Transcript Molecules

Molecules
Molecules are dynamic, physically-extended shapes. Like ball bearings linked with springs
zipping through space, they spin, vibrate and collide with one another. All these forms of
motion contribute to the internal energy of the molecule. Many molecules are polar, which
causes their various parts to attract or repel other molecules. In all this variety of motion, the
quantized nature of the microscopic world rules: only specific tumbling speeds occur, only
discrete internal vibration modes occur, only quantized energy is transferred in molecular
collisions. In addition, molecular collisions can affect electrons, causing them to jump up into
higher energy orbits—or give up extra energy in a relaxation process, which involves the
emission of a photon. In complex molecules the number and variety of electron orbitals is
very large because individual atomic orbitals combine into a complex array of orbitals that
extend across the entire molecule. Beside having an electronic absorption/emission
spectrum like free atoms (at visible light wavelengths), a molecule has vibrational and spin
spectra at infrared wavelengths.
Atoms and molecules in groups reside in distinct state of matter: solid, liquid, gas or plasma
(ionized gas). Beside these general states, mixed states involving two or more metals
(alloys), or multiple discrete materials suspended in another medium (colloids) are possible.
States of matter are temperature and pressure dependent. At very high temperatures atoms
are moving so fast that electrons are knocked free from their atoms, creating ionized
plasma—the only state of matter in stars. At lower temperature, gas molecules retain their
electrons but still move fast enough (100’s of meters per second) to escape condensation
(transformation to a liquid state). In other words, their high kinetic energy keeps them from
being pulled together by intermolecular forces.
The average speed of a gas molecule, vGas (meters/sec), is given by vGas = sqrt(3kT/mGas),
where T is temperature (degrees Kelvin), k is Boltzmann constant (1.38*10-23 joule/Kelvin),
and mGas is the mass of the gas molecule (in kilograms). For example, nitrogen gas (N2)
which is 75% of our air, is 28 atomic mass units (amu; 1 amu = 1.66*10-27kg), so at room
temperature (298 Kelvin) the average speed of a nitrogen molecule is 515 m/sec.
“Intermolecular forces are electromagnetic forces which act between molecules or between
widely separated regions of a macromolecule. Listed in order of decreasing strength, these
forces are: Ionic interactions , Hydrogen bonds , dipole-dipole interactions , and
London dispersion forces (Van der Waals force),” (http://en.wikipedia.org/wiki/Intermolecular_forces).
All of these are variations of electrical attraction: the strongest (ionic) involves charge
separation, the intermediate (hydrogen and dipole) are attributed to permanent molecular
dipoles and the weakest (London) is caused by the net attractive force generated between
molecules by temporarily-induced dipoles arising from their dynamically shifting electron
clouds.
At lower temperatures, gas molecules slow down sufficiently that intermolecular forces can
overcome their kinetic energy—molecules condense into a liquid phase. That is, they are
strongly attracted to one another, but not yet bound in place, so they freely roam around. At
still lower temperature, molecular kinetic energy is so low that the molecules vibrate about in
fixed positions—they solidify into a solid state. These changes of state are called phase
transitions.
©J Shepanski 2006
Molecules (2 of 2)
Each state of matter has distinct characteristics. Plasma is a highly charged “gas” of positive
ions and free roaming electrons. Gas has no definite shape or volume. Liquid has a definite
volume, but no fixed shape. And solids have both fixed volume and shape. A solid, pure
substance—a chemically-uniform combination of atoms/molecules—has two basic molecular
configurations: a crystal—a highly-ordered arrangement of atoms/molecules that have special
electrical, optical and sonic properties; and an amorphous glass, wherein the atoms/
molecules are randomly arranged in fixed positions. Metals have a special property in that their
valence orbitals intermix to such an extent that their outermost electrons roam free, forming an
“electron sea” around the inner electronic shells of the atoms, making them very good
conductors of electricity. On the other hand, non-metals hold tightly to their valence electrons,
which make them insulators—poor electrical conductors. Semiconductors are intermediate
materials that are normally insulating, but under special circumstances they become good
conductors. Modern technology’s ability to control the properties of semiconductors has
enabled the computer revolution—a good example of the fact that non-pure substances can
also be highly-arranged and have special properties.
Organic molecules—those chiefly consisting of carbon, oxygen and hydrogen—have a
tremendous variety of configurations and properties. These can form very large interacting
constructs—macromolecules: carbohydrates, lipids, proteins and DNA—the stuff of life.
Energy
Energy is that aspect of matter/energy that causes change, that pushes matter apart or pulls it
together. It is an enactment of the four forces (potential energy), or an embodiment of motion
relative to one’s frame of reference (kinetic energy). Energy is a hard thing to pin down—it is
immaterial—but it has a specific definition in physics: energy is that which performs work, that
is, moving an object against a force over a distance.
Kinetic energy, KE, is energy of motion, and its quantity is given by KE = ½ mv2, where m is
the mass of an object and v is its velocity. The common units for energy is joules (J), mass is
kilograms (kg) and velocity is meters per second (m/sec). The rate at which energy is used is
called power, and is measured in watts (W; 1 W = 1 J/sec). Thus a 100 W light bulb uses up
100 joules of energy every second (and people, just living, use energy at about the same rate).
Kinetic energy on the microscopic scale—the colliding motion of atoms and molecules—is
called thermal energy. The movement of thermal energy from one place to another is called
heat—that is, heat is the transfer of molecular translational kinetic energy (MTKE) from a
hotter to cooler location—it is a manifestation of entropy. A measure of the average MTKE of a
material is its temperature. The internal energy of a material is comprised of this MTKE, plus
the rotational and vibrational kinetic energy of the molecules, plus the binding energy that
holds the molecules together, plus the binding energy that hold the atoms and their nuclei
together, plus the energy of being wrapped up in their intrinsic mass (recall E = mc2). As MTKE
dissipates, vibrational and rotational KE are also sapped away (down to the lowest quantum
mechanical state of motion). At absolute zero (0 degrees Kelvin), all MTKE is gone.
©J Shepanski 2006
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Potential energy is energy of position within a force field—work has to be done on something to
put it in a potential energy state. That expended energy (i.e. the work done), does not
disappear, it is converted into potential energy within the force field (against which the work was
done). Energy does not disappear—it is always conserved—but it changes form. {Even in
Relativity, KE is converted to (i.e. stored as) a small increase in perceived mass, which will be
released back into another form if the object’s relative speed returns to zero.} For example,
picking a rock off the ground and placing it on a table, you exert work on the rock, lifting it
against the force of gravity. The work you exert is equal to the increased potential energy the
rock now possesses as it sits on the elevated table.
Electrons and protons mutually pull on one another via the electric field of the electromagnetic
force. When an electron is “kicked up” to a higher-energy atomic orbital, something has done
work on it to move it to a higher potential energy in the electric field. (This could be done by
thermal agitation, or by photon absorption.) When the electron relaxes down to its ground state,
this extra potential energy is given up, often by photon emission.
A photon is pure energy, and consists of alternating electric and magnetic fields—the two fields
are different aspects of the electromagnetic force. A changing electric field produces a magnetic
field, and a changing magnetic field produces an electric field ( Maxwell’s Laws). A photon is
the procession of these time varying fields, which mutually build one another as they propagate
forward at the speed of light. The more energy the photon carries, the more concentrated these
fields become—this does not make the electromagnetic (EM) wave travel faster, but it
decreases it wavelength. A photon’s energy, E (joules) is given by E = hc / l, where l is the
photon’s wavelength (meters), c is the speed of light in a vacuum (3*108 meters/sec) and h is
Planck’s constant (6.63*10-34 joules*sec). For example, a green photon has a wavelength of
5*10-7 meters; by solving E = hc / l, we find it’s energy is 3.98*10-19 joules.
