ch19d1_reduced

Seen disorder on the molecular level 33 b boltzmanns

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: level 33 B) Boltzmann’s Eqn. & Microstates Statistical Thermodynamics Uses statistics and probability to link microscopic & 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 > Wi )S > 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 & away from each other Linear: Nonlinear: 3N - 5 3N - 6 N = # atoms in molecule (N > 2) # microstates inc. as complexity of molecule inc. - there are many more vibrational motions 38 D) Predicting Sign of )S 1) Phase changes Solid ----> Liquid ----> Gas )S > 0 )S > 0 2) Number of Molecules Inc. F2(g) ----> 2 F(g) )S > 0 3) Inc. # Atoms in a Molecule Inc. degrees of freedom )S > 0 39 4) Mixing of Substances Generally, )Ssoln > 0 5) Temp. Changes Inc. Temp., KE inc. - molecules move faster - broadens distribution of speeds )S > 0 6) Vol. Inc. Vol. inc. - greater # positions available to atoms )S > 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 & 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 & Spontaneity G = H ! TS State Fnc: )G = Gfinal ! Ginitial At constant T & 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 & P )G = )H ! T )S )G < 0 spont. )G > 0 NONspont. )G = 0 equilibrium 49...
View Full Document

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.

Ask a homework question - tutors are online