Thermodynamics

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Thermodynamics

• Beyond Simply Energy

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2 H2 O2 ? 2 H2O

• Given a chemical reaction
• Does it happen?
• How fast does it happen?
• Is it an equilibrium reaction?
• How does it compare with a competing reaction?
  (If I mix H2, O2 and N2, what do I get?)

3
Joes Rule of the Possible

• If it can happen, it will happen.
• But, that doesnt tell you how much, how fast,
  how often, how easily
• Thermodynamics picks up where Joes Rule leaves
  off.

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Thermodynamics

• Thermodynamics deals with energy, as the name
  implies, but not just energy. It includes the
  study of all the different possible states of a
  system and how the system moves between different
  states.

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States

• I mix 1 molecule of O2 and 1 molecule of H2 in an
  evacuated 1 L flask. How many different states
  of this system are there?
• A nearly infinite number of them!

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States of a system
H2
O2
O2
H2
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States of a system
O2
O2
H2
H2
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What the can we do?

• Thermodynamics deals with statistical analysis of
  ensembles of states.
• In our case, we are usually looking at a single
  representative state of the system that is the
  most probable state.

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Putting the thermo in thermodynamics

• As the name implies, thermo-dynamics is about
  energy (thermoheat).
• What does this mean for a reaction?

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Reaction Energies

• The energy change associated with a chemical
  reaction is called the enthalpy of reaction and
  abbreviated ?H.
• ? H Hfinal - Hinitial

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Enthalpy of Reactions

• There are actually a number of different types of
  enthalpies because enthalpy depends on
  conditions. THEY ARE ALL JUST SPECIFIC TYPES OF
  A GENERAL CONCEPT CALLED ENTHALPY.
• ? H Hfinal - Hinitial

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Types of ? H

• ? H generic version
• ? Hrxn generic version
• ? Hº - enthalpy change under Standard Temperature
  and Pressure (298 K, 1 atm)
• ? Hf enthalpy of formation, refers to a
  specific reaction type

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General Reaction Scheme hot pack
14
Endothermic Reaction cold pack
Ea
Energy
Products
Reactants
?H
Reaction Coordinate
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Where does the Energy go?

• In the case of a chemical reaction, you need to
  keep the different types of energy separate in
  your mind
• Bond energy energy INSIDE the molecules
• Thermal energy (heat) kinetic energy of the
  molecules
• Energy of the bath kinetic energy of solvent
  or other molecules in the system

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Energy changes

• ? H represents the change in INTERNAL MOLECULAR
  ENERGY.
• ? H Hfinal - Hinitial

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Exothermic Reaction hot pack
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Exothermic energy changes

• ? H Hfinal Hinitial lt 0
• HinitialgtHfinal
• This energy is internal to the molecule.
• The excess gets absorbed by the rest of the
  system as heat causing the molecules to move
  faster (more kinetic energy) and the temperature
  to increase.

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Endothermic Reaction cold pack
Ea
Energy
Products
Reactants
?H
Reaction Coordinate
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Endothermic energy changes

• ? H Hfinal Hinitial gt 0
• HinitialltHfinal
• This energy is internal to the molecule and must
  come from somewhere.
• The additional energy required by the system gets
  absorbed from the rest of the system as heat
  causing the molecules to move slower (less
  kinetic energy) and the temperature to decrease.

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The hard part is getting over the hump.
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Ea Activation Energy

• The tale of a reaction is not limited strictly to
  the identity and energetics of the products and
  reactants, there is a path (reaction coordinate)
  that must get followed.
• The hump represents a hurdle that must be
  overcome to go from reactants to products.

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How do you get over the hump?

• If you are at the top, it is easy to fall down
  into the valley (on either side), but how do you
  get to the top?

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How do you get over the hump?

• The molecules acquire or lose energy the same
  way by colliding with each other!
• The energy comes from the bath, the rest of the
  system.

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Types of ? H

• ? H generic version
• ? Hrxn generic version
• ? Hº - enthalpy change under Standard Temperature
  and Pressure (298 K, 1 atm)
• ? Hf enthalpy of formation, refers to a
  specific reaction type

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Enthalpy is a State Function

• Whats a state function?
• A state function is a value that is a function
  only of the initial and final states of the
  system, not the path you take to get there!

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Climbing Mt. Everest

• Suppose you start at Himalayan Base Camp 1,
  climb to the summit of Everest over the course of
  3 weeks, then return to Himalayan Base Camp 1.

