Introduction to Entropy

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Introduction to Entropy

• by Mike Roller

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Entropy (S)
a measure of randomness or disorder
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Entropy Times Arrow
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(No Transcript)
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Second Law of Thermodynamics
occurs without outside intervention ?

• In any spontaneous process, the entropy of the
  universe increases.
• ?Suniverse gt 0
• Another version of the 2nd Law
• Energy spontaneously spreads out if it has no
  outside resistance
• Entropy measures the spontaneous dispersal of
  energy as a function of temperature
• How much energy is spread out
• How widely spread out it becomes
• Entropy change energy dispersed/T

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Entropy of the Universe

• ?Suniverse ?Ssystem ?Ssurroundings

Positional disorder
Energetic disorder
?Suniverse gt 0 ? spontaneous process Both ?Ssys
and ?Ssurr positive Both ?Ssys and ?Ssurr
negative ?Ssys negative, ?Ssurr positive
?Ssys positive, ?Ssurr negative
spontaneous process.
nonspontaneous process.
depends
depends
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Entropy of the Surroundings(Energetic Disorder)
System
Entropy
Heat
?Ssurr gt 0
?Hsys lt 0
Surroundings
System
Surroundings
Heat
Entropy
?Ssurr lt 0
?Hsys gt 0
Low T ? large entropy change (surroundings) High
T ? small entropy change (surroundings)
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Positional Disorder and Probability
Probability of 1 particle in left bulb ½ "
2 particles both in left bulb (½)(½) ¼ "
3 particles all in left bulb (½)(½)(½)
1/8 " 4 " all " (½)(½)(½)(½)
1/16 " 10 " all " (½)10 1/1024 "
20 " all " (½)20 1/1048576 "
a mole of " all " (½)6.02?1023 The
arrangement with the greatest entropy is the one
with the highest probability (most spread out).
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Entropy of the System Positional Disorder
Ludwig Boltzmann
Ordered states
Low probability (few ways)
Ludwig Boltzmann
Low S
Disordered states
High probability (many ways)
High S
Ssystem ? Positional disorder S increases with
increasing of possible positions

• Ssolid lt Sliquid ltlt Sgas

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The Third Law of Thermodynamics

• The Third Law
• The entropy of a perfect crystal at 0 K is zero.
• Everything in its place
• No molecular motion

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Entropy Curve
Solid
Gas
Liquid
? vaporization
S (qrev/T) (J/K)
? fusion
0
Temperature (K)
0
S (absolute entropy) can be calculated for any
substance
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Entropy Increases with...

• Melting (fusion) Sliquid gt Ssolid
• ?Hfusion/Tfusion ?Sfusion
• Vaporization Sgas gt Sliquid
• ?Hvaporization/Tvaporization ?Svaporization
• Increasing ngas in a reaction
• Heating ST2 gt ST1 if T2 gt T1
• Dissolving (usually) Ssolution gt (Ssolvent
  Ssolute)
• Molecular complexity more bonds, more entropy
• Atomic complexity more e-, protons, neutrons

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Recap Characteristics of Entropy

• S is a state function
• S is extensive (more stuff, more entropy)
• At 0 K, S 0 (we can know absolute entropy)
• S gt 0 for elements and compounds in their
  standard states
• ?Srxn ?nSproducts - ?nSreactants
• Raise T ? increase S
• Increase ngas ? increase S
• More complex systems ? larger S

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Entropy and Gibbs Free Energy

• by Mike Roller

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Entropy (S) Review

• ?Suniverse gt 0 for spontaneous processes
• ?Suniverse ?Ssystem ?Ssurroundings

? positional
? energetic

• We can know the absolute entropy value for a
  substance
• S values for elements compounds in their
  standard states are tabulated (Appendix C, p.
  1019)
• For any chemical reaction, we can calculate
  ?Srxn
• ?Srxn ?S(products) - ?S(reactants)

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?Suniverse and Chemical Reactions

• ?Suniverse ?Ssystem ?Ssurroundings
• For a system of reactants and products,
• ?Suniverse ?Srxn ?Hrxn/T
• If ?Suniverse gt 0, the reaction is spontaneous
• If ?Suniverse lt 0, the reaction is not
  spontaneous
• The reverse reaction is spontaneous
• If ?Suniverse 0, the reaction is at equilibrium
• Neither the forward nor the reverse reaction is
  favored

