Chem 1120 1st Edition Lecture 27 Outline of Last Lecture I. Intro to Entropy/SpontaneityII. Spontaneity and ReversibilityIII.Entropy and the Second Law of ThermodynamicsOutline of Current Lecture I. Positional EntropyII. Other Molecular Interpretations of EntropyA. The Story of 4 AtomsCurrent Lecture I. Positional entropy: These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.Is there a molecular explanation? -Assume only two molecules -With the valve open there is a 50:50 chance of each molecule being in eitherflaskProbabilities: .5*.5 = .25 2*.5*.5 = .5 .5*.5 = .25-Assume 3 moleculesP: (.5)^3 = .125 3*(.5)^3 = .375 3*(.5)^3 = .375 (.5)^3 =.125-Assume 10 molecules P: 0:10 1:9 2:8 3:7 4:6 5:5 6:4 7:3 8:2 9:1 10:0More unequal distributions as the number of molecules gets larger, very un-equal distributions become very improbable-For 1 mole of gas, the probability of all molecules being in one flask is (1/2)^N, where N = 6.022 X 10^23-Spontaneous compression is improbable and 50:50 distributions become highly probable II. Model 3: Entropy as Energy DispersalEnergy will try to disperse over a larger number of particles and energy lev-els It is more probable that energy will disperse over many particles than to be concentrated in a few Molecular Motion——> Molecules exhibit different forms of motion:Translation- molecule (atom) moves through space, smallest energy level gapRotation- molecule spins around its center of gravity, bigger energy level gapVibration- molecule changes its shape by bond stretching or bending, even bigger energy level gapElectronic- biggest energy level gapEntropy of a system is related to the number (W) of possible distributions of energy (microstates) among the energy levels of its moleculesS = k*ln(W) k = Boltzmann constant = 1.381 X 10^-23 J/KA. “The story of 4 Atoms”:1. A sample consists of 2 atoms, A and B2. The sample contains 2 energy units denoted by *3. There are 3 possible energy distributions: A**B A*B* AB**4. Atoms A and B contact C and D that have no energy5. There are now 10 possible energy distributions6. A and B retain all of the energy in only 3 distributions 7. Energy dispersal has a 70% probability8. With large numbers of atoms dispersal is certainInitially atoms A and B possessed 2 units of energy, C and D none. We can assume there were 3 en-ergy levels.The second law of thermo is obeyed since 2.30 k - 1.10 k > 0 (surroundings don't change)At higher temperatures, more energy levels become accessible which means larger W values and greater entropyTranslational energy levels are more closely spaced in larger volumes, which means larger W values and higher entropy (quantum mechanics)Liquid molecules can translate, rotate, and vibrate; the molecules of a solid can Only vibratemelting——>adds translational & rotational energy levels——>larger W——> higher SGas molecules more freely translate, rotate and vibrate, and they occupy a much larger volumeevaporation ——> more closely spaced translational energy levels and more accessible rotational and vibrational energy levels ——> larger W——>
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