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Climbing Mt. Everest

• Back at base camp, I figure out my altitude
  change. What is it?
• ZERO Im back where I started

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Climbing Mt. Everest

• I did a lot of work along the way, but all that
  matters is Im back where Im started. The net
  change in altitude is NADA, ZERO, ZILCH!

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Enthalpy as a State Function

• Enthalpy is like that. It doesnt care how you
  got where you are going, it simply looks at the
  difference from where you started.

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Path doesnt matter!
Actual path
Products
? H
Reactants
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Energy Considerations

• Energy is an important consideration in any
  physical or chemical process.
• You need to climb the hill!

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Have you ever seen a ball roll uphill?

• The universe is a lazy place!
• Everything seeks its lowest energy state.
• Given the chance, systems always seek the lowest
  energy possible.

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Am I lying?

• How did the ball get to the top of the hill in
  the first place?

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Little nit-picking definitions

• There are always two (at least) regions to
  consider
• The system the object under study
• The surroundings the rest of the universe

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You can go upbut someone goes down.

• You can add energy to the system, but you must
  take it from the surroundings.
• The issue with my lazy mans definition of the
  universe is a thing called spontaneity.

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Spontaneity is

• Spontaneity means that the observed change
  happens without a push. It naturally occurs
  without being forced.
• The ball spontaneously rolls down the hill. We
  can force it back up the hill, but we have to put
  in energy.

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Still seems like Im lying

• If what I say is true, then ALL observed changes
  in the world around us that happen without being
  forced would have to be downhill in energy.
• Is that true?

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If energy were the whole story

• Why would water evaporate?
• It is an endothermic process with an activation
  barrier, so it requires energy to be put into the
  system. Yet, water spontaneously evaporates even
  at near freezing temperatures. (And actually
  sublimes when frozen!)

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• BUT
• ENERGY CHANGES ARENT THE WHOLE STORY!

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The rest of the story

• The energy of the molecules and their motions are
  one part of the story the thermo part.
• There is also the distribution of atoms within
  the allowed states. It not only matters what the
  average energy of the system is, but which
  molecules have what energies and what positions!

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The rest of the story

• is entropy (S) - is a measure of the
  distribution of states.
• Entropy is sometimes defined as disorder or
  randomness. It is really more complicated than
  that and represents the total number of different
  micro-states available to the system.

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States of a system
O2
O2
O2
O2
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States of a system
O2
O2
O2
O2
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States of a system
O2
O2
O2
O2
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Imagine 3 molecules!
O2
O2
O2
O2
O2
O2
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Imagine 3 molecules!
O2
O2
O2
O2
O2
O2
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Imagine a MOLE of MOLECULES!!!
O2
O2
O2
BIG EFFING MESS!!!!
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
THANK GOD FOR STATISTICS
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
O2
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Entropy is

• a state function.
• Entropy gets handled much the same as enthalpy.
• There are tables of entropy values, and it is
  usually the change (? S) that matters more than
  the absolute amount.

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Some examples

• What has more entropy 1 mole of water or 1 mole
  of steam? Why?
• 1 mole of steam the molecules in steam are not
  associated with each other and are, therefore,
  free to explore more positions and energy states!

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Some examples

• What has more entropy 1 mole of water or ½ mole
  of water mixed with ½ mole of methanol? Why?
• The mixture there are the same number of
  molecules in both systems, but the mixture allows
  for more possible distributions of the molecules!

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Clicker question

• In the following process what is the sign of ?S
• 2 H2 (g) O2 (g) ?2 H2O (g)
• Positive
• Negative
• Zero
• I dont know, Im just glad to be here.

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Clicker

• If delta S is negative, and that is the only
  consideration, should the reaction
• Happen
• Not Happen
• I dont know
• You are a beautiful animal
• Your mother

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Suppose I want an exact number?

• Appendix II

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The Laws of Thermodynamics

• 1st Law Conservation of Energy
• 2nd Law The Entropy of the universe is always
  increasing for spontaneous changes.
• 3rd Law A perfect crystal at 0 K has no entropy.

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3rd Law

• The third law is interesting (and important).
  Unlike enthalpy, we have an absolute zero for
  entropy. Thats why Appendix II shows S values
  not ?S values.

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Suppose I want an exact number?

