ch19d1_reduced

# Seen disorder on the molecular level 33 b boltzmanns

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Unformatted text preview: level 33 B) Boltzmann’s Eqn. &amp; Microstates Statistical Thermodynamics Uses statistics and probability to link microscopic &amp; macroscopic worlds. Microstate Single possible arrangement of the positions and kinetic energies of the molecules - snapshot Exceptionally LARGE # microstates Can use probability and statistics to determine total # microstates for a thermodynamic state 34 W = # microstates Very Large # for a mole of particles Related to Entropy Boltzmann Eqn. S = k C ln W k = Boltzmann’s constant = 1.38 x 10!23 J/K S is a measure of # microstates associated w. a particular macroscopic state 35 )S = k C ln Wfinal ! k C ln Winitial Wf = k C ln -----Wi When Wf &gt; Wi )S &gt; 0 Entropy inc. w. # microstates Ex: Inc volume of a gas greater vol - greater # of positions available to the particles and greater # microstates ˆ Entropy inc. as vol. inc. 36 C) Molecular Motions and Energy Ideal gas particles are idealized points w. no vol. and no bonds - translational motion only Real molecules - translational motion - rotational motions spin about an axis Linear: 2 axes of spin Nonlinear: 3 axes of spin 37 - vibrational motions Atoms periodically move toward &amp; away from each other Linear: Nonlinear: 3N - 5 3N - 6 N = # atoms in molecule (N &gt; 2) # microstates inc. as complexity of molecule inc. - there are many more vibrational motions 38 D) Predicting Sign of )S 1) Phase changes Solid ----&gt; Liquid ----&gt; Gas )S &gt; 0 )S &gt; 0 2) Number of Molecules Inc. F2(g) ----&gt; 2 F(g) )S &gt; 0 3) Inc. # Atoms in a Molecule Inc. degrees of freedom )S &gt; 0 39 4) Mixing of Substances Generally, )Ssoln &gt; 0 5) Temp. Changes Inc. Temp., KE inc. - molecules move faster - broadens distribution of speeds )S &gt; 0 6) Vol. Inc. Vol. inc. - greater # positions available to atoms )S &gt; 0 40 E) Ex: The )Hf° of liquid acetone is - 247.6 kJ/mol at 25 °C. The )Hf° for the vapor is -216.6 kJ/mol at 25 °C. What is the entropy change when 1.00 mol of liquid acetone vaporizes at 25 °C? 41 F) Ex: A sample of 2.00 mol of an ideal gas expands from a vol. of 1.0 L to 10.0 L at constant temperature. What is the entropy change, )S? Is the sign of )S consistent w. your expectations? 42 IV) Third Law &amp; Standard Entropy A) 3rd Law A perfectly crystalline substance at 0 K has entropy of zero Can measure Absolute entropy, o also called standard entropy, S - entropy value for standard state of species Standard State Pure substance: 1 atm pressure Species in Soln: 1 M 43 Can calculate from heat capacities ° ST = m 0 T Cp(T) dT ------------T 1) Values for compounds do NOT correspond to formation from the elements 2) Absolute entropy of an element in its solid state … 0 3) Values on order of 10's of joules (not kJ like enthalpy) 44 B) Entropy Change for a Rxn. )Srxn = 3 n S° ! 3 m S° ° prod. react. n = coef. in bal. eqn. for each product m = coef. in bal. eqn. for each reactant 45 1) Ex: Calculate the entropy change for the formation of H2O from its elements at 25 °C. So(H2) = 130.58 J/molCK So(O2) = 205.0 J/molCK So(H2O, liq) = 69.91 J/molCK 2 H2 (g) + O2 (g) W 2 H2O (R) )Srxn = 2 So(H2O, liq) ! [2 So(H2) + So(O2)] ° = (2 mol) (69.91 J/molCK) ! [(2 mol) (130.58 J/molCK) + (1 mol)(205.0 J/molCK)] = ! 326.3 J/molCK 46 V) Gibbs Free Energy &amp; Spontaneity G = H ! TS State Fnc: )G = Gfinal ! Ginitial At constant T &amp; P )G = )H ! T )S Under standard state conditions, )Go = )Ho ! T )So How does this relate to spontaneity? 47 ! qsys ! )Hsys )Ssurr = --------- = ----------T T )Suniv = )Ssys + )Ssurr = )Ssys ! )Hsys + -----------T Rearrange: ! T )Suniv = )Hsys ! T )Ssys )G = ! T )Suniv 48 Now have an eqn. which relates spont. to the system. At constant T &amp; P )G = )H ! T )S )G &lt; 0 spont. )G &gt; 0 NONspont. )G = 0 equilibrium 49...
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## This note was uploaded on 10/03/2013 for the course CHEM 1220 taught by Professor Zellmer during the Fall '13 term at Ohio State.

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