The following outline reviews some physics and chemistry that you may or may not have learned before, and which may or may not be relevant to the course you are taking. The review is intended for students who feel insecure about their science background for whatever reason, and in that spirit, to "level the playing field." Students in my courses are not generally or specifically responsible for the material in this outline, but specific information from the outline may be applied in (or applied to) specific lectures, and a general ability to reason scientifically is assumed, which may require general familiarity with the material. The review is by no means complete; science is never completed, nor is a science completely encompassing. The review is not a substitute for any prerequisite studies. It was originally intended for Environmental Geology 284, but is general enough to be used in any science course.
Now that the legalese is complete...the outline is in three parts: I. Philosophy; II Review of Physics; and III. Review of Chemistry. However, physics and chemistry are inseparable, leading to interesting turf wars between physicists and chemists. As to the order chosen here: Physicist Leon Lederman (past director of Fermi Lab!) wrote in a recent NY Times article that science education should begin with physics, then chemistry, then biology, then geology. I enthusiastically agree: how can one understand the energy of bonding, the energy in ATP during photosynthesis, or the energy of earthquake waves, without first knowing what energy is? The philosophy section briefly discusses the scientific method, and was left in the outline because it gives an example of how we "know" the Earth is "round" using some physics--science is not indoctrination, and one shouldn't accept such bold proclamations without proof. Science is open ended. The Earth is not exactly "round" afterall.
If any of the following explanations are not complete enough for you, these references may help, some of which are cited in the body of the outline.
I. Introduction: Course Overview, Philosophy, How Science Works
A. Environmental Geology
B. Three Branches of Philosophy (Why do professors have Ph.D.s?)
Science is a way of knowing, i.e. an epistemological approach. It is based in a metaphysics of materialism. The American Heritage dictionary defines materialism as "the philosophical doctrine that physical matter in its movements and modifications is the only reality and that everything in the universe, including thought, feeling, mind, and will, can be explained in terms of physical laws."1. Metaphysics: What is there? What is reality?2. Epistemology: What can we know? How do we know?
Aesthetic: The study or theory of beauty and the psychological responses to it.( from Webster's New World Dictionary). Aesthetics is a branch of ethics.3. Ethics: What is good (moral judgement)? What should we do?
Aesthetic varies from individual to individual, and there are both aesthetically pleasant and unpleasant aspects of any subject (What is your reaction to Chicago? Yosemite?).
Do not confuse "environmentalism" (working to solve environmental problems) with "preservationism" (an ethic devoted to the aesthetic preservation of nature).
C. How Science Works, An example from Erastosthenes (276-196 B.C.)
1. Observations:
a. Seafarers observed that ship masts were seen on the horizon before the ship.
b. Heavenly bodies (Sun and Moon) were round, so why not Earth.
c. The Earth's shadow is round on a lunar eclipse.
d. Erastosthenes heard that at noon on the summer maximum (what we call the summer solstice, June 21) at Syene (Aswan), Egypt, sundials cast no shadow, and the sun reflected off the water of deep wells.
2. Hypothesis: The earth is round.
Erastosthenes assumed that Syene (Aswan) had direct rays of the sun (0-degree shadows); in modern terms he assumed Syene was on the Tropic of Cancer at 23.5 degrees. Modern Cairo is at about 30 degrees N. Latitude, or a difference of 6.5 degrees. Erastosthenes in Alexandria measured the vertical angle (θ )of the shadow at 7.2 degrees = .126 radians. The Greeks invented trigonometry (the following formula works only if the angle is measured in radians, not degrees!) :3. Implications (or corollary if hypothesis proved): We can calculate the circumference of the Earth using the shadows.
R = radius of earth
D = arc length, ie. Distance from Syene to Alexandria
Erastosthenes estimated, or had a friend estimate, the distance (D) at 5000 stadia (500 miles) by walking to Syene. Knowing D and θ, he calculated the Earth's radius, R=500/.12566 = 3980 miles. Compare modern estimate of 3960 miles (estimate from Tipler's Physics)!
He calculated the circumference at about 25,000 miles.
According to some philosophers of science (namely Karl Popper), nothing is "proven" positively, only disproven (or modified). The theory of a round earth has been modified. The Earth is not round, it is slightly oblate. There are still Flat Earth societies.4. "Prove" in science means "to test." Obviously, a test for a round earth would be to circumnavigate the Earth and compare the distance, a feat not accomplished until Magellan's crew sailed around the world in 1521.
II. Review of Physics
A. Matter: What things are made of, constituent, substance, or material (from Webster's).
What is space? It is volume. When we describe a system, we often describe its size, ie. Volume. Volume is a state variable abbreviated V. The SI unit of volume is a liter which is a cubic decimeter. Other units of volume include the gallon, the cubic foot, the pint, and the fluid ounce, which is 1/16 pint. Unfortunately, the term ounce is also confusingly applied to a unit of weight (see Force below).1. Matter occupies space and is perceptible to the senses in some way (from Webster's).
