Chapter 17: Free Energy and
Thermodynamics II
Chem 102
Dr. Curtis
Heat transfer and changes in the entropy of the
surroundings
• Spontaneous processes: Entropy of the universe
increases
• Strange question: Why is the freezing of water
spontaneous at 0 oC?
• Entropy decreases, right?
• Yes, but the water is the system, what about the
surroundings?
Suniv =
Ssys +
Ssurr
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Heat transfer and changes in the entropy of the
surroundings
Suniv =
Ssys +
Ssurr
• Spontaneous: ΔSuniv > 0
• ΔSsys can be negative, as long as ΔSsurr is more positive
than ΔSsys is negative
• ΔSsurr > -ΔSsys
3
Heat transfer and changes in the entropy of the
surroundings
• Back to freezing of water
• ΔSsys is negative
Heat
System
• But the process is exothermic, releasing heat to the
surroundings, increasing the entropy of the
surroundings
• Exothermic process: Increases entropy of surroundings
• Endothermic process: Decreases entropy of surroundings
4
Temperature dependence of ΔSsurr
• Freezing of water is spontaneous at 0 oC, but non
spontaneous at a higher temperature. Why?
• Heat released to the surroundings has less impact at
higher temperatures
• For freezing of water:
Suniv =
Ssys +
Ssurr
Negative
Positive and large at low T
Positive and small at high T
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Quantifying ΔSsurr
• qsys = heat of the system
• qsys < 0 = exothermic (ΔSsurr > 0)
• qsys > 0 = endothermic (ΔSsurr < 0)
Ssurr /
Ssurr
qsys
1
/
T
Ssurr =
qsys
T
• At constant pressure, qsys = ΔHsys, so at constant P, T:
Ssurr =
Hsys
T
7
Calculate ΔSsurr
• C3H8(g) + 5 O2(g) → 3 CO2(g) + 4 H2O(g) ΔHrxn = -2044 kJ
• Calculate ΔSsurr at 25 oC, determine sign of ΔSsys and ΔSsurr
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Gibbs Free Energy
• For convenience, let’s drop the sys and assume if you
see ΔS or ΔH it is for the system
• Gibbs Free Energy: G = H -TS
(system)
• Therefore, the change in G is (system)
G=
• At constant T and P,
H
G=
T S
T Suniv
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Gibbs Free Energy
G=
H
T S
G=
T Suniv
• Use ΔG (at constant T, P) as a criterion for spontaneity
• ΔG is proportional to -ΔSuniv
• If ΔG < 0, process is spontaneous
• If ΔG > 0, process is nonspontaneous
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Effect of ΔH, ΔS, and T on spontaneity
• Case 1: ΔH negative, ΔS positive
• Exothermic and entropy of system increases
• Process is spontaneous at all temperatures
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Effect of ΔH, ΔS, and T on spontaneity
• Case 2: ΔH positive, ΔS negative
• Endothermic and entropy of system increases
• Process is non spontaneous at all temperatures
12
Effect of ΔH, ΔS, and T on spontaneity
• Case 3: ΔH negative, ΔS negative
• Exothermic and entropy of system decreases
• Process is spontaneous at low temperatures
• Process is non spontaneous at high temperatures
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Effect of ΔH, ΔS, and T on spontaneity
• Case 4: ΔH positive, ΔS positive
• Endothermic and entropy of system increases
• Process is spontaneous at high temperatures
• Process is non spontaneous at low temperatures
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G=
H
T
S
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Example
• Given a ΔH and ΔS, calculate ΔG
• Consider the reaction: C2H4(g) + H2(g) → C2H6(g)
• Given: ΔH = -137.5 kJ, ΔS = -120.5 J/K
• Calculate ΔG at 25 oC,
• Is the reaction spontaneous?
• How does ΔG vary with temperature?
T = 298 K
G=
G=
H
T S=
137.5 ⇥ 103 J
(298 K)( 120.5 J/K)
101, 591 J
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Calculating entropy in a reaction
• Third Law: As temperature approaches absolute
zero, entropy approaches a constant. The entropy
of a perfectly ordered crystal at absolute zero is
zero.
• Nothing in the universe has zero entropy
• Entropy is inherent to the molecules in a reaction
• Look it up in a table
• Has units of J / mol K
• “Extensive” property - depends on how much is present
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Standard state
• We will be calculating ΔSo values
• Standard State (sometimes called Standard Conditions)
• Gas: Pressure = 1 atm
• Liquid or Solid: Pure substance in its most stable
state at P = 1 atm and T = 25 oC
• Solution: 1 M concentration
• Then, in a reaction (depending on number of moles)
Srxn = Sproducts
Sreactants
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Note: The units are J/(mol K): Number of moles matters
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Standard Entropy of a Reaction
Srxn =
X
np S (products)
X
nr S (reactants)
• Reaction must be balanced!
• np is the number of moles of each product
• nr is the number of moles of each reactant
• Standard states
• Similar to calculation for enthalpy of reaction
• Unlike enthalpy of reaction, elements have an entropy at
25 oC
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Example
Srxn =
X
np S (products)
X
nr S (reactants)
• Calculate the standard entropy of reaction for:
2 NH3 (g) ! N2 H4 (g) + H2 (g)
Compound
So (J/mol K)
NH3(g)
192.8
N2H4(g)
238.5
H2(g)
130.7
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Relative entropies
• As we discussed before: Sgas > Sliquid > Ssolid
• As we see in the table:
H2O (g) > H2O (l) (at
298 K)
• Trend with molar mass
• Higher molar mass is
generally higher S
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Allotropes
• Some elements exist in two (or more) forms within the
same state called allotropes. Usually different crystal
forms of a solid.
• Allotropes will have different So values based on
structure
• Examples:
• C(s)
• S6(s) vs. S8(s)
• O3(g) vs. O2(g)
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Molecular complexity
• In general, the more complex the molecule, the higher
the entropy
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Dissolution
• Dissolved ions in solution have a higher entropy than the
crystalline solid
• Makes sense: More spread apart, more random
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Recall: Standard enthalpy of reaction
Hrxn =
X
np Hf (products)
X
nr Hf (reactants)
• ΔHfo = Heat of formation of a substance in standard state
• np is the number of moles of each product
• nr is the number of moles of each reactant
• For an element in its standard state, ΔHfo = 0
• ΔHrxno < 0: exothermic
ΔHrxno > 0: endothermic
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Example
Hrxn =
X
np Hf (products)
X
nr Hf (reactants)
• Calculate the standard enthalpy of reaction for:
2 NH3 (g) ! N2 H4 (g) + H2 (g)
Compound
ΔHfo (kJ/mol )
NH3(g)
-45.9
N2H4(g)
50.6
H2(g)
0
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Calculating ΔGorxn
• Now we have calculated ΔSorxn and ΔHorxn
• put them together (with T) to get the Gibbs Free Energy
change in a chemical reaction
Grxn =
Hrxn
T Srxn
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Calculate the ΔGorxn
2 NH3 (g)
Srxn =
Grxn =
Hrxn
T Srxn
! N2 H4 (g) + H2 (g)
16.4 J/mol · K
Hrxn = 142.4 kJ/mol
• Is the reaction spontaneous at 25 oC?
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Calculate the ΔGorxn given Free Energies of
Formation
• Sometimes you will be given Free Energies of Formation
• Can calculate the reaction free energy from:
Grxn =
X
(np Gf (products))
X
(nr Gf (reactants))
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