Chemistry Team 2011-12
Solids and Periodicity (Advanced)
Chris Seok
Definition & Types of Solids:
Definition of a Solid:
Solids have rigid shape and size, unlike gases and liquids. Solids melt into and freeze out of the liquid state, and
sublime into and depose out of the gas state. We can predict the structure of properties of solids and organize
them into specific categories.
Types of Solids:
Reference: http://www.chemguide.co.uk/atoms/structsmenu.html#top
Ionic: solids made up of the bound attraction between anions and cations i.e. negative and positive charges.
[High melting/boiling points (the stronger the charges & smaller the ionic radii on the ions the better); brittle
(easily cut by shear stress); usually soluble; poor conductor when solid, good conductor when liquid/aqueous]
Network Covalent: 3D array of covalently bonded atoms forming one large “network.” Different allotropes can
form different networks with different properties, i.e. diamond’s rigid tetrahedron structure and graphite’s
weaker layered structure. [High melting point/boiling point; usually insoluble in water; MOST are poor
conductors]
Metallic: (obviously metal) solids consist of lots of metal atoms grouped together. The electrons of all the
atoms “delocalize” and form a “sea of electrons,” sharing the electrons among all the atoms. REMEMBER
WHY THE DELOCALIZATION OCCURS (Due to band gap theory which we can derive from energetic
analysis in molecular orbital theory). [High melting/boiling point; not very soluble; good conductor]
Molecular: solids held together by intermolecular forces between molecules (aka van der Waals forces). These
forces include (from weakest to strongest):
London dispersion force (induced dipole – induced dipole; electron clouds momentarily and randomly
aggregate the electrons at one end, inducing positive and negative charges. These clouds then attract)
Dipole-dipole interactions (dipole – dipole; the polar character of a molecule gives it permanent
negative and positive ends)
Hydrogen bonds (dipole – dipole; special case of dipole-dipole interactions. Characterized as attraction
between electronegative atom (oxygen, fluorine, nitrogen) with hydrogen atom attached to another
electronegative atom. Explains high boiling point of water.)
[Low melting/boiling point; solubility in water depends on whether it’s polar or not; poor conductors]
Solid Characteristics:
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Chemistry Team 2011-12
Solids and Periodicity (Advanced)
Chris Seok
Crystalline or Ordered solid: Short-range & Long-range order (e.g.: table salt crystals)
Non-crystalline or Amorphous solid: No long-range order (e.g.: glass, silicon, anything rapidly cooled)
**Since the degree of order in a solid is dependent on the structure of the molecules/ions and the cooling rate
from liquid to solid, a
nything that is cooled slowly enough from a liquid will have time to “orient into” the more stable crystalline
structure & thus will be more crystalline in nature.
*AS ALWAYS, USE COMMON SENSE WHEN FIGURING OUT PHYSICAL PROPERTIES (EX.:
GRAPHITE IS A NETWORK COVALENT SOLID; YET IT HAS DELOCALIZED ELECTRONS DUE TO
ITS STRUCTURE => CONDUCTS ELECTRICITY)
**Again, remind yourself that most physical properties are due to electronic states of the atoms, not the lattice
structure (e.g.: a CCP is not more opaque than an SC because it’s more closely packed; you must do band gap
theory with molecular orbitals & energetics analysis in order to find out if the gap between orbitals allows for
photon absorption)
Lattices & Cubic Solid Applications
Lattice Formation/Stabilization in Solids
In most solid formations (but lattice comparisons mainly focus on ionic solids for simplicity & application),
solids form a regular, stable, long-range lattice. Why? It’s more stable energetically. This can be proven
mathematically, and is represented by the Madelung constant (ask me for a proof if you wish).
History & Systemization of the Lattice Structure
References: http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch13/unitcell.php
http://en.wikipedia.org/wiki/Crystal_family
Robert Hooke, Niels Steensen, and Christian Huygens all made observations as to the consistency and the
similarities between crystal shapes.
Abbé René Just Haüy ("Father of Modern Crystallography") (1781) - worked at Sorbonne on the cleavage of
calcite crystals ⇒ the base unit of calcite must be a rhombohedral since they always break into those shapes.
By using mathematics, he proved that there can only be 7 different types of distinct space-filling volume
elements, AKA 7 crystal systems (http://en.wikipedia.org/wiki/Crystal_system)
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Chemistry Team 2011-12
Solids and Periodicity (Advanced)
Chris Seok
(ex.: cubic, triclinic systems)
August Bravais (1848) - proved that in 3-D, there are only 14 ways to arrange points in space within the 7
crystal systems (AKA the 14 Bravais lattices). We can now use this system of lattices and their centerings to
create structures for ionic solids, molecular solids, covalent solids, metallic solids, so on.