Avoid interchanging the term inertia with momentum: Momentum is the measure of a quantity of motion (from Webster's). Momentum is a vector (has direction and magnitude); inertia is a name for a property. For example, there is linear momentum (p=mv ) and angular momentum ( L = I x ω ).2. A fundamental property of matter is Inertia: the tendency of matter to remain at rest if at rest, or, if moving, to keep moving in the same direction, unless affected by some outside force (from Webster's).
B. Mass: the quantity of matter in a body as measured in its relation to inertia (from Webster's).The SI unit of Mass is the kilogram. It was originally the mass of a liter of water. There is no English unit for mass
C. Force: the cause, or agent, that puts an object at rest into motion or alters the motion of a moving object. (from Webster's; notice cause and effect!)Note: definitions of Force and Mass are intertwined.
1. In order to measure mass relative to inertia, we need to affect the body with some "outside force."
2. These relations were not clearly defined until Sir Isaac Newton (1642-1727) For historical context, remember these dates: Jamestown 1608, Pilgrims 1620, Restoration 1660
Newton's Three Laws (from Principia, 1686)a. Newton's first law: Matter in motion stays in motion unless objected upon by an outside force, or Matter at rest stays at rest unless objected upon by an outside force.
b. Newton's second law: F=ma (example: Weight is a force.)
(1) a=acceleration, a change in velocity in m/s/s.
(2) m=mass, the quantity of matter, in kg
The SI unit of Force is the Newton which is a kilogram-meter/s/s. Other units include the pound and, unfortunately, the ounce, which is 1/16 of a pound. Don't confuse fluid ounce = 1/16 pint.(3) F=force
The earth has a constant acceleration due to gravity, g, of 9.81 m/s/s. The moon has a constant acceleration due to gravity of 1.63 m/s/s, or about 1/6 or 17% that of earth. Your professor's diet plan: go to the moon and you will lose about 83% of your weight. Unfortunately, like all diet plans, it doesn't work, because your mass will be the same, and you will regain your weight when you return to earth.
Some examples of interaction (II. C. 2. c.):c. Newton's third law, also called the law of interaction (a.k.a. action-reaction, a.k.a. forces occur in pairs). If body A exerts a force on body B, an equal but opposite force is exerted by B on A. Equal and opposite does not mean they cancel!
When the Sport Utility Vehicle slams into my Honda Civic, it is nice to know that I hit him with the same force that he hits me. Unfortunately, that force is enough to throw and crush my Civic, but may only nudge his SUV and maybe dent its fender.
Your weight deforms the earth under foot (footprints etc.), but it also is absorbed by your bones causing shin splints, runner's knees etc. That is why it is always better for a runner to run on grass than asphalt, and better to run on asphalt than concrete.
The force of thrust out of a jet or rocket engine is the same force of jet or rocket propulsion in the other direction.
3. Newton also observed that forces added as vectors. Therefore, the effect of individual forces acting on a body can be evaluated separately, then added to give the total effect.
D. Density and Specific Gravity: Which weighs more, a pound of lead or a pound of feathers?
1. Density is the amount of mass per volume of a body, ρ = m/V, and is an example of an intensive property in that it does not depend upon the amount present. cf. Mass and volume are extensive properties in that they depend upon the amount present.
2. An intensive property in science is commonly expressed as a ratio of two extensive properties.
3. Specific gravity: The ratio of the mass of a substance to the mass of an equal volume of water. It is dimensionless, just a number. Because the density of water is 1 g/cc (more on this later), the number is the same as density of the substance when the density is expressed in g/cc units.E. Four Fundamental Forces--2 macroscopic, 2 nuclear
1. Gravity
Demonstrate: Two objects fall at same rate. Galileo placed under house arrest by the inquisition for Dialogue Concerning Two Chief World Systems--Ptolemaic and Copernican where he presented these and other observations in defense of the Copernican system.a. Galileo Galilei (1564-1642) observed that the acceleration of gravity is a constant for objects of differing mass and/or density:
We are attracted to one another in more ways than one! The force of attraction of any two objects seen on the surface of the earth is overshadowed by the force of attraction between each of the two objects to the earth.b. Newton's Law of Gravity (From Principia 1686)(1) Force acts attractively between any two objects with mass.
(2) The force is directed along a path between the two objects center of mass.
(3) The magnitude of the force depends on the product of the two masses divided by the square of the distance between the centers of mass.
(4) Henry Cavendish, English physicist and chemist, determined the universal gravitation constant, G, in 1798 using a torsion balance.
G = 6.672 x 10-11 N m2 kg -2. Cavendish
presented the result in a paper entitled "Weighing the Earth".
The Mass of the Earth can be determined with:
(5) Gravity is actually the weakest of the four forces because it requires so much mass to even be noticeable. It is the "glue" of the universe, and will ultimately determine the fate of the universe.
2. Electro-Magnetic
a. Electostatic force
DuFay observed what he called vitreous (glass) electricity, that glass rubbed with silk produced a charge Ben Franklin later called positive. Actually, the silk rubbed electrons off the glass. DuFay also observed what he called resinous (amber) electricity, that amber rubbed with fur produced an opposite charge--it undid the vitreous effect. Actually, the amber attained electrons rubbed off the fur. Ben Franklin called the vitreous electricity positive, and resinous electricity negative (lacking vitreous).(1) Force acts between two objects with charge, attractively between objects with opposite charges, repulsively between objects with similar charges.
(2) Force is directed along a path connecting the centers of the charges.
(3) The magnitude of the force depends on the product of the two charges (in coulombs, C) divided by the square of the distance between the centers of charges.
(4) Charles Augustin de Coulomb (1736-1806), French physicist, determined the Coulomb constant, k = 8.988 x 109 Nm2 / C2.
(5) Electostatic forces are much stronger than gravity, but are weaker than the nuclear forces. Electostatic forces are involved in chemical bonding, particularly in ionic bonds.
b. Magnetic force
(1) dipolar.
(2) magnetic materials are due to an unpaired electron spin.
(3) Electric and Magnetic Forces are unified: a moving charge generates a magnetic field. A magnetic field can induce a current (moving charges).
(4) There is an inverse-square law to the magnetic field (from which a magnetic force on another moving charge can be calculated). The magnetic field decreases with the square of the distance from the axis of the moving charge (current) source.
(5) parallel currents in a wire attract.
This is why downed powerlines are so dangerous because a loop in a wire conducting current can actually make the loose end move. Leave alone means DON'T STAND AND WATCH!(6) opposite currents in a wire repel.
3. Strong Nuclear force (a.k.a. Hadronic force)
a. holds nucleons--protons and neutrons--together in a nucleus against the Coulomb force of repulsion between 2 protons.b. The force that is tapped in nuclear energy.
4. Weak Nuclear force.a. produces small degree of instabilty, therefore determines stable versus unstable isotopes.
b. Is responsible for Beta decay, which is essentially the emission of a "highly energized electron" from the nucleus, specifically from a neutron in the nucleus, leaving in the daughter product an additional positive charge (proton) and one less nuetron in the atomic configuration of the parent.
F. Energy, Work, and Power: Definitions and types of energy
1. Energy is the capacity for doing work and overcoming resistance.
W = F d2. Work is the transference of force from one body or system to another, measured by the product of the force and the amount of displacement in the direction of the force.
The SI unit of work and energy is the Joule, which is a Newton-meter. Other units include calorie, diet calories, British Thermal Units, electron-Volts, foot-pounds.
P=F v3. Power is an amount of Energy per unit time, i.e. force times velocity.
The SI unit of Power is the Watt which is a Joule/second. Other units of power include horsepower.
Energy is neither created or destroyed, but may change form. Energy is always conserved, so it can be budgeted. The total energy budget for a system can be described as the sum of the first three: potential, kinetic, and internal energy. However, internal energy involves many other forms of energy, and energy can be transferred between systems in a variety of forms. The following list summarizes the most common forms of energy:4. Types of Energy
U=mgha. Potential Energy: the energy stored in a body by its relative position in a force field. The force field may be gravitational, electrical, mechanical (coiled spring), or other. An example of gravitational potential energy is (m = mass, g = gravitational constant, h = distance from the center of force field, centered in the interacting gravitational body; for objects in Earth's gravity, this is simply the height.) :
Ek = ½ mv2b. Kinetic Energy is the energy of motion, with velocity v.
Tc. Internal Energy of a system consists of all of the systems's 1) molecular translational, rotational, and vibrational energies; 2) electronic energies; and 3) nuclear energies. When the internal energy of a system changes, heat and/or work is released or absorbed. Temperature is a scale used to measure the internal energy of a system. Temperature is a state variable in that it describes the state of a system independent of how it got that way. It is the unstated or zeroth ( 0th ) law of thermodynamics that two systems at the same temperature have the same internal energy, regardless of their respective past events.
