Zumdahl

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Zumdahls Chapter 16

• Spontaneity, Entropy, Free Energy, and
• Why All Things Happen
• The Universe Becomes Less Predictable

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Spontaneous Processes and Entropy

• One of the main objectives in studying
  thermodynamics, as far as chemists are concerned,
  is to be able to predict whether or not a
  reaction will occur when reactants are brought
  together under a special set of conditions (for
  example, at a certain temperature, pressure, and
  concentration).

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Entropy is Probability

• S k ln W in modern symbolism.
• W is an actual count of how many different ways
  the Universe could be arranged without being
  detectably different macroscopically.
• And it is usually enormous!
• For example, how many different poker hands might
  be in some players possession?
• W ? (52)(51)(50)(49)(48) / 5! or 2,598,960.
• For 4 players, thats 1.48?1024 different games.
• Over twice Avogadros Number!

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Poker Microstates

• One microstate in poker might be a flush all
  cards of the same suit.
• Wflush 4(13)(12)(11)(10)(9) / 5! 5148 as the
  number of ways to get a flush on the deal.
• But Wflush / Wtotal gives 5051 odds against.
• So flushes-on-the-deal are fairly ignorable.

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Chemical Microstates

• Positional
• In a solid, molecules are frozen in position.
• But a liquid can swap molecular positions without
  macroscopic consequence Sliq gt Ssolid
• A gas is far more chaotic Sgas gtgt Sliquid!

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2nd Law of Thermodynamics

• In any spontaneous process, the entropy of the
  Universe increases.
• We must include consideration of a systems
  environment to apply this law.
• For example, condensing a gas implies a large
  decrease in the systems entropy! ?Ssys ltlt 0
• Fortunately, the (latent) heat of vaporization
  gets released to force the surroundings to occupy
  higher energy levels, so ?Ssurr gtgt 0 and ?Suniv gt
  0!

?Suniv ?Ssys ?Ssurr ? 0
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Norse Mythology

• Valhalla is the abode of the Norse gods.
• But, contrary to many other mythologies, Norse
  gods are not immortal.
• Valhalla is held up by a giant tree, the roots of
  which are being gnawed by a serpent.
• The serpent will succeed, and when it does,
  Valhalla and the Universe will fall.
• The serpents name is

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Universal Chaos, Suniv

• The Norsemen were right!
• There is Chaos growing in the Universe all the
  time at the expense of Order. It is now a
  fundamental principle of Science.
• Its called entropy, S, and is a state function
  that must always increase for the Universe as a
  whole, but some Systems S may decrease.

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Entropy (S) is a measure of the randomness or
disorder of a system.
DS Sf - Si
If the change from initial to final results in an
increase in randomness
Sf gt Si
DS gt 0
DS favors a spontaneous reaction for a chemical
reaction -DS favors a non-spontaneous reaction
for a chemical reaction or does not happen
18.2
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Spontaneous Physical and Chemical Processes

• A waterfall runs downhill
• A lump of sugar dissolves in a cup of coffee
• At 1 atm, water freezes below 0 0C and ice melts
  above 0 0C
• Heat flows from a hotter object to a colder
  object
• A gas expands in an evacuated bulb
• Iron exposed to oxygen and water forms rust

18.2
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spontaneous
nonspontaneous
18.2
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Enthalpy is a factor in whether a reaction is
spontaneous but is not the only factor.
Spontaneous reactions
18.2
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An exothermic reaction (-DH) favors a spontaneous
reaction since products are at a lower potential
energy But does not Guarantee it.
Reactants
-DH
Potential Energy
Products
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Guidelines for Determining if DS is or -.
1. For any substance, the solid state is more
ordered than the liquid state and the liquid
state is more ordered than gas state
Ssolid lt Sliquid ltlt Sgas
DS gt 0
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Guidelines for Determining if DS is or -.

1. Entropy often increases when one material
   dissolves in another.
2. Entropy increases as Temperature increases.

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Guidelines for Determining if DS is or -.
4. When gases are produced (or consumed)

• If a reaction produces more gas molecules than
  it consumes, DS0 gt 0.
• If the total number of gas molecules diminishes,
  DS0 lt 0.
• If there is no net change in the total number of
  gas molecules, then DS0 may be positive or
  negative BUT DS0 will be a small number.

