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Chapter 16Spontaneity, Entropy,
and Free Energy
Why do some things happen and others
don’t?
Chapter 16
Table of Contents
Copyright © Cengage Learning. All rights reserved 2
16.1Spontaneous Processes and Entropy
16.2 Entropy and the Second Law of Thermodynamics
16.3 The Effect of Temperature on Spontaneity
16.4 Free Energy
16.5 Entropy Changes in Chemical Reactions
16.6 Free Energy and Chemical Reactions
16.7 The Dependence of Free Energy on Pressure
16.8 Free Energy and Equilibrium
16.9 Free Energy and Work
Section 16.1
Spontaneous Processes and Entropy
Return to TOC
Copyright © Cengage Learning. All rights reserved 3
Objectives
• To compare kinetics with thermodynamics• To define spontaneity• To answer why some things happen and others
don’t.• To define Entropy• To assign positive or negative sign depending
on the process • To understand why a diverging diamond
interchange is safer than other designs
Section 16.1
Spontaneous Processes and Entropy
Return to TOC
Copyright © Cengage Learning. All rights reserved 4
Thermodynamics vs. Kinetics
• Domain of Kinetics Rate of a reaction
depends on the pathway from reactants to products.
• Thermodynamics tells us whether a reaction is spontaneous based only on the properties of reactants and products.
Section 16.1
Spontaneous Processes and Entropy
Return to TOC
Copyright © Cengage Learning. All rights reserved 5
Spontaneous Processes and Entropy
• Thermodynamics lets us predict whether a process will occur but gives no information about the amount of time required for the process.
• A spontaneous process is one that occurs without outside intervention.
• Examples??
Section 16.1
Spontaneous Processes and Entropy
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Copyright © Cengage Learning. All rights reserved 6
Section 16.1
Spontaneous Processes and Entropy
Return to TOC
Copyright © Cengage Learning. All rights reserved 7
Consider 2.4 moles of a gas contained in a 4.0 L bulb at a constant temperature of 32°C. This bulb is connected by a valve to an evacuated 20.0 L bulb. Assume the temperature is constant.
What should happen to the gas when you open the valve?
Section 16.1
Spontaneous Processes and Entropy
Return to TOC
Copyright © Cengage Learning. All rights reserved 8
The Expansion of An Ideal Gas Into an Evacuated Bulb
What is the driving force for the process? Why does it happen?
Section 16.1
Spontaneous Processes and Entropy
Return to TOC
Copyright © Cengage Learning. All rights reserved 9
Entropy
• The driving force for a spontaneous process is an increase in the entropyentropy (S) of the universe.
• Entropy (S) is a measure of molecular randomness or disorderdisorder.
Section 16.1
Spontaneous Processes and Entropy
Return to TOC
Copyright © Cengage Learning. All rights reserved 10
Entropy
• Thermodynamic function that describes the number of arrangements that are available to a system existing in a given state.
• Nature spontaneously proceeds toward the states that have the highesthighest probabilitiesprobabilities of existing.
• Is a deck of cards usually ordered or disordered?• There are so many ways for a deck of cards to be
disordered, but• Only one way for it to be ordered…
Section 16.1
Spontaneous Processes and Entropy
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Copyright © Cengage Learning. All rights reserved 11
The Microstates That Give a Particular Arrangement (State)
Section 16.1
Spontaneous Processes and Entropy
Return to TOC
Copyright © Cengage Learning. All rights reserved 12
Positional Entropy
• A gas expands into a vacuum because the expanded state has the highesthighest positionalpositional probabilityprobability of states available to the system.
• Therefore: Ssolid < Sliquid << Sgas
• Why do solutions form?• Why do ice cubes get smaller, even though they
are in the freezer?• If a process moves in a direction of greater
disorder or higher entropy, the sign is positive.
Section 16.1
Spontaneous Processes and Entropy
Return to TOC
Copyright © Cengage Learning. All rights reserved 13
Concept Check
Predict the sign of S for each of the following, and explain:
a) The evaporation of alcohol
b) The freezing of water
c) Compressing an ideal gas at constant temperature
d) Heating an ideal gas at constant pressure
e) Dissolving NaCl in water
+
–
–
+
+
Section 16.1
Spontaneous Processes and Entropy
Return to TOC
Copyright © Cengage Learning. All rights reserved 14
Objectives Review• To compare kinetics with thermodynamics• To define spontaneity• To answer why some things happen and others
don’t.• To define Entropy• To assign positive or negative sign depending
on the process • Why is a diverging diamond safer? #12• Work Session Page 782 # 1, 19, 23 (think IGL
and volume), 25, 33, 35
Section 16.2
Atomic MassesEntropy and the Second Law of Thermodynamics
Return to TOC
Copyright © Cengage Learning. All rights reserved 15
Objectives
• To define the Second Law of Thermodynamics• Wait, what was the first? I’m constantly
forgetting it…
Section 16.2
Atomic MassesEntropy and the Second Law of Thermodynamics
Return to TOC
Copyright © Cengage Learning. All rights reserved 16
Second Law of Thermodynamics
• In any spontaneous process there is always an increase in the entropy of the universe.
• What is the sign of a spontaneous process?• The entropy of the universe is increasing.• The total energyenergy of the universe is constant, but the
entropyentropy is increasing.
Suniverse = ΔSsystem + ΔSsurroundings
Section 16.2
Atomic MassesEntropy and the Second Law of Thermodynamics
Return to TOC
Copyright © Cengage Learning. All rights reserved 17
Second Law of Thermodynamics
Suniverse = ΔSsystem + ΔSsurroundings
• How can life exist if it requires cells to take small molecules to make bigger ones?
• Is this a spontaneous process? • Does S increase?• Is this consistent with the 2nd Law of
Thermodynamics?
• For a spontaneous process, how are ΔSsys & ΔSsurr related?
Section 16.2
Atomic MassesEntropy and the Second Law of Thermodynamics
Return to TOC
Copyright © Cengage Learning. All rights reserved 18
Objectives Review
• To define the Second Law of Thermodynamics• 1st Law of Thermodynamics:• The amount of energy in the Universe is constant• Work Session #8
Section 16.3
The Mole The Effect of Temperature on Spontaneity
Return to TOC
Copyright © Cengage Learning. All rights reserved 19
Objectives
• To predict spontaneity of a process based on ΔS and ΔH
• To understand the effect of temperature on Spontaneity
Section 16.3
The Mole The Effect of Temperature on Spontaneity
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Copyright © Cengage Learning. All rights reserved 20
Which side is favored by Entropy?
• H2O (l) H2O (g) water is the system…
• 18 ml 31 L @1atm, 100C• Positional Probability?
• What is the sign of ΔSsystem?
• What direction is the heat flow? ΔHsystem?
• …what about the surroundings?• Positional Probability?
• What is the sign of ΔSsurr? Heat flow? ΔHsurr?
• What is the overall ΔS of the universe?
• ΔSuniv = ΔSsys + ΔSsurr
Section 16.3
The Mole The Effect of Temperature on Spontaneity
Return to TOC
Copyright © Cengage Learning. All rights reserved 21
Concept Check
For the process A(l) A(s), which direction involves an increase in energy randomness(-ΔH)? Positional randomness(+ΔS)? Explain your answer.
As temperature increases/decreases , does energy or positional randomness take precedence? Why?
At what temperature is there a balance between energy randomness and positional randomness?
Section 16.3
The Mole The Effect of Temperature on Spontaneity
Return to TOC
Copyright © Cengage Learning. All rights reserved 22
ΔSsurr = - ΔH T
• The sign of ΔSsurr depