallic bonding– Most metals have one, two, or at most three valence electrons
– These electrons are highly delocalized from a specific atom – have a “sea of valence electrons”
– Free electrons shield positive core of ions from one another (reduce ER)
– Metallic bonding is also non-directional
– Free electrons also act to hold structure together
– Wide range of bonding energies, typically good conductors (why?)
Chapter 2 -
2.7 Secondary Bonding or van der Walls Bonding
• Also known as physical bonds
• Weak in comparison to primary or chemical bonds
• Exist between virtually all atoms and molecules
• Arise from atomic or molecular dipoles– bonding that results from the coulombic attraction
between the positive end of one dipole and the negative region of an adjacent one
– a dipole may be created or induced in an atom or molecule that is normally electrically symmetric
Chapter 2 -
2.7 Secondary Bonding or van der Waals Bonding
• Fluctuating Induced Dipole Bonds– A dipole (whether induced or instantaneous)
produces a displacement of the electron distribution of an adjacent molecule or atom and continues as a chain effect
– Liquefaction and solidification of inert gases
– Weakest Bonds
– Extremely low boiling and melting pointAtomic nucleus
Atomic nucleus
Electron
cloud
Electron
cloudInstantaneous
Fluctuation
Chapter 2 -
2.7 Secondary Bonding or van der Waals Bonding
• Polar Molecule-Induced Dipole Bonds– Permanent dipole moments exist by virtue of an
asymmetrical arrangement of positively and negatively charged regions
– Polar molecules can induce dipoles in adjacent nonpolar molecules
– Magnitude of bond greater than for fluctuating induced dipoles
+ -
Polar Molecule
Induced Dipole
Atomic nucleusElectron Cloud
Chapter 2 -
2.7 Secondary Bonding or van der Waals Bonding
• Permanent Dipole Bonds– Stronger than any secondary bonding with induced
dipoles
– A special case of this is hydrogen bonding: exists between molecules that have hydrogen as one of the constituents
H Cl H Cl
Hydrogen Bond
Chapter 2-
Bonding in Solids• Permanent dipoles (hydrogen
bonds)– Van der Waals interactions between
polar molecules– Best known example – hydrogen
bonding• These interactions are fairly strong,
very complex, and surprisingly not well understood!
Chapter 2-
c02f16
Many molecules do not have a symmetric distribution/arrangement of positive and negative charges (e.g. H2O, HCl)
MATERIAL OF IMPORTANCEWater
Chapter 2 - 53
• Bond length, r
• Bond energy, Eo
• Melting Temperature, Tm
Tm is larger if Eo is larger.
Properties From Bonding: Tm
r o r
Energyr
larger Tm
smaller Tm
Eo =
“bond energy”
Energy
r o r
unstretched length
Chapter 2 - 54
• Coefficient of thermal expansion,
• ~ symmetric at ro
is larger if Eo is smaller.
Properties From Bonding :
= (T2 -T1) LLo
coeff. thermal expansion
L
length, Lo
unheated, T1
heated, T2
r or
smaller
larger
Energy
unstretched length
Eo
Eo
Chapter 2-16
• Elastic modulus, E cross sectional area Ao
L
length, Lo
F
undeformed
deformed
L F Ao
= E Lo
Elastic modulus
PROPERTIES FROM BONDING: E
E ~ dF/dr|ro elastic modulus
Chapter 2 - 56
Ceramics(Ionic & covalent bonding):
Large bond energylarge Tm
large Esmall
Metals(Metallic bonding):
Variable bond energymoderate Tm
moderate Emoderate
Summary: Primary Bonds
Polymers(Covalent & Secondary):
Directional PropertiesSecondary bonding dominates
small Tm
small E large
secondary bonding
Chapter 2 - 57
Type
Ionic
Covalent
Metallic
Secondary
Bond Energy
Large!
Variablelarge-Diamondsmall-Bismuth
Variablelarge-Tungstensmall-Mercury
smallest
Comments
Nondirectional (ceramics)
Directional(semiconductors, ceramicspolymer chains)
Nondirectional (metals)
Directionalinter-chain (polymer)inter-molecular
Summary: Bonding