Q = mcΔTd. Heat is the energy of atoms or molecules in motion. Heat can be derived from within a system by a chemical or nuclear reaction (see "chemical potential" and "nuclear" energy below), a phase change, or absorbed from its surroundings.(1) Heat exchange: When a system releases or absorbs heat to or from its surroundings, that amount of heat is related to the system's change in temperature, ΔT, by:
Q = mLwhere m is mass, c is specific heat; the term mc can be replaced by heat capacity, C=mc.(2) Latent heat constants and the heat of a phase change: When a substance changes phase, i.e. goes from a solid to a liquid (or back again), or from a liquid to a gas (or back again), heat is aborbed (or released when going back) while the system remains at the same temperature. This is the energy needed to move atoms further apart in the liquid than in the solid, or in the gas than in the liquid. The amount of heat required depends upon the amount (mass) of the substance undergoing the phase change, and is given by:
Note: Heats associated with phase changes are large compared to heats associated with temperature changes. That is why phase change heat energy is commonly used in engineering applications. Energy derived from water vapor going to water liquid is the energy of the steam engine. Water's high latent heat of vaporization is also why a burn from steam at 100 °C (212 °F) is worse than a burn from water at 100 °C (212 °F). Water's high latent heat of fusion is why ice at 0 °C (32 °F) cools a drink more than water at 0 °C (32 °F). Who wants a watered down drink anyway?.where L is a constant characteristic of the substance. If the phase change is from a solid to a liquid (or back), the heat required (Q) is called the heat of fusion and L is called the latent heat of fusion. If the phase change is from a liquid to a solid (or back), the heat required (Q) is called the heat of vaporization and L is called the latent heat of vaporization.
We discussed two state variables so far, Volume and Temperature. As long as we are on the topic of work, we need to define a new state variable, Pressure:e. Work was defined previously: the transference of force from one body or system to another, measured by the product of the force and the amount of displacement in the direction of the force.
P=F/A(1) Pressure is a force exerted against an opposing body and distributed over a surface between them. Pressure is a force (F) per unit area (A).
P = ρghOf particular interest in many sciences is the pressure under a column of a gas (e.g. atmospheric pressure), liquid (e.g. hydrostatic pressure), or solid (e.g. lithostatic pressure). That pressure is given by:
Note 1: We take atmospheric pressure for granted, so much so that pressures are often measured from a zero (0) that starts at 1 atmosphere (760 mm Hg; note this unit of pressure is the height of a column of mercury with ρ = 13.53 g/cc) called "zero gauge". The relationship between pressure and height is used in altimeters to determine altitude. However, the relationship is NOT linear as implied by the equation because the density of the atmosphere changes with height. Also, altimeters must always be set relative to local pressure conditions; pilots always adjust for this (you hope) just before take-off and landing.where ρ is the density (of the gas, liquid, or solid), g is Earth's constant acceleration of gravity, and h is the height of the column above the point where the pressure is measured.
Note 2 (not for the squeamish or faint hearted): Blood pressures are measured in mm-Hg units ABOVE atmospheric. For example a blood pressure of 120 / 80 (systolic over diastolic) is 120 mm-Hg over 80 mm-Hg. This is in excess of one atmosphere. Our species has evolved (except in Kansas) in conditions of 1 atmosphere for several billion years. However, conditions outside Earth's atmosphere are truly zero pressure ("-760 mm-Hg gauge"), and when measured from this vantage point, our outward blood pressure becomes 880 mm-Hg over 840 mm-Hg. In addition, a law in chemistry (Henry's Law) states that the amount of dissolved gas in a fluid is proportional to the pressure overlying (or surrounding) the fluid: if the pressure goes to zero, dissolved gases exsolve (come out of solution). This is what causes "the bends" in scuba diving, and why divers must decompress slowly when returning to the surface. Finally, the volume of a gas expands to infinity as the pressure releases and goes to zero (by the relation V = nRT/P; the Ideal Gas Law; see below). Several recent science fiction movies that I wish I hadn't seen (e.g. Outland, Total Recall) have explored the implications of these three effects.
Pressures in fluids have special uses. You've heard of the psi for bike and car tires. A tire takes advantage of...(2) Pressure is most often used to describe states of fluids which include liquids and gases. The SI unit of pressure is the Pascal which is a Newton per square meter. Other units include the psi (pounds per square inch).
Pascal's principle of pressures in fluids: Pressure applied to an enclosed fluid is transmitted to every point in the fluid and to the walls of the container.
W=PΔV and/or W = VΔP(3) Work can be defined as a Pressure times a change in volume, or a Volume times a change in pressure.
This is the work of a engine, igniting gases that expand against a piston, or the work of sail power which is derived from pressure differences created by gases travelling at different velocities on each side of the sail (the pressure difference is related to the different velocities by Bernoulli's equation not listed here).