(ex.: for cubic solids, there are three types of Bravais lattices: simple, body-centered, face-centered cubic (or
cubic close-packed).
We can figure out volumes/atomic radii/cell lengths if we use the hard sphere model and assume that all the
atoms are touching each other at the ‘edge’ of their electron clouds.
Go to these sites for reference to solving those problems for cubic solids and their respective Bravais lattices:
http://www.seas.upenn.edu/~chem101/sschem/metallicsolids.html
http://www.okstate.edu/jgelder/solstate.html
http://www.chm.davidson.edu/vce/crystals/sc.html
Coordination numbers: Usually not that important; defined as “# of ‘closest neighbors’”. Obviously differs
between when you’re on the surface or inside (in bulk). When talking about bulk coordination number, use the
# of peripheral atoms bonded to the central atom (for CCP, take one of the edge atoms, take the number of
atoms directly connected to it [6], then multiply it by two to represent the opposite side of the surrounding
atoms/ligands [12]).
Tangent on Periodicity
Periodic Trends:
You should know most of these...will not bother to explain.
http://chemwiki.ucdavis.edu/Inorganic_Chemistry/Descriptive_Chemistry/Periodic_Table_of_the_Elements/Per
iodic_Trends
Note that shielding effect (the decreasing pull on every electron by the nucleus for any non-hydrogen-like
atoms/ions due to the fact that the electrons are all repulsing each other) increases as you go down a group but
constant as you go across a period; this means that the electron-nucleus attraction INCREASES as you go
across a period (b/c atomic number increases).
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Chemistry Team 2011-12
Solids and Periodicity (Advanced)
Chris Seok
Reference: http://en.wikipedia.org/wiki/Shielding_effect
In-Depth explanation of Electronegativity
What is Electronegativity? Fundamentally, an artificial scale first created by Linus Pauling in the 50s to
quantitatively show how electrons are shared (equally or unequally) between atoms and how one can
characterise the spectrum of bonds. (initially normalized to fluorine, which was seen as the most
electronegative; now normalized to hydrogen, the least electronegative)
Pauling got the Nobel Prize for Chemistry in 1954 for defining partial charge (symbolized by Sx for a
compound X) for a given bonded diatomic compound XY (close to formal charge):
,
Where Vx = number of valence electrons in the bonding state (Pauling referred to it as Gx for the group number
[columns!], but that’s ONLY true with the OLD IUPAC notation; with new IUPAC notation, Gx becomes
nonsensical)
Nx = number of non-bonding electrons
Bx = number of bonding electrons
THUS when we use FORMAL CHARGE we are assuming nonpolar bonds - a perfectly covalent bond - AKA
no dipole moment (the ratio of the EN, x to the EN, x + EN, y is .5)
For a diatomic compound, if the partial charge for the more EN atom is -x, then the partial charge for the less
EN atom will be +x.
So now we have a way to symbolize perfect covalence and how polar a bond may be. But how do we quantify
the difference between an ionic and covalent bond, esp. if the bond is polar?
Well first Pauling observed that
BEproduct - BEreactant ~ k(
)2
⇒
BEAB = (either geometric or arithmetic mean of BEAA and BEBB; Pauling claims that the geometric mean is more
accurate but uses arithmetic mean in his book) + (1 eV’s worth of energy symbolized by k)(
)2,
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Chemistry Team 2011-12
Solids and Periodicity (Advanced)
Chris Seok
where all BEs are bonding enthalpies (best described by kJ mol-1, which makes the constant k ~ 96.48 kJ mol-1.
The red part is the contribution from the covalent character of the bond and the blue term is the contribution
from the ionic character/dipole moment/EN disparity of the bond.
http://www.webelements.com/periodicity/electronegativity_pauling/
This |
by:
|
| is known as the Bond dipole moment. For a given salt MXN, it can usually be approximated
|=
With this and an experimental chart, Pauling could quantify ionic character by saying that ionic bonds have a
>1.7 while covalent bonds have a
< 1.7.
Pauling then created a formula to describe % ionic character of ONE BOND.
Although still inaccurate and usually off by ~10%, the Pauling EN formula for calculating the bond enthalpy
was pretty accurate when compared with experimental results. This is also consistent with the system that was
set up - metals are GOOD electron donors, nonmetals are POOR electron donors.
http://www.meta-synthesis.com/webbook/36_eneg/electroneg.html
Now the small dipole charges can be represented by
or
(on the side of the bond with the deficit/surplus
of charge, respectively). An arrow with a perpendicular segment at the end can also be drawn like such:
If you’re indicating dipole moment of a bond instead of the small charges on the atoms, convention says
to draw the arrow towards the more EN atom.
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