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Chm 1311 Lecture for 29 June 1999

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Energies

There are all kinds of energies, but they are usefully divided into Kinetic and Potential. Kinetic energy is energy of motion, energy which is visible to us as mass, m, moving with velocity, v; it has a magnitude ½mv². Potential energy is energy we don't see but only infer by the ability of systems which possess it to release it in forms we can see.
Hiroshima, 1945
Hiroshima, 1945
MS Encarta '97
An example of invisible potential energy which was only understood in this century is that of rest mass, mo. Mass has an inherent energy of E=moc², a discovery due to Einstein which "explains" the energy of radioactivity. The products of radioactive processes (fission and fusion) weigh less than their reactants by an amount E/c² where E is the energy released in the process and c is the speed of light (3×108 m s-1). The great salvation of this discovery is that it preserves the fundamental law of physics (and thus of chemistry), that of the Conservation of Energy now as the Conservation of Matter-Energy. We can not only take comfort in the fact that energy (or matter-energy) isn't being lost to the universe but also that we can measure energies invisible in one form by converting them into another.

Chemical
Potential

A form which chemists deal with daily is the energy inherent in chemical compounds, for example, that which makes foodstuffs valuable for our bodies or gasoline valuable for our internal combustion engines. That energy, which is realized in those instances by oxidation of the compounds, is called chemical potential, and it varies with what one makes of the materials. For instance, burning iso-octane (the "octane rating" standard) in your car, combines it with oxygen to produce CO2 and H2O (and, if your engine isn't well tuned, perhaps various NOX molecules as well), but it would certainly be possible to "burn" iso-octane in F2 in the laboratory, producing CF4 and HF instead. That would release a different amount of chemical potential since we're creating different products.
Since a compound's energy content is one of the properties which make it significant for us, measuring that and relating that content to its chemistry is and important ability. Unfortunately, there are some very firm Rules of Nature that tell us that it is not always possible to convert energies quantitatively into whatever form we like. For example, different cars will acquire different kinetic energies from burning the same amount of the same fuel. Is this a violation of the Conservation of Energy rule? No, because they will release different amounts of heat in the process, and the sum of the work done in moving the car plus the "waste" heat evolved will always be the chemical energy change from the combustion of the fuel!
Fortunately, it is always possible to "waste" as much of the energy change in a process as one likes as heat. That is, while you cannot make a perfectly efficient engine, you can make a perfectly inefficient one! We chemists take advantage of that by burning fuels in sealed cylinders (no engine strokes to propel an automobile possible there!) and measuring the heat evolved. The cylinders are called Parr Bombs (no relation), and the procedures for operating them are very carefully designed to extract the most accurate possible heat measurement.

Measurement
of Heat

We can know that heat has been transferred from one body to another because the first loses temperature while the second gains it. But not the same temperature change (necessarily). The heat content of a material is extensive; larger bodies hold more heat than smaller ones. (Which is why tiny shrews have to eat more than their body weight each day while elephants would explode if they tried that.) In addition, different materials hide heat in different ways; that tendency is measured by the heat capacity or, better still, by the heat capacity per gram (specific heat) or per mole (molar heat capacity). Those latter two are handy because they are no longer extensive! By taking the ratio of the heat content to the mass (or moles), we've rendered those heat capacities as intensive properties of the substance.
Bomb
Calorimetry
Parr Bomb Animation So the Parr Bomb detonates a combustible sample in some 30 atm (!) of pure oxygen in a sealed container which bleeds its resultant heat into a water bath. Since the specific heat of water is well known (and worth memorizing at exactly 1 cal/gm°C, at 15°C, being, in fact, the definition of the calorie; while in SI, it would be 4.186 J/gm K), the temperature jump of a known weight of water tells you how much heat the combustion evolved. Given the sample size, you then can know the Heat of Combustion of the compound (per mole, say).

"Hiding heat" sounds mysterious, but it isn't. The specific heat of ice is about 2 J/gm K since the only motion consuming energy is the vibration of the water molecules in their crystal lattice. When the temperature rises sufficiently, ice melts, and the water now has a specific heat of about 4 J/gm K because in addition to quivering in place due to the attractive - repulsive forces between pairs of molecules, each can now migrate in the fluid and spin like a top; all of those motions consume ("hide") energy. However, when the temperature becomes so high that the water boils, the vapor has a lower specific heat, down near 2 J/gm K again, because while they can still migrate (fly about) and spin, the molecules can no longer quiver next to one another since, as a gas, the molecules are quite far apart!

In addition, molecules with more "degrees of freedom" (big suckers that can vibrate easily internally) will have higher molar heat capacities than smaller molecules. Fortunately, heat capacity is trivial to measure once you have a well-characterized standard (water) against which to compare everything.

Kinetic
Theory
of Gases

All of this follows from a mental (and mathematical) model of molecules as entities which have individual kinetic energies...no big revelation there. What is fascinating is that the model ends up predicting that the temperature of a sample is directly related to the average kinetic energy of its components. So that says that any two bodies at the same temperature have molecules with the same average kinetic energy regardless of what the two materials are! Cool. Many of these revelations we owe to Ludwig Boltzmann, a Viennese physicist who committed suicide in 1906; his discoveries had not then been confirmed and no one believed his Kinetic Theory. We understand now, Lugwig, and you're a hero posthumously! Thanks.
We'll get more heavily into Kinetic Theory when we chat about gases in Chapter 10.

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Last modified 29 June 1999. Chris Parr