• 2 H2 (g) O2 (g) ?2 H2O (g)
• ?S0 SS0products SS0reactants
• ?S0 2S0(H2O(g))
• 2S0(H2(g)) S0(O2(g))
• ?S0 2mol188.8 J/molK
• 2mol130.7 J/molK 1 mol205.2 J/molK
• ?S0 - 89 J/K

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From a thermodynamic standpoint

• Delta S - 89 J/K is
• Good
• Bad
• Indifferent
• You are still a beautiful animal.

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2 H2(g) O2 (g) ?2 H2O (g)

• ?S0rxn -89.0 J/K
• Again, this assumes stoichiometric quantities of
  everything.
• Does this number make sense?
• What does a NEGATIVE change in entropy mean?

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2 H2(g) O2 (g) ?2 H2O (g)

• ?S0rxn -89.0 J/K
• What does a NEGATIVE change in entropy mean?
• ?S0rxn S (products) S (reactants)lt0
• S(products) lt S(reactants)
• of product states lt of reactant states
• Does this make sense?
• ABSOLUTELY there are fewer molecules so there
  are fewer states!

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Does this number make sense?

• 2 H2 (g) O2 (g) ?2 H2O (g)
• ?S0 - 89 J/K
• ?S is negative meaning
• The products have LESS entropy than the
  reactants.
• 3 moles of gas vs. 2 moles of gas
• 2 different gases vs. 1 gas

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2 particles vs. 3 particles!
H2
H2O
H2O
O2
H2
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• 2 H2 (g) O2 (g) ?2 H2O (g)
• So, why does it happen if ?S is negative?
• ?H is also negative (?H0 -241.8 kJ/mol) the
  lazy man wins this one!

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Thermodynamics is

• All about balancing H and S to determine
  spontaneity.

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Spontaneous change

• A spontaneous change is one that happens
  naturally, without being forced by an outside
  agent.
• Spontaneous change
• Water evaporating at room temperature.
• A rock rolling down hill.
• Non-spontaneous change
• Freezing water at room temperature.
• Rolling a rock uphill.

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Spontaneous change

• A spontaneous change is thermodynamically
  favorable.

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Spontaneous change

• Thermodynamics is all about balancing enthalpy
  and entropy.
• Some processes are enthalpically and entropically
  favorable.
• Some process are enthalpically and entropically
  unfavorable.
• What about when one property is favorable and the
  other is unfavorable?

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Balancing entropy and enthalpy

• Gibbs Free Energy
• ? G ? H -T ? S
• If ? G gt0 then reaction is NOT spontaneous.
• If ? G lt0 then reaction IS spontaneous
• If ? G 0 thenthe reaction is at equilibrium
  more later!

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Balancing entropy and enthalpy

• Gibbs Free Energy
• ? G ? H -T ? S
• 4 possibilities
• ? H is -, ? S is -
• ? H is -, ? S is
• ? H is , ? S is
• ? H is , ? S is -

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Balancing entropy and enthalpy

• ? G ? H -T ? S
• ? H is -, ? S is -
• ? H is -, ? S is this is the best!!!
• ? H is , ? S is
• ? H is , ? S is - this is the worst!!!

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Balancing entropy and enthalpy

• ? G ? H -T ? S
• ? H is -, ? S is this is the best!!!
• ?G will ALWAYS be negative
• ? (-) ()()

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Balancing entropy and enthalpy

• ? G ? H -T ? S
• ? H is , ? S is - this is the worst!!!
• ?G will ALWAYS be positive
• ? () ()(-) ()()

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Balancing entropy and enthalpy

• ? G ? H -T ? S
• ? H is , ? S is
• Its gonna depend on the temperature.
• ? G ( ?H) (T)( ?S) ( ?H)-(T ?S)
• Is T ?S bigger than or smaller than ?H?

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Balancing entropy and enthalpy

• ? G ? H -T ? S
• ? H is -, ? S is -
• Its gonna depend on the temperature.
• ? G (- ?H) (T)(- ?S) (- ?H)(T ?S)
• Is T ?S bigger than or smaller than ?H?

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2 H2 (g) O2 (g) ?2 H2O (g)

• ?S0 - 89 J/K
• ?H0 - 241.8 kJ
• This reaction is spontaneous at some
  temperatures, not all!