The total number of gas molecules goes down, DS
is negative.
18.3
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Guidelines for Determining if DS is or -.
5. Entropy increases as number of moles of gases
increases during chemical reaction.
N2 (g) 3 H2 (g) -gt 2 NH3 (g)
- DS
6. Entropy increases as the complexity of the
molecule increases.
C4H10 or CH4
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How does the entropy of a system change for each
of the following processes?
(a) Condensing water vapor
Randomness decreases
Entropy decreases (DS lt 0)
(b) Forming sucrose crystals from a
supersaturated solution
Randomness decreases
Entropy decreases (DS lt 0)
(c) Heating hydrogen gas from 600C to 800C
Randomness increases
Entropy increases (DS gt 0)
(d) Subliming dry ice
Randomness increases
Entropy increases (DS gt 0)
18.2
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Standard Entropy Values S
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Thermodynamics
State functions are properties that are
determined by the state of the system, regardless
of how that condition was achieved.
energy, enthalpy, pressure, volume, temperature
, entropy
6.7
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Entropy Changes in the System (DSsys)
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3 Factors Involved in Determining Whether a
Reaction is Spontaneous or Not

• DH a negative value (exothermic reactions)
  favors a spontaneous reaction
• DS a positive value (disorder increases) favors
  a spontaneous reaction
• Temperature If the above factors conflict
  temperature determines if reaction is spontaneous
  or not

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Why do Chemical Reactions Occur? Free Energy

• Free Energy

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Gibbs Free Energy
For a constant-temperature process
Gibbs free energy (G)
DG DHsys -TDSsys
DG lt 0 The reaction is spontaneous in the
forward direction.
DG gt 0 The reaction is nonspontaneous as
written. The reaction is
spontaneous in the reverse direction.
DG 0 The reaction is at equilibrium.
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DS
DGDH-TDS
DH DS
-DH DS
Spontaneous at all Temperatures
Spontaneous at High Temperatures
DH
DH -DS
-DH -DS
Spontaneous at Low Temperatures
NonSpontaneous at all Temperatures
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Why do Chemical Reactions Occur? Free Energy
?H ?S ?G
(-) favorable () favorable (-) spontaneous always
() unfavorable (-) unfavorable () nonspontaneous always
(-) favorable (-) unfavorable (-) spontaneous _at_ Low T () nonspontaneous _at_ High T
() unfavorable () favorable () nonspontaneous _at_ Low T (-) spontaneous _at_ High T
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DG CHANGE IN GIBBS FREE ENERGY
DG DHsys -TDSsys

1. Determine if reaction is spontaneous or not.
2. wmax free energy available to do useful work. DG
   wmaximum

DHsys represents energy available for useful work
-TDSsys represents energy that cant Be
harnessed to do useful work
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Ways to Obtain DGreaction

• From DGfo Values
• From Gibbs Free Energy Equation

DG DHsys -TDSsys
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18.4
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What is the standard free-energy change for the
following reaction at 25 0C?
DG0 -6405 kJ
lt 0
spontaneous
18.4
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Temperature and Spontaneity of Chemical Reactions
DH0 177.8 kJ Does not favor spontaneous
reaction
DS0 160.5 J/K Favors spontaneous reaction
DG0 DH0 TDS0
0 DH0 TDS0
-DG spontaneous DG0equilibrium DGnonspontaneo
us
DH0 TDS0
TDH0/ DS0
T 177.8 kJ/ 0.1605 kJ/K 1108K
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Gibbs Free Energy and Phase Transitions
Ice melting Liquid vaporizing Solid subliming
Phase changes happen at equilibrium
DG0 0
DG0 DH0 TDS0
TDH0/ DS0
T 40.6 kJ/mole 373 K 100 C
0.1093 kJ/mole K
18.4
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Gibbs Free Energy and Chemical Equilibrium
-DG spontaneous DG0equilibrium DGnonspontaneo
us
QltK forward rxn spontaneous QK
equilibrium QgtKforward rxn nonspontaneous
DG DG0 RT lnQ(K)
R is the gas constant (8.314 J/Kmol)
T is the absolute temperature (K)
(K)Q is the reaction quotient
(products/reactants)
DGo is change in Gibbs Free Energy under
standard state conditions
DG is change in Gibbs Free Energy under
experimental conditions
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Chemical equilibrium

