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CH 301 Quiz #4 Notes.docx

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University of Texas at Austin
CH 301
Dave A.Laude

Quiz #4 Notes 11. Theory: Statistical Thermodynamics This study deals with the system of a molecule one at a time. To find internal energy:  E = 1/2kT o Energy per molecule per degree of motion freedom in a system To find internal entropy:  S = k ln W o Absolute entropy per molecul-23n a system Constant k (Boltazmann constant) = 1.38 x 10 J/K for both equations 12.Calculation: Statistical Mechanics Determination of Internal Energy Each atom has three directions to move (N atoms will have 3N ways to move)  Translation – the molecule change location o Ex: water moving to the left because all 3 atoms move left = 3 ways all molecules can move  Rotation – the molecule spins o Ex: water spinning counterclockwise  Nonlinear molecules rotate 3 ways  Linear molecules rotate 2 ways  Vibration – the molecule twists o Ex: water vibrating  Nonlinear molecules vibrate 3N – 6 ways  6 comes from 3 transitions + 3 rotations  Linear molecules vibrate 3N – 5 ways  5 comes from 3 transitions + 2 rotations The amount of energy associated with each movement depends on temperature.  From equipartition theory o The average energy per motion is E = 1/2kT  T = Kelvin  K = Boltzmann constant  So, the o Translation of a molecule are 3 x 1/2kT = 3/2kT o Rotation of a molecule are 3 x 1/2kT = 3/2kT o Rotation of a linear molecule are 2 x 1/2kT = 2/2kT  Ex: non-linear molecule (most molecules) have o 3/2kT + 3/2kT = 3kT of motional energy at room temperature  Ex 2: linear molecule (like CO or I ) has 2 2 o 3/2kT + 2/2kT = 5/2kT of motional energy at room temperature  What about vibration? At room temp, there isn’t enough energy to excite vibration so we ignore them. 13.Calculation: Statistical Mechanics Determination of Entropy As temperature K decreases, the motional energy of matter J decreases. [S decreases as well] This is how we form perfectly ordered crystals. S (absolute entropy) = k ln W  W = # of possible orientation = # of orientations molecules Quiz #4 Notes Ex: CO C = O O = C VS. C = O C = O C = O O = C C = O C = O  2 ways to orient and four molecules of CO  There are 2 = 16 possible orientations. -23 -23  S = k ln W = 1.38 x 10 ln 16 = 3.8 x 10 J/K for CO H-bonding affects orientation  Ex: HCl has W <2 n 14.Theory: First Law of Thermodynamics First law: the total energy of an isolated system is conserved.  ∆Esys= q + w  q and w aren’
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