For a process occurring at constant temperature and pressure in a closed system (a closed system exchanges energy, but not matter, with its surroundings; see MSP p. 20-22), spontaneous change is accompanied by a decrease in "free energy". A spontaneous chemical reaction decreases the "free energy" stored in chemical bonds. It is released during spontaneous chemical reactions when bonds are broken and new, more stable (less energetic) bonds are formed. The release of this free energy may manifest itself as either or both of the following: a decrease in enthalpy ( ΔH) of the system, and/or an increase in entropy (ΔS) of the system.f. Gibbs Free Energy (example Chemical Potential Energy):
ΔG = ΔH-TΔS
In words, "a change in the Gibbs Free Energy ( ΔG ) is related to a change in the enthalpy ( ΔH ) minus a change in the organizational energy ( TΔS )." Enthalpy is a measure of the internal energy (see "internal energy" above) and pressure-volume state (see "work" above) of a system. Entropy is a measure of the order/disorder in a system. A change in entropy corresponds to a change in the organizational energy, increasing or decreasing the order of the system. In a chemical reaction, the enthalpy change is called the "heat of the reaction" and may be released to, or absorbed from, the surroundings. In a chemical reaction, the entropy change most commonly corresponds to phase changes, and disorder associated with heating.
Special Note: A chemical reaction can be exothermic ( ΔH is - ) or endothermic ( ΔH is + ) and still be spontaneous. In an exothermic reaction, the enthalpy term usually dominates and the reaction is said to be "enthalpy driven". In an endothermic reaction, the positive enthalpy term is countered by entropy and the reaction is said to be "entropy driven."
E = mc2g. Nuclear Energy
the famous equation of Albert Einstein governs nuclear energy which is obtained when a very small amount of mass (m) is converted into a very large amount of energy. The mass (m) is multiplied by the square of the speed of light (c).
h. Wave Energy
E ∝ A2 (an amplitude-square law, A is the wave amplitude)(1) Mechanical waves (sound waves, earthquake waves)
E = hν (a form of Planck's law, h is Planck's constant, 6.626 x 10-34 Js, and ν is spectral frequency)(2) Electromagnetic waves [gamma rays, x-rays, uv, light, heat (infared), microwaves, radio, etc.]
III. Review of Chemistry
A. Matter divided into Substances and Mixtures
1. Substances divided into Elements and Compounds
a. Element: Any substance that cannot be separated chemically into different substances. All matter is composed of elements.
(1) Historically, and ignorantly, it was thought there were 4 "elements": earth, air, fire, and water.
(2) Now there are over 100 "atomic elements" (See Periodic Table).
"Chemically" and "chemical" refer to processes that change the bonds between elements, thereby changing the compounds and/or their properties. Generally, chemistry is the study of bonding between elements and its affect on the properties of resultant compounds.b. Compounds: Chemical combinations of two or more elements.
2. Mixtures are groups of substances that can be separated by physical methods (e.g. crushing, centrifuging, filtering, etc.). Mixtures may have their own properties.
a. Homogeneous mixtures or solutions, examples: seawater, magma
b. Heterogeneous mixtures: concrete, rocks, living things
B. From Gases to Atoms
1. Atom: the smallest individual particle that retains all the properties of a given chemical element.
a. Greeks had a concept of an atom or fundamental particle.b. Atomic theory was revived in science between 1803 and 1808 by John Dalton (1776-1844), a British school teacher, who observed that gases reacted in whole ratios without destroying mass.
2. PV=nRT relationships (Avogadros Law +Boyles Law+Charles Law= the ABC's of the Ideal Gas Law)a. Avogadros Law of 1811, V ∝n where n is the number of moles of the gas.
(1) Equal Volumes of Gases at the same STP have the same number of particles.
(2) 1 GAW = 1 mole = 6.023 x 1023
b. Boyles Law of 1662, P∝1/V
c. Charles Law of 1787, V ∝ T (The Absolute Temperature Scale)d. R is the ideal gas constant; R = 8.3143 J / mol / °K
C. Dimitri Mendelev and the Periodic Table of 1871.e. For liquid water, mass equated with volume: 1 kg water = 1 liter (1 cubic decimeter) at 4 °C and 1 atm. Causes confusion! But solves problems!
1. Elements rarely occur in an isolated (native) condition (native conditions were known for some metals like iron, copper, tin, zinc, gold, silver, lead etc.) and the structure of atoms was unknown (the nucleus was not discovered until 1907), properties of compounds were known (particularly chlorides, hydrides, and oxides). It was recognized that some of the properties were periodic. Periodic means that it repeats. In this case, the properties repeat with increasing atomic number (elemental mass).2. From the chloride, hydride, and oxide compounds, Mendelev calculated relative elemental masses. To line up known properties in a table, he began filling a table with 12 rows and 8 columns arranged by elemental mass. (See Mendelev's periodic Table of 1871, (p. 174 Petrucci). He predicted the properties of undiscovered elements, for example: Germanium.
3. A good example of property periodicity can be seen in the property of Ionization Energy (p. 184 Petrucci), albeit a more modern concept than what existed in Mendelev's time.D. The Modern (from 20th century) understanding of the atom (to Ions and Isotopes)
Discovered in 1919 by Ernest Rutherford (JJ Thomson's positive rays lead him to postulate that atoms had a fundamental + charge). Rutherford was looking at passage of alpha particles in air.1. Atom made of three subatomic particles recognized by properties of mass and charge.a. Proton--has a mass of 1 amu and a charge of +1
Discovered in 1932 by James Chadwick bombarding Be and B with alpha particles.b. Neutron--has a mass of 1 amu and is charge neutral.