The relationship between wavelength (l, meters), wave frequency (f, cycles per second or Hz,
hertz), and wave speed (v, meters/sec), is given by v = lf. For example, an 1000 Hz EM radio
wave has a wavelength of 300,000 meters. In contrast, sound travels at 340 meters/sec, so a
1000 Hz sound wave has a wavelength of 0.34 meters.
In general, any kind of wave—sound, water or seismic waves—carries energy, and the shorter
their wavelength the more energy they carry. Most waves need a material medium through
which to propagate—the wave is actually a temporary deformation in the propagation medium.
In contrast, photons carry their propagation “medium” with them (the E and M fields), which
allows them to travel through the vacuum of space. By far, the majority of wave phenomena we
encounter day-to-day are manifestations of the EM force. Sound waves, for example, are
compression waves within a solid/liquid/gas, but these compressions, at the microscopic scale,
are atoms bumping up against one another’s electron clouds and being repelled away.
The EM force and energy associated with it, fills our daily lives. Light from the sun is absorbed
by plants. The process of photosynthesis involves a charge separation (electric potential
energy, EPE), which ultimately is transformed into chemical energy: sugar. But chemical energy
is simply molecules configured in energy-storing shapes—another manifestation of EPE.
©J Shepanski 2006
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When our bodies burn sugar, we release chemical energy to power chemical reactions—
which are governed by the EM force and quantum mechanics. Some of the energy from
these reactions goes into heat (i.e. molecular vibrations—atoms bouncing off one another
like tiny springs—the elasticity is provided by deformation of atoms’ electron clouds). Some
energy is used to power muscles—which ultimately is traced to atoms pushing against each
other. Along another energy path, chemical energy stored in fossil fuels is burned to produce
light (visible photons) and heat. Some of the heat is used to boil water (increase molecular
KE), which drives turbines (atoms pushing on atoms), which turn generators to produce
electricity (electromagnetic induction).
At sub-atomic scales, the powerful repulsion between protons in an atom’s nucleus is
overpowered by the more powerful attraction of nucleons (protons and neutrons) via the
strong nuclear force. From an energy perspective, the strong nuclear force creates a deep
potential well which makes an intact atomic nucleus energetically favorable—as long as the
nucleus does not become too large. Larger nuclei extend beyond the attractive range of the
strong nuclear force, making these nuclei susceptible to fission via the repulsion of protons.
Although gravity and the EM forces are most familiar to us, our lives ultimately depend on
the strong and weak nuclear forces. Deep in the sun, these forces govern nuclear fusion—
the combining of two nuclei into one, plus a lot of energy—which is the primary source of
energy for our solar system.
Review Questions
1) How is the behavior of molecules similar to ball bearings connected by springs? How do
you think molecules are different?
2) What make a molecule polar?
3) When atoms combine to form molecules, what happens to the valence electron orbitals of
the atoms?
4) What are the four major states of matter? What characterizes them?
5) What is the ultimate source of intermolecular forces?
6) Why do metals conduct electricity so easily? How are insulators different?
7) What is the energy of motion called? What equation calculates it?
8) How much power does an average person use, just by living?
9) What is the transfer of thermal energy called?
©J Shepanski 2006
Review Questions (2 of 2)
10) What five things make up the internal energy of a material?
11) What happens at absolute zero?
12) What is energy of position within a force field called?
13) Does energy disappear after work is done? If so, where did it go? If not, where did it go?
14) I sure am tired after climbing a mountain. Do I have higher or lower gravitational
potential energy? Where did it come from, or where did it go?
15) What is the wavelength of a 100 Hz radio wave? Is it longer or shorter, or the same
length as a 100 Hz sound wave?
16) How does a photon work?
17) How does a sound wave work?
18) I drove my car to work today. Briefly trace the flow of energy that got me here—start
with the sun.
19) What process is the primary source of energy for the solar system?
20) Is life possible without the Pauli exclusion principle? Why or why not?
©J Shepanski 2006