Until now, we have been consumed with describing individual atoms of elements. However, isolating individual atoms in most elements is an arduous task given the scale. Most matter is composed of many, many atoms.
Matter
Pure substances*
Elements
Compounds
Mixtures
Homogeneous
Heterogeneous*Pure is very hard to achieve in quantity
More than one atom
Pure substances – typically more than one atom
So what is holding the polyatomic elements together?
Image by E.B. Watson
Covalent bonds – the sharing of electrons
1s1 to 1s2 ([He])
1s1 & [He] 2s2 2p5
to [Ne]
[He] 2s2 2p5
to [Ne]
Two hydrogen atoms in close proximity can share their electrons so that each takes on an electronic structure similar to He – a noble gas.
The diatomic H-H system:
Covalent bonding
Images by E.B. Watson
Electron Swapping
Best with elements of nearly identical electronegativity.
e.g. H2
Hydrogen is 1s1
Another proton and electron would make He, a much more stable configuration- so when you bring two hydrogens together they share their electrons so each has 2 (sort of).
The Covalent Bond Model
This electron sharing is a very strong bond. This tends to by asymmetrical, and therefor difficult to pack into repeating lattices
H2 O2 Cl2 F2
Image from Gill, 1996
Coordinate covalent bonds – the shared electron is donated by atom.
Most carry an overall negative charge(CO3)2-, (OH)-, (HCO3)-, (PO4)3-
lithium (Li) 1s22s1
The 2s electrons are delocalized – move around
For atoms with appropriate electron structure, electron swapping is quite easy when matter is condensed
Metallic bonding
Image by E.B. Watson
Covalently bonded atoms have no charge, but most examples will orient themselves in an electric field
Couloumb’s law
So there must be an ionic character to the bond
Ionization - losing or gaining valence electrons
Can only attract so far – “solid spheres”
Ionic bonding
Electronegativity!
Ionic and covalent bonding are endmembers there is a range of between these two extremes. How do we know if the bonding is dominated by one form or another.
Measuring electronegativity
EAB > ½ E(A2) + ½E(B2)
EAB = ½ E(A2) + ½E(B2) +
is excess energy due to ionic attraction
(+ and -)
= 23(XA - XB) ---X is electronegativity --
Silcates Si-O Sulfides M-S
Fe 1.65 Fe-S: |1.8-2.5| = 0.7
S 2.5
Si 1.8 Si-O: |1.8-3.5| = 1.7
O 3.5
Silcates vs. Sulfides
A compound containing just two elements "-ide“.The metal is named first:
NaCl sodium chloride
Multiple valence stateFe3+ or Fe2+. Higher valence state with the suffix "-ic" and the lower with "-ous":
Fe2O3 ferric oxideFeO ferrous oxide
Today we tend to use a more explicit approachFe2O3 iron(III) oxideFeO iron(II) oxide
Ionic compoundsIonic compounds
More than two elements with polyatomic anions such as
hydroxide OH-
carbonate (CO3)2-
nitrate (NO3)-
phosphate (PO3)3-
The compound names follow pretty logically:KOH potassium hydroxideCaCO3 calcium carbonate
Polyatomic anions can have more than one configuration, e.g.
nitrate (NO3)-
nitrite (NO2)-
CO2 carbon dioxide (Greek "di" for 2)CO carbon monoxide (Greek "mono" for 1)CCl4 carbon tetrachloride (Greek "tetra" for 4)
Empirical Formulas
Always used in ionic compounds
NaCl CaF2 CH2O
Covalent compounds
Used for largely covalent compounds
While CH2O accurately describes the ratio of elements in glucose, it fails to characterize the whole molecule
Molecular Formulas
You are already familiar with atomic mass…
Recall that the atomic mass of an element is the mass of the individual isotopes proportionally distributed.
Molecular mass is obtained by summing the atomic mass for the number of atoms of each element.
CaF2 at. mass tot. mass
1 atom Ca 40.1 au 40.1 au
2 atoms F 19.0 au 38.0 au
m.m.m.m. 78.1 au78.1 au
Avogadro's number
Mg + ½ O2 MgO
A mole is the number of atoms or molecules (6.02 x 1023) needed to make a mass (g) equivalent to the atomic or molecular mass.
