Summary Notes (Mod. 1)
Friday, June 10, 2005
1:37 PM
1.1 - Phases and Phase Diagrams
· Transitions
o Condensation: gas -> liquid
o Vaporization/evaporation: liquid -> gas
o Fusion: solid -> liquid
o Freezing: liquid -> solid
o Sublimation: solid -> gas
o Deposition: gas -> solid
· Sublimation, fusion, and evaporation are all endothermic processes because energy is required to overcome the attractive intermolecular forces in the denser phase to spread them out in the less-dense phase (solid -> gas, for example)
· Phase diagrams
o These are graphs of temperature vs. pressure to show where each phase is stable
o Special notes:
· At the "triple point", all 3 phases co-exist
· Beyond the critical point (Tc, Pc), neither gas nor liquid exists - we only have something called super-critical fluid
· If the S-L line has a positive slope, it means that as we increase pressure, we become solid. This further implies that solid is the densest phase. However, if the S-L line has a negative slope, we move into a liquid area as we increase pressure. As such, liquid is considered to be the densest phase (H2O is a good example of this.)
1.2 - Clausius-Clapeyron Equation
· The L-G line in a phase diagram tells us:
o How the vapor pressure of a liquid changes with the temperature
· Recall that vapor pressure is when you put a liquid in a closed container, and stuff starts evaporating into vapor until you reach an equilibrium point. At that point, the pressure exerted by the vapor is the vapor pressure.
o How the boiling temperature changes with external pressure
· The Clausius-Clapeyron equation is as follows:
· Among other things, we can use it to deduce the normal boiling point of a substance. The normal boiling point is the boiling point under standard conditions - 1 atm of pressure - and so we can plug this into the equation to find out when liquid turns into gas under 1 atm of pressure.
1.3 - Intermolecular Forces
· The condensation of gas or the freezing of liquid occurs because as we lower the temperature, the kinetic energy of the molecules also decreases. If the kinetic energy dips low enough, there won't be enough energy to overcome the attractive intermolecular forces, and so the molecules cannot help but be drawn together.
· Different substances have different physical properties for the following categories, depending on the strength of their intermolecular forces:
o Boiling point (high with strong attractive forces)
o Melting point (high with strong attractive forces)
o ΔHvap (high with strong attractive forces)
o ΔHfus (high with strong attractive forces)
o ΔHsub (high with strong attractive forces)
o Vapor pressure (low with strong attractive forces)
o Surface tension (high with strong attractive forces)
o Viscosity (high with strong attractive forces)
· There are many kinds of intermolecular forces which act between molecules:
o Dipole-dipole forces
· These occur between molecules with a permanent dipole moment - that is, molecules which are permanently polar due to one of the constituent atoms being more electronegative than the other(s)
o London dispersion forces
· These occur between all types of molecules - regardless of whether they are polar or non-polar - because of the fact that electrons are in constant motion within a molecule
· So at any given moment, it is possible that one end of the molecule could have more electrons than the other, thus making it a polar molecule
· We use the term μinst to denote an instantaneous, temporary dipole moment created by the random movement of electrons, and the term μind to denote a molecule which has a temporary dipole moment because it is beside another molecule which has a μinst, and thus has had an attractive/repulsive effect on its electrons
§ The polarizability of a molecule measures how easily it can be affected by the μinst of other cells
§ Larger cells are more polarizable than smaller cells because their charge cloud are more diffuse, or spread out - and thus are more sensitive to the μinst of nearby molecules
o Hydrogen bonding forces
· These occur between cells containing N, O, or F
· When hydrogen is covalently bonded to N, O, or F, it is positive and is thus attracted to lone pairs of electrons on other molecules - it's almost like a very strong dipole-dipole interaction
· Strength comparison of various bonds…
o Covalent and ionic bonds - REAL bonds - are the strongest. They are considered "chemical bonding forces"
o Intermolecular forces are easier to break
· H bonds are stronger than dipole-dipole bonds and London Dispersion Forces
· Thusly, if you are ever asked to compare the intermolecular forces between X number of substances, first consider:
o Is there any hydrogen bonding going on? If so, how many hydrogen bonds can each molecule form?
o If that doesn't decide anything, consider dipole-dipole interactions - are some of the substances extremely polar, and some others very non-polar?
o Also, consider London Dispersion Forces - remember that bigger (and thusly heavier) molecules are more susceptible to London Dispersion Forces because their charge clouds are diffuse
1.4 - Heating Curves
· Heating curves show us how the temperature varies with the amount of heat added
· We can obtain the following information from heating curves:
o The heat capacities of solid, liquid, and gas - how much temperature change can we induce with a given amount of heat added?
o The enthalpies of fusion and vaporization - how much heat do we have to add to fuse (melt) a substance? Or to vaporize (evaporate) it?
1.5 - Introduction to Solids
· 2 main types of solids:
o Crystalline - they have regular repeating patterns of molecules and have sharp, exact melting points (because everything melts at the same time because the structure is constant everywhere)
o Amorphous - they have no regular repeating pattern and so they melt over a range of temperatures
· There are different types of bonds which hold crystalline solids together in their crystal lattices:
o Ionic bonds
· These hold together positive and negative ions
· Examples: NaCl and NH4Cl
o Covalent bonds
· These hold together atoms by strong covalent bonds, like a "giant molecule"
· Examples: Diamond, SiO2
o Molecular bonds
· Here we have weak intermolecular forces holding molecules together
· Examples: H2O, S8, P4, CO2
o Metallic bonds
· These hold together metal cations with strong metallic bonds
· Examples: Cu, Zn, Al, etc.