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2 H2 (g) O2 (g) ?2 H2O (g)

• ?S0 - 89 J/K
• ?H0 - 241.8 kJ
• G ? H -T ? S
• G (-241.8 kJ) T(-0.089 kJ/K)
• 0 (-241.8 kJ) T(0.089 kJ/K)
• 241.8 kJ T(0.089 kJ/K)
• T 2717 K

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2 H2 (g) O2 (g) ?2 H2O (g)

• G ? H -T ? S
• G (-241.8 kJ) T(-0.089 kJ/K)
• T 2717 K
• When Tlt2717, the reaction is spontaneous.
• When Tgt2717, the T ? S term is now bigger than ?
  H and the reaction is no longer spontaneous.
• This reaction is better at lower temperatures!

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Clicker Question

• Who is the most powerful superhero of all?
• Superman
• Batman
• Santa Claus
• Joe
• Anyone but Joe

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What Holiday are you celebrating?

1. Hanukkah
2. Christmas
3. Kwanzaa
4. Christmukkah
5. None of the above

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Question

• Is the following reaction spontaneous at 298 K?
• 8 H2(g) S8(s) ? 8 H2S (g)
• If I care about spontaneous, I care about ?G!

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? G0 ? H0 - 298 ? S0

• But if you look in Appendix II, youll find the
  magic 3rd column
• ? Gf0

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8 H2(g) S8(s) ? 8 H2S (g)

• From Appendix II
• H2(g) S8(s) H2S (g)
• ? Gf0 0 kJ/mol 49.7 kJ/mol -33.4
  kJ/mol
• ? Hf0 0 kJ/mol 102.3 kJ/mol -20.6
  kJ/mol
• S0 130.7 J/mol K 430.9 J/mol K 205.8 J/mol K

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8 H2(g) S8(s) ? 8 H2S (g)

• ?Grxn0 S? Gf0(products) - S? Gf0 (reactants)
• 8 mol -33.4 kJ/mol 8 mol 0 kJ/mol1 mol
  49.7 kJ/mol
• -267.2 kJ 49.7 kJ
• ?Grxn0 -316.9 kJ
• ?Grxn0 lt0, reaction is spontaneous.

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? G0 ? H0 - 298 ? S0

• 8 H2(g) S8(s) ? 8 H2S (g)
• ?Hrxn0 S ? Hf0(products) - S ? Hf0
  (reactants)
• ?Hrxn0 8-20.6kJ/mol 80102.3kJ/mol
• ?Hrxn0 -267.1 kJ
• ?Srxn0 S S0(products) - S S0 (reactants)
• ?Srxn0 8205.8 J/molK-8130.7 J/molK430.9
  J/molK
• ?Srxn0 169.9 J/K

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? G0 ? H0 - 298 ? S0

• ?Hrxn0 -267.1 kJ
• ?Srxn0 169.9 J/K
• ?Srxn0 0.1699 kJ/K
• G0 -267.1 kJ - 298 (0.1699 kJ/K)
• G0 -317.73 kJ
• Compare to ? G0 calc using ? G0f -316.9 kJ

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Why the difference?

• Remember ?H0f and ?G0f are relative. S0 is
  absolute.
• By definition ?G0f is 0 for an element as is ?H0f
  but not S0

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Question

• Is the following reaction spontaneous at 500 C?
• 8 H2(g) S8(s) ? 8 H2S (g)
• If I care about spontaneous, I care about ?G!
• But now theres no naught!

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8 H2(g) S8(s) ? 8 H2S (g)

• Can we take the short way?
• ?Grxn0 S? Gf0(products) - S? Gf0 (reactants)
• Wont work no naught!
• Only ? G0 ? H0 - T ? S0 works if T is not 298.

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? G0 ? H0 - 298 ? S0

• ?Hrxn0 -267.1 kJ
• ?Srxn0 169.9 J/K
• ?Srxn0 0.1699 kJ/K
• Same as beforeI only have one Appendix II!!!
• Can this be right?
• Yes and no.

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ASSUMING

• ? H0 and ? S0 are temperature independent.
• Is this a good assumption? Not perfect. We
  already said that heating a material usually
  increases its entropy. But it is a better
  assumption for H and the S has a T term soits
  the best we can do!

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? G0 ? H0 - T ? S0

• ?Hrxn0 -267.1 kJ
• ?Srxn0 169.9 J/K
• ?Srxn0 0.1699 kJ/K
• Same as beforeI only have one Appendix II!!!
• G0 -267.1 kJ (500C273.15K) (0.1699 kJ/K)
• G0 -398 kJ
• Even more spontaneous at 500 K.