Discovered in 1897 by J.J. Thomson during cathode ray experiments. He also calculated the charge-to-mass ratio. Mass was determined from Thomson's charge-to-mass ratio by Robert Millikan (1868-1953) at the U. of Chicago, from 1906 to 1914, in a series of now famous experiments (Millikan's oil drop experiments).c. Electron--has a mass of 1/1878 amu and a charge of -1
Originally, the atom was thought to be a mixture of positive and negative charges, the plum pudding model proposed by JJ Thomson. Ernest Rutherford (a New Zealander working at Manchester University) discovered the nucleus. He had set Hans Geiger and an 18 year old undergraduate Ernest Marsden to work on alpha (a helium cation with charge +2, and one of the known "emanations") scattering. They expected alphas to pass through foils slightly deflected by these random charge centers, but their "experiment was troubled by stray particles. An experiment discovered alphas bounced back: "It was quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you." (Pg. 49 of Richard Rhodes). Rutherford, with Frederick Soddy, later proved that alpha particles were positively charged helium nuclei.2. Ernest Rutherford discovered the nucleus in 1907.
Interatomic chemical bonding always involves the transfer or sharing of electrons, and include ionic, covalent, and metallic bonds. Intermolecular chemical bonding involves intermolecular charge attractions between polar molecules, and include hydrogen and van der Waals bonds. We are concerned with only the two main types of interatomic chemical bonds, ionic and covalent. There is a continuum from ionic to covalent bonding based on the cation/anion electronegativity difference (L. Pauling, see Petrucci, p. 220).3. The nucleus of an atom has protons and neutrons and thus almost all of the mass. Protons of a particular element are fixed, and since they charge balance electrons, they are responsible for most of the properties of an element. Therefore, the modern periodic table is ordered by the number of protons--the atomic number abbreviated Z.E. Chemical Bonding4. Isotopes: are atoms of an element which, because of differing numbers of neutrons in their nuclei, have different masses. Term was coined by Frederick Soddy. The total number of protons and neutrons, each 1 amu, essentially determines the mass of the atom in amu's. Therefore, the total number of protons and neutrons is called the mass number, abbreviated A. The number of neutrons in the nucleus of an atom is determined as A-Z.
5. An ion is an electrically charged atom or group of atoms formed when a neutral atom or group of atoms gains or loses an electron. A cation is a positively charged ion and forms when electrons are lost. An anion is a negatively charged ion and forms when electrons are gained.
6. The Rutherford Atom Model; Bohr's quantum modification.
1. Ionic bond: A pure ionic bond involves the complete transfer of electrons from one element to the other forming ions (oppositely charged) that are held together by the Coulombic force.a. Forms weaker bond (than covalent), though stronger than intermolecular bonds that are also held together by the Coulombic force.
Metal: An element with a small number of valence electrons, electrons in the outermost (highest principal quantum number) electron shells. Electrons are readily Lost, due to low Electron affinity, so that a metal Oxidizes and forms a cation.b. Bonds form between a metal and a non-metal based on the electronegativity difference.
LEO (the lion cat, or cation) says GER
(1) Electron affinity (likeness) is the energy release (-) when a neutral atom absorbs an electron. The halogens have the highest (most negative) values, IA and IIA metals the lowest (most positive) values. It is hard to measure, but it is a great concept.(2) L. Pauling's electronegativity scale is better. Pauling studied bond energies and came up with the scale by comparing how elements compete for electrons in bonds. (He won a Nobel Chemistry Prize for bond resonance energy, and the Nobel Peace Prize for disarmament activism). One can see the relation to the periodic table (Table 8-6, p. 186 Petrucci).
(3) Leads to concept of Oxidation state [also loosely called the valence state because it describes the configuration of the outermost (valence) electrons]
(a) Oxidation state rules 1-6, p. 221 Petrucci
Quantum shells apply to both ionic and covalent bonds, but for ionic bonds, the position of the orbitals is not so critical because the anion achieves a noble gas configuration. The cation with its outer electrons stripped either forms a noble gas configuration with the "inner electrons"or other stable configuration [18, 18+2, Various; p 199 Petrucci].(b) Concept is important to all bonding (not just ionic) because the oxidation state determines the number of electrons available to fill "quantum shells."
(c) Except in gaseous state, ionic compounds form crystals because charged particles surround themselves with oppositely charged particles and you are left with a repeating array of ions. Table salt, p. 199 Petrucci!
