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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...
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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.
 Fall '13
 Zellmer
 Chemistry, Equilibrium, pH, Kinetics

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