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C6H12O6(s) 6 O2(g) ? 6 CO2(g) 6 H2O(g)
Compound C6H12O6(s) O2(g) CO2(g) H2O(g)
?Hf (kJ/mol) -1275 0 -393.5 -242
S (J/mol K) 212 205 214 189
?Suniverse ?Srxn ?Hrxn/T
?Srxn ?S(products) - ?S(reactants) 6
S(CO2(g)) 6 S(H2O(g)) S(C6H12O6(s)) 6
S(O2(g)) 6(214) 6(189) (212)
6(205) J/K ?Srxn 976 J/K ?Hrxn ??Hf
(products) - ??Hf(reactants) 6 ?Hf(CO2(g))
6 ?Hf(H2O(g)) ?Hf(C6H12O6(s)) 6
?Hf(O2(g)) 6(-393.5) 6(-242) (-1275)
6(0) kJ ?Hrxn -2538 kJ

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C6H12O6(s) 6 O2(g) ? 6 CO2(g) 6 H2O(g)
Compound C6H12O6(s) O2(g) CO2(g) H2O(g)
?Hf (kJ/mol) -1275 0 -393.5 -242
S (J/mol K) 212 205 214 189
?Suniverse ?Srxn ?Hrxn/T
?Srxn 976 J/K (per mole of glucose) ?Hrxn
-2538 kJ (per mole of glucose) At 298
K, ?Suniverse 0.976 kJ/K (-2538 kJ/298
K) ?Suniverse 9.5 kJ/K

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Gibbs Free Energy (G)
G H TS At constant temperature, ?G ?H
T?S (systems point of view)
?G ?H T?S Divide both sides by T -?G/T
-?H/T ?S

• ?G means ?Suniv
• A process (at constant T, P) is spontaneous if
  free energy decreases

Josiah Gibbs
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?G and Chemical Reactions

• ?G ?H T?S
• If ?G lt 0, the reaction is spontaneous
• If ?G gt 0, the reaction is not spontaneous
• The reverse reaction is spontaneous
• If ?G 0, the reaction is at equilibrium
• Neither the forward nor the reverse reaction is
  favored
• ?G is an extensive state function

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Ba(OH)2(s) 2NH4Cl(s) ? BaCl2(s) 2NH3(g) 2
H2O(l)
?Hrxn 50.0 kJ (per mole Ba(OH)2) ?Srxn
328 J/K (per mole Ba(OH)2)
?G ?H - T?S
?G 50.0 kJ 298 K(0.328 kJ/K) ?G 47.7
kJ Spontaneous
At what T does the reaction stop being
spontaneous? The T where ?G 0. ?G 0 50.0 kJ
T(0.328 J/K) 50.0 kJ T(0.328 J/K) T 152 K
?not spontaneous below 152 K
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Effect of ?H and ?S on Spontaneity
?G ?H T?S ?G negative ? spontaneous reaction
?H
?S

• Spontaneous?
• Spontaneous at all temps
• Spontaneous at high temps
• Reverse reaction spontaneous at low temps
• Spontaneous at low temps
• Reverse reaction spontaneous at high temps
• Not spontaneous at any temp

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Ways to Calculate ?Grxn

• 1. ?G ??Gf(products) - ??Gf(reactants)
• ?Gf free energy change when forming 1 mole of
  compound from elements in their standard states
• 2. ?G ?H - T?S
• 3. ?G can be calculated by combining ?G values
  for several reactions
• Just like with ?H and Hesss Law

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

• 1. ?G ??Gf(products) - ??Gf(reactants)
• ?Gf(O2(g)) 0
• ?Gf(H2(g)) 0
• ?Gf(H2O(g)) -229 kJ/mol
• ?G (2(-229 kJ) 2(0) 0) kJ -458 kJ
• 2. ?G ?H - T?S
• ?H -484 kJ
• ?S -89 J/K
• ?G -484 kJ 298 K(-0.089 kJ/K) -457 kJ

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

• 3. ?G combination of ?G from other reactions
  (like Hesss Law)
• 2H2O(l) ? 2H2(g) O2(g) ?G1 475 kJ
• H2O(l) ? H2O(g) ?G2 8 kJ
• ?G - ?G1 2(?G2)
• ?G -475 kJ 16 kJ -459 kJ

Method 1 -458 kJ Method 2 -457 kJ Method 3
-459 kJ
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What is Free Energy, Really?

• NOT just another form of energy
• Free Energy is the energy available to do useful
  work
• If ?G is negative, the system can do work (wmax
  ?G)
• If ?G is positive, then ?G is the work required
  to make the process happen
• Example Photosynthesis
• 6 CO2 6 H2O ? C6H12O6 6 O2
• ?G 2870 kJ/mol of glucose at 25C
• 2870 kJ of work is required to photosynthesize 1
  mole of glucose