Chemistry
103A; Sections 5, 6, 7, 8; Lecture 39, 29 Nov 00
We were talking about:
Crystal Lattices
There are seven basic crystal lattice systems. These seven
basic crystal systems are described on p 612 of your text.
We showed graphics of some of these systems
Cubic
Tetragonal
Orthorhombic
Hexagonal
(No graphics for trigonal, monoclinic, or triclinic.)
Cubic Systems
There are three types of cubic crystal systems.
Simple cubic
Body-centered cubic - bcc
Face-centered cubic - fcc
Unit Cells
The unit cell is the smallest geometric unit whose repetition
(by translation, but without rotation) will create the crystal.
We will describe a number of unit cells in class.
Counting Atoms in a Unit Cell
When we count the number of atoms in a unit cell we count
only the parts of atoms that are entirely within the unit cell.
Atoms entirely within the unit cell (such as the center
of a bcc cell) count as one atom.
Atoms centered in the face of a unit cell (such as the
faces in an fcc cell) count as one-half atom.
Atoms on an edge of the unit cell count as one-quarter
atom.
Atoms at the corners of a cubic, tetragonal, or orthorhombic
cell count as one-eighth of an atom.
The unit cell must conform to the stoichiometry of the compound
in the crystal. That is, for a compound like NaCl the unit cell must have
the same number of Na+ ions as Cl-
ions. Likewise, in a compound like ZnCl2, there must be twice
as many Cl- ions as Zn2+
ions, and so on. (This does not mean that, for example the unit cell of
NaCl must contain only one NaCl unit.)
Structures of Metals
Most metals are either body-centered cubic, face-centered
cubic, or hexagonal.
For example,
Ag fcc
Au fcc
Bi hex
Cu fcc
Fe bcc
Ir fcc
Ni fcc
Pb fcc
Pt fcc
Zn hcp
Dimensions of Atoms
We can use the dimensions of a unit cell to calculate
the diameters of metal atoms .
Example:
Iridium has a face-centered cubic unit cell and a density
of 22.56 g/cm3. What is the radius of an Ir atom?
Ionic Crystals
Ionic crystals are a little more interesting than crystals
of the metals because the unit cells contain more than one type of atom.
The simplest of the ionic crystals are the one-to-one
crystals like NaCl, KCl, NaF, CsBr, ZnS, and so on.
In CsCl the ions are approximately the same size and
the crystal structure is cubic (bcc) with Cs+ ions at the corners
and Cl- ions in the center. (Or you
could say that the Cl- ions are at
the corners and the Cs+ ions are at the centers.) Another way
to say this is that each of the ions forms its own simple cubic lattice,
but the two lattices interpenetrate each other.
In NaCl the Cl-
ion is larger than the Na+ ion and the crystal structure is
cubic with the Cl- ions forming a
fcc structure and the Na+ ions in the octahedral hole sites.
(You could just as easily think of the Na+ ions as forming the
fcc structure and the Cl- ions filling
octahedral sites.)
In ZnS the S2-ions
are considerably larger than the Zn2+ ions. In this crystal
the S2-ions form a fcc structure
and the Zn2+ ions occupy tetrahedral hole sites. (Once again,
you can reverse this description.)
We should check these to make sure that the unit cell satisfies
the stoichiometry of the compound.
Molecular and Network Solids
Ice, dry ice, iodine are molecular solids. In molecular
solids the smallest unit of the compound is the molecule. In the solid
phase the molecules pack themselves together in the way that give the ensemble
the minimum energy.
The forces that hold molecular crystals together are the
familiar intermolecular forces, dispersion forces, dipole-dipole forces,
and hydrogen bonding forces.
(Hydrogen bonding forces are responsible for the unusual
property of water that the solid is less dense than the liquid at 0 oC.
When water freezes the average distance between water molecules increase
slightly to allow room for the formation of hydrogen bonds. Since hydrogen
bonding in the dominant intermolecular force in water, forming more hydrogen
bonds will lower the energy of the crystal.)
The most familiar network solids are diamond and graphite.