2. Covalent Bonds: A pure covalent bond involves the sharing of electrons between elements. Electrons occupy each other's quantum shells.
a. Forms the strongest bonds. Two examples are diamond, where carbon bonds with itself--the hardest substance known--and Si-O. We will spend a lot of time on the silicon and oxygen bond. Also, H2O and CO2.
b. Bonds form usually between nonmetals, or nonmetals and metalloids (Silicon is a metalloid).3. Quantum Mechanics: Understanding bonding, especially covalent bonds, keeps chemists busy. Orientation of quantum orbitals and their associated energy levels lends properties to substances.
The 19th century had a classical interpretation for temperature change and its associated heat energy. The kinetic theory for ideal (nonreacting) gases gave a linear (proportional) relation between temperature and the translational kinetic energy of the gas molecules (it is actually quantized, but at a very refined level). However, other energies were recognized including rotational, vibrational, and electronic. The equipartition of energy theory proposed that the sum total of energy in a system was evenly divided among the four, but it failed.a. 20th century history of ... Quantum Mechanics: The dreams reality is made of!(1) Equipartition of energy theory fails. Max Planck, 1900
See EM spectra (pg. 146 PET). To test your understanding of waves, diagram a wave and label the wavelength and amplitude. Reason out that c = n λ / t, where n is the number of wavelengths passing in time t, is the same as c = ν λ.(a) Electromagnetic radiation includes heat.
Special Note for frequency, in cycles per second: Today's computer processors, cycling at 60 to 260 MHz, can interfere with TV/radio broadcast bands.
In order to explain wavelengths of EM spectra, including light, radiating from a "blackbody" (a perfect absorber and/or re-emmitter of radiation), Max Planck had to replace the linear relationship between energy and temperature with a linear relationship between energy and frequency. E = hν(b) The theory failed to explain "blackbody" radiation.
Modern understanding: Photographic film will overexpose if exposed to too much brightness of light (too many electrons kicked off the film), but the color (frequency) is preserved (albeit washed out) because the energy of the departing electrons is the same. When you overexpose film, primary colors DO NOT change because the energy imparted to the film depends on EM frequency only, and not the brightness. Einstein's conclusion: there is a particle (photon)-wave duality in light.(2) Einstein's photoelectric effect. Albert Einstein, 1905. Won Nobel Prize for this work.(a) The number of electrons ejected from a metal surface exposed to light is proportional to the intensity (or brightness) of the light, BUT(b) The energy of the electrons is proportional to the frequency by Planck's law!
(3) Niels Bohr's Atomic Model (1913)
(a) Bohr took Rutherford's "solar system" model, but added the idea of quantized energy to the energy states of the electrons. He postulated that the quantized energy does not radiate from the electron's motion, as it does for charged particles in classical mechanics.
(b) Instead, electrons occupied different orbitals based on their degree of excitation. Excitation was caused by absorption of EM, and emmission of EM was caused by de-excitation of the electrons.
(c) Mixing classical mechanics (the Coulombic force balancing centrifugal force, and a relation for angular momentum of an electron) with Planck's quantum law, he predicted:
i) The ionization energy of hydrogen.
ii) The radius of the innermost electron (called the Bohr radius), is still valid today!!! 0.53 Å )
iii) Emmission spectra of hydrogen from a integer change in energy (from one shell to the next).
(d) The energy of an electron orbiting hydrogen was an integer multiple of h/2π. The integer multiple itself is called the principal quantum number, n.
This work led directly to the development of the electron microscope. Because the wavelength of an electron is so small, it remains the most refined microscope to date.(4) Matter has a wavelength! (Louis de Broglie, 1924). Now, not only does light exhibit particle (photon) behavior, matter at the atomic scale displays wavelike properties! λ = h/mv
(5) Erwin Schrodinger (Vienese, 1926) used the wave equation (a 2nd order PDE) to describe matter waves.
(6) Werner Heisenberg's uncertainty principle (1927): Because waves diffract, now matter in motion can diffract and this leads to an uncertainty in predicting the electron's position and/or momentum. Depending on the design of the experiment, you know one or the other, but not both.
(7) Max Born's Postulate (1928) The wave function is the probability of finding an electron.
4. The Four Quantum numbers for describing electron location and energies about the nucleus (lends properties to bonds). Three of the four (n,l, and ml ) are integers required to solve Schrodinger's equation. The fourth quantum number, ms (the spin) was proposed by Ulenbeck and Goudsmit, 1925 to explain hydrogen spectra subtleties, and was proven experimentally by Stern and Gerlach in 1922.a. The principal quantum number, n, is a nonzero integer: n = 1,2,3,... They correspond to rows on the periodic table!!!!!!! Also lettered K (n=1), L (n=2), M, etc. Example: The copper (Cu) K-shell x-ray is an x-ray produced by knocking an electron out of copper's n=1 shell. This is a common x-ray used in medicine.
