Chem 1120 1st Edition Lecture 27 Outline of Last Lecture I Intro to Entropy Spontaneity II Spontaneity and Reversibility III Entropy and the Second Law of Thermodynamics Outline of Current Lecture I Positional Entropy II Other Molecular Interpretations of Entropy A The Story of 4 Atoms Current 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 either flask Probabilities 25 5 5 25 2 5 5 5 5 5 Assume 3 molecules P 5 3 125 125 3 5 3 375 3 5 3 375 5 3 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 0 More unequal distributions as the number of molecules gets larger very unequal 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 Dispersal Energy will try to disperse over a larger number of particles and energy levels 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 gap Rotation molecule spins around its center of gravity bigger energy level gap Vibration molecule changes its shape by bond stretching or bending even bigger energy level gap Electronic biggest energy level gap Entropy of a system is related to the number W of possible distributions of energy microstates among the energy levels of its molecules S k ln W k Boltzmann constant 1 381 X 10 23 J K A The story of 4 Atoms 1 A sample consists of 2 atoms A and B 2 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 energy 5 There are now 10 possible energy distributions 6 A and B retain all of the energy in only 3 distributions 7 Energy dispersal has a 70 probability 8 With large numbers of atoms dispersal is certain Initially atoms A and B possessed 2 units of energy C and D none We can assume there were 3 energy 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 entropy Translational 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 vibrate melting adds translational rotational energy levels larger W higher S Gas molecules more freely translate rotate and vibrate and they occupy a much larger volume evaporation more closely spaced translational energy levels and more accessible rotational and vibrational energy levels larger W higher S
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