· We classify crystalline solids by the geometry of the unit cell:
o Cubic
o Trigonal
o Tetragonal
o Hexagonal
o Monoclinic
o Triclinic
o Orthorhombic
1.6 - Cubic Packing Arrangements
· Simple cubic packing
o Description: The spheres in each layer are lined up directly with the spheres in the layer above and below it
o Spheres per cell: 1 (1/8 of a sphere at each corner)
o Edge length: 2 x r
o Packing efficiency (volume of spheres in a cell/volume of cell): 0.5236
· Body-centered cubic packing
o Description: The spheres of one layer are placed in the holes between the spheres of the layers above and below it. The contact between the spheres happens in the middle (body) of the unit cell.
o Spheres per cell: 2 (1/8 of a sphere at each corner, and 1 full sphere in the middle)
o Edge length: 2.3r
o Packing efficiency: 0.6802
· Face-centered cubic packing
o Description: The contacts between spheres happen on the face of the unit cell.
o Spheres per cell: 4 (1/8 of a sphere at each corner, 1/2 of a sphere on each face)
o Edge length: 2.2r
o Packing efficiency: 0.7405
1.7 - Closest-packed Structures
· These are ways to pack atoms together such that the amount of unused space is minimal
· There are 2 main kinds of closest-packed structures:
o ABAB closest packing
· We start off with Layer 1, which is packed such that all the holes between atoms are trigonal - that is, the hole is surrounded on any given plane by 3 atoms
· We place Layer 2 on top of Layer 1 such that Layer 2's atoms cover some of Layer 2's trigonal holes are on top of atoms in Layer 1, and some are on top of holes in Layer 1 as well
· Then we place Layer 3 in the exact same position as Layer 1 - its spheres and holes are on top of Layer 1's spheres and holes
· Thus we call it "ABAB" closest packing because there are only 2 distinct positions for layers
· The unit cells resulting from this closest packing structure can combine in groups of 3 to produce a hexagonal-faced prism
o ABCABC closest packing
· Here we are exactly the same as ABAB closest packing for Layers 1 and 2, so the difference lies in how we place Layer 3
· We place the spheres in Layer 3 over the locations where there is a hole in both Layer 1 and Layer 2, so that all holes are now covered - thus, the position of Layer 3 is necessarily distinct from Layer 1 and 2, and so we call it "ABCABC" closest packing
· The unit cells resulting from this closest packing structure can be divided into face-centered cubic unit cells
1.9 - Ionic Solids and Interstitial Sites
· Now we are going to talk about how different atoms are packed together, unlike before when we were talking about packing the same kinds of atoms together
· For a lot of ionic solids, we have one of the ions forming a cubic lattice - like what we talked about before - and the other one occupying the holes in that lattice
· There are a few different holes which we should be familiar with:
o Trigonal hole
· If we assemble 3 spheres such that they appear to each be a point on a triangle, there will be a hole between these 3
§ Therefore the co-ordination number (the number of spheres making up the hole) is 3
· However, this hole is too small to worry about - nothing of practical interest will ever fit inside
o Tetrahedral hole
· This is when the spheres surrounding the hole make up the shape of a tetrahedral molecule - imagine the locations of the four "corners" of a tetrahedral shape - that is where the spheres surrounding this hole are located
§ So the co-ordination number is 4
· The ratio (as described under the "Octahedral hole" point) is 0.225
o Octahedral hole
· Here we have the spheres surrounding the hole in an octahedral shape - where we have 4 spheres lying 2 x 2 in a plane, and then spheres directly above and below the hole in the middle of those original four
§ So the co-ordination is 6
· The ratio of the radius of a sphere which could fit into the hole to the radius of the spheres surrounding the whole is 0.414
§ So obviously, if we place a sphere into that hole whose radius is less than 0.414 of the surrounding spheres, then it's not going to disturb the surrounding spheres. However, in nature, what often happens is that the sphere is a little too big for the hole, which means that the surrounding spheres are pushed apart and are no longer touching each other…
o Cubic hole
· The hole in the center of a normal 2 x 2 x 2 sphere
§ Thus the co-ordination number is 8
· The ratio (as described under the "Octahedral hole" point) is 0.732
· Consider the face-centered cubic cell:
o Along each of the edges, there is 1/4 of an octahedral hole, as well as a full octahedral hole right in the middle of the cell
o Each corner sphere forms a full tetrahedral hole with the half spheres on each of the 3 faces beside that corner
o So all in all, we have 4 octahedral holes and 8 tetrahedral holes in the face-centered cell
· In general, in a closest-packed structure containing N spheres, there are N octahedral holes and 2N tetrahedral holes
· When we are dealing with binary ionic solids, remember that R- (the negative ion) usually makes up the crystal lattice, and R+ (the positive ion) fills in the holes
· We can use this information to predict what kind of holes a given positive ion occupies, based on the size ratio between the positive and negative ions
o 0.225 < R+/R- < 0.414 || The positive ions occupy tetrahedral holes
o 0.414 < R+/R- < 0.732 || The positive ions occupy octahedral holes
o R+/R- > 0.732 || The positive ions occupy cubic holes
· Ionic crystal structures to remember:
o Sodium chloride
· Cl- ions form an fcc lattice, and Na+ ions occupy the octahedral sites
o Cesium chloride
· Cl- ions form a simple cubic lattice, and Cs+ ions occupy cubic holes in Cl- lattice