Generally, directionality of bonds may be important in covalent species - bonds are generally weaker*
Directionality less important for ionic bonds - radius ratios determine structures.
* exception diamond
As atoms approach, there is a coulombic attraction
Ep (potential energy) = -e2/r
But as ions approach, their electron distributions overlap, so there is a repulsion.
Ep=-e2/r + (be2)/r12
Balance between the overall attraction of atoms and the inter-electron repulsions
Attraction F = kc q1 q2 r-2
Repulsion F is elastic rebound
Images by E.B. Watson
NaCl vs. NaF
F:1s2 2s2 2p5
Cl:1s2 2s2 2p6 3s2 3p5
Both are strongly electronegative
So what differences might you expect?
As it tuns out, the ions are not hard spheres, but more squishy!
There is some variation allowed in the range of “acceptable” radius ratios (cation/anion) in this
configuration.
Image from Blackburn and Dennen, 1994
Ionic bonding is a reduction of excess energy because of (+) or (-) charges. Ionically-bonded compounds are charge balancedcontrols stoichiometry, or ratio of atoms in the compound
Na+ + Cl- = NaClCa++ + 2F- = CaF2
The atoms are not stationary.
T Vibration
25oC 0.025 nm
600oC 0.060 nm
Image from Blackburn and Dennen, 1994
Certain anion/cation ratios produce a predictable polyhedra in IONIC bonding.
CN Type Rc/Ra
2 Linear <0.155
3 Triangle >0.155
4 Tetrahedron >0.225
6 Octahedron >0.414
8 Cube >0.732
12 Closest Packing 1
No Yes
Yes, but... Preferred
CN Rc/Ra
3 Tri 0.155-inf
4 Tetra 0.225-inf
6 Oct 0.414-inf
8 Cube 0.732-inf
Symmetrically-packed structures
• Atoms are spheres
• Bonds must be either non-directional or highly symmetical
Cubic packing
Hexagonal packing
Molecular structures
• Composed of atoms characterized by strongly directional bonding with low symmetry.
• Result is clusters, chains, and layers of atoms that are strongly bonded internally, but weakly bonded to one another.
• Examples: ice, organic molecules
Symmetrically-packed structures can be monatomic or multiatomic.
Symmetrical packing applies to the larger anions.
Monoatomic - Native Elements (Au, Ag, S)
Multiatomic - Most oxides and many silicates
Quartz: Two oxygens for every silicon.
Charge of Si = +4, O = -2
We then say the stoichiometery is 1:2
Important: Si, Ti, Al, Fe, Mg, Ca, Na, K, P, O, S
Today’s $10K question: how do we reconcile the overall stoichiometry (i.e. the chemical formula SiO2) with the coordination of SiO4?
The tetrahedra link together such that the oxygens are shared
This illustrates the general principles of the architecture of crystals
Endmember types
Polyhedra-frame structures
• Bonding dominantly ionic
• Anions group around cations to make coordination polyhedra
Silicates (SiO2 minerals) built of silicate tetrahedra which share corners with one another - this makes a framework. It imparts certain properties to the minerals: strong, hard, etc.
Image from Klein and Hurlbut, 1985
Halite (NaCl)
Two ways to model NaCl: left, atoms of Na and Cl shown, right, atoms of Cl shown with coordination polyhedra (octahedra)
How are these
related?
QUARTZ
Six-fold symmetrical arrangement of tetrahedra all joined by common oxygen atoms.
Rule 1. Interatomic Distance. A coordination polyhedron of anions is formed about each cat-ion. The cation-anion distance being determined by the radius sum and the coordination number of the cation by the radius ratio.
Rule 2. Electrostaic Valency Principle. In a stable coordination structure, the total strength of the valence bonds that reach an anion from all neigh-boring cations is equal to the charge of the anion.
Rule 3. Sharing of Polyhedral Elements I. The existence of edges. and particularly of faces, common to two coordination polyhedra decreases the stability of ionic structures.
Rule 4. Sharing of Polyhedral Elements II. In a crystal containing different cations, those with large valence and small coordination tend not to share polyhedral elements with each other.
Rule 5. Principle of Parity. The number of essentially different kinds of constituents in a crystal structure tends to be small.
Pauling's Rules