• Chemical Equilibrium predicts how reaction will
  proceed and how far can it go.
• Chemical equilibrium does not indicate rates of
  reactions, just extent of reaction at equilibrium
  and how far the reaction is from equilibrium
• Dynamic nature of chemical reaction
• aA bB lt------gt cC dD
• A, B decrease with time, C, D increase with time
  until no change.
• Equilibrium rxn proceeds to a point where
  reactant to product balanced the reverse rxn,
  product to reactant.

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Equilibrium Equations and Equilibrium Constants

• Consider the following general equilibrium
  reaction
• aA bB ? mM nN
• Where A, B, are the reactants
• M, N, . are the products
• a, b, .m, n, . are coefficients in the balanced
  equation.
• At equilibrium, the composition of the reaction
  mixture obeys an equilibrium equation.

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Equilibrium Equations and Equilibrium Constants

• The value of K varies with temperature.

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The Law of Mass Action

• K equilibrium constant kforward/kreverse for
  single-step reactions
• K depends on temperature ONLY
• Dont use solids or pure liquids (i.e. water) for
  the Law of Mass Action only gases or aqueous
  solutions
• Gases have partial pressure equilibrium constants

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What about non-equilibrium reactions?

• Use the reaction quotient equation!
• Can use Q to figure out which direction the
  reaction will go
• Q K reaction is at equilibrium
• Q gt K reverse reaction rate is greater
  than forward reaction rate (leftward shift)
• Q lt K forward reaction rate is greater
  than reverse reaction rate (rightward shift)

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4 rules to determine what value to use for the
concentrations in Q

• Rule 1 Solvents (e.g. water) l is equal to
  the mole fraction of the solvent. Thus, H2O
  always equals 1. or (l)1 so ignore
• Rule 2 Pure solids in equilibrium with a
  solution (e.g. CaCO3(s), Fe(OH)3(s)) s always
  equals 1.
• Rule 3Gases in equilibrium with a solution (e.g.
  CO2(g), O2(g)) i equals the partial pressure
  of the gas (atm)
• Rule 4 Compounds dissolved in water i is
  always reported in units of moles/liter (molar).

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Homework 58

• Using dat from Appendix 4, calculate ?G for the
  reaction
• 2H2S (g) SO2 (g) ? 3S (s) 2 H2O (g)
• For the following conditions at 25C
• PH2S 1.0 x 10-4 atm
• PSO2 1.0 x 10-2 atm
• PH2O 3.0 x 10-2 atm

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Answer

• 58. ?G 3(0) 2(-229) - 2(-34) 1(-300.)
  -90. kJ
•  
• ?G ?G RT ln -90. kJ
• ?G -90. kJ 39.7 kJ -50. kJ

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66. Consider the following reaction at 298K 2
SO2(g) O2(g) ? 2 SO3(g) An equilibrium
mixture contains O2(g) and SO3 (g) at partial
pressures of .50 atm and 2.0 atm respectively.
Using data from Appendix 4 determine the
equilibrium partial pressure of SO2 in the
mixture. Will this reaction be most favored at a
high or low temp assuming standard conditions?

• ?G final -initial
• ?G 2(-371 kJ) - 2(-300. kJ) -142 kJ
• ?G -RT ln K,
• ln K 57.311
•  
• K e57.311 7.76 1024
• K 7.76 1024 1.0 10-12 atm
• From the negative value of ?G, this reaction is
  spontaneous at standard conditions.
• There are more molecules of reactant gases than
  product gases, so ?S will be negative
  (unfavorable).
• Therefore, this reaction must be exothermic (?H
  lt 0). When ?H and ?S are both negative, the
  reaction will be spontaneous at relatively low
  temperatures where the favorable ?H term
  dominates.