Many minerals are network solids. For example, quartz (SiO2),
silicates, silicon carbide, etc. Boron nitride, BN, has the same crystal
structure as diamond and it is reputed to be slightly harder than diamond.
Solutions
We talked a little bit about solutions in Lecture 8 (Chapter
5) Solutions are members of the class of substances called mixtures. Recall
that there were two categories of mixtures:
homogeneous mixtures and
inhomogeneous mixtures.
Solutions are homogeneous mixtures.
Add sugar or salt to water - stir - the sugar or salt
seems to disappear.
We say the sugar or salt dissolved
to form a solution.
A binary solution is a solution that contains two components.
We can talk about the two components as:
solvent = the major
component, and
solute = the minor component.
In a solution the solute is separated into individual molecules,
atoms, or ions, and distributed evenly throughout the solvent.
Main characteristics of a solution
1) Homogeneous
2) Stable
3) Can't be separated by filtration
4) Continuously variable composition
5) Usually transparent
6) Can be separated (distillation, etc)
Types of solutions
Solvent
Solute
Examples
gas
gas
air
(We usually don't think of gas mixtures as solutions,
but they satisfy all the criteria.)
liquid
gas
carbonated water
liquid
liquid vodka, engine
coolant
liquid
solid
sea water
(champagne is all three)
Solvent
Solute
Examples
solid
gas
H2 in Pt or Ir
solid
solid
alloys
In this chapter we will discuss mainly solutions where
the solvent is a liquid.
Concentration Units
The concentration is a measure of the relative amounts
of solute and solvent. There are many units of concentration, of which
the most important for us are:
Molarity (We have already used molarity in Chapter 8.)
Molarity is defined by,
.
(We stress once again that molarity is mol of solute per
Liter of solution, not per liter of solvent. Molarity is defined
so that we can always know how many mols of solute there are in any given
amount of solution.)
Molality
Molality is similar to, but not the same as molarity.
Molality, m, is defined by,
.
Note that for water solutions 1.00 kg of water has a volume
of 1.00 L. If the solution is dilute the volume of the solution formed
from 1 L of water is still approximately 1 L, so that the molarity and
molality are about the same. However, in concentrated water solutions and
in solutions where the solvent is not water the molarity and molality are
very different.
Mole Fraction
Mole fraction is essentially self-defined. In equation
form the mole fraction (usually symbolized by X) is
Other units which are important in medicine and medical technology,
food, and in monitoring the environment are:
Weight percent (wt%). Weight percent is defined
as,
Volume percent or percent by volume (vol%). Percent
by volume is usually used for liquid-liquid solutions, as in alcoholic
beverages. It is defined by,
Parts per million (ppm). Parts per million is usually
used to describe the concentration of trace contaminants in otherwise pure
materials. ppm is defined by
Since for very dilute solutions the mass of the solution
and the mass of the solvent are very nearly the same one could just as
well write,
Parts per billion (ppb). Nowadays, with increasingly
accurate methods of analysis and increasing concern over minute amounts
of some suspected pollutants, we frequently see reports with concentrations
in the ppb range. ppb is defined similarly to ppm as,
Example calculation:
Calculate the molarity of a 0.89 wt% aqueous solution
of NaCl.
Solubility
The solubility of a substance (solute) is the amount of
solute that will dissolve in a given amount of solvent. It is usually expressed
in units of g solute/100mL solvent. The solubility is a measured quantity
and there are tables of solubility for various substances.
Solubility depends on temperature. For most solutes
the solubility increases with increasing temperature.
A solution is said to be unsaturated
if the amount of solute is less than the solubility. The solution is saturated
if the amount of solute in solution is equal to the solubility.
It is possible to prepare a supersaturated
solution in which the amount of solute in solution is greater than the
solubility. This is not an equilibrium state and a disturbance of the solution
will cause the excess solute to precipitate out. (We say that a super saturated
solution is metastable in the same way that
super heated and super cooled liquids are metastable.)
A supersaturated solution can be prepared by dissolving
as much solute as possible in hot solvent and allowing the solution to
cool slowly and quietly to room temperature. Since there are random probabilities
involved this will not always work, but sometimes it will work.