b. The orbital quantum number, l, ranges 0 to n-1: l = 0,1,2,...,n-1and determines the shape of the electron probability distribution. It also gives rise to column arrangement of periodic table.(1) l = 0 are s orbitals (Beach Balls: Figure 7-16, p. 157 PET)
(2) l = 1 are p orbitals (Dumbbells: Figure 7-18, p. 158 PET)
(3) l = 2 are d orbitals (Propellers and a Hoola Hooping Dumbbell: Figure 7-19, p. 160 PET)
s orbitals correspond to Group IA and IIA and p orbitals correspond to Groups IIIA through Group VIIA plus Group 0 or the Representative Elements. d orbitals correspond to Groups IIIB through VIII and IB and IIB or the Transition Elements.(4) l = 3 are f orbitals
c. The magnetic quantum number, ml , ranges -l...,0,...+l There is potentially 1 electron pair per ml quantum number, so for example a p orbital has three boxes (-1,0,1) and a d orbital has five (-2,-1,0,1,2)5. Three rules for using the Four Quantum numbersd. The electron spin quantum number, m s, has the value +½ or -½.
a. Minimum energy--Inner shells not always filled first! Fill by (n+1) with lowest n.b. Wolfgang Pauli's Exclusion principle: No two electrons can have the same set of four quantum numbers alike. The first three quantum numbers determine an orbital shared by 2 electrons. An easier way to say it is: No two electrons have the same spin.
c. Hund's Rule: When orbitals of identical energy are available, they are occupied singly before pairing begins. This minimizes energy (electrons of similar charge get away from each other first), but maximizes unpairing.
F. Building Blocks=Molecules and Unit Cells1. Molecules: A combination of atoms that can exist as an individual identifiable unit possessing a unique set of measurable properties. It is a building block of some, NOT ALL, compounds. Other compounds do not have stable molecules. Instead, they have a crystalline structure completed with a repeating unit cell.a. H2 is diatomic because although the H ground state is neutral, there is an unpaired electron in an s orbital. Molecule is linear. (p. 230 PET)
b. H2S -- 90 degree bonding predicted (92 degree measured) between s-orbitals of hydrogen and unpaired p-orbitals of sulfur (p. 230 PET).c. CH4 i.e. methane--Hybridization of orbitals (specifically sp3) is required to explain the tetrahedral bonding. The three p-orbitals and one s-orbital of carbon combine to form four sp3-orbitals. Each sp3-orbital bonds with an s orbital of hydrogen (p. 232 PET)
d. H2O i.e. liquid water (for solid water, see unit cell below)--Distorted oxygen-centered tetrahedron, with 104.5° bond angle (c.f. 109.5° for tetrahedron) between hydrogen s-orbital and oxygen sp3-orbital. Two hydrogens bond with 2 of four sp3 orbitals in oxygen. The distortion is due to 2 remaining "lone pairs" (2 remaining sp3-orbitals each balanced with 2 paired electrons) in oxygen! (p. 233 PET)
e. CO2 i.e. carbon dioxide -- Carbon dioxide is a complex molecule, beyond the scope of most introductory chemistry texts. However, CO2 is an exceedingly important substance in the environment. Using the rules for Lewis structures, where the outermost valence electrons are combined to complete an octet around both oxygen atoms and the carbon atom, one can see that double bonding must exist in CO2 between the central carbon atom and each oxygen atom. However, both a linear and orthogonal (90°) molecular structure are conceivable from the Lewis structure. Consideration of orbital geometry precludes the orthogonal (90°) molecular structure. The 90° molecule would require unhybridized p-orbitals, but then 2 available p-orbitals from each oxygen would have to overlap (in sigma and pi orientations) with only 2 available p-orbitals from the carbon. Furthermore, the carbon atom p-orbital would not be complete, violating Hund's rule. Instead, a linear molecule results from sp hybridization in the carbon and sp2 hybridization in the oxygen. Each of 2 sp-orbitals from carbon forms a sigma bond with one of 3 sp2 orbitals in an oxygen (the other 2 sp2 orbitals in the oxygen are filled and comprise 2 lone pairs), while each of 2 remaining 2p orbitals in carbon forms a pi bond with a remaining 2p orbital in each oxygen. The sp hybridization of the carbon gives the molecule its linear shape, connecting the trigonal planes of the sp2 hybridization of the oxygen. Properties consistent with a linear molecular structure have been observed in carbon dioxide, e.g. infra-red atomic absorption patterns, confirming the linear molecular structure.2. Crystal: A solidified form of a substance in which atoms are arranged in a definite pattern (called a lattice) that is repeated regularly in three dimensions. The building block for a crystalline compound is called a unit cell.a. Lattice: A three dimensional pattern of points in space. The three dimensional pattern of atoms or groups of atoms in a solid or crystal.
b. Unit Cell: the smallest structural unit of a crystal, having sides parallel to the crystal axes, and whose exact repetition--by translation only--in three dimensions along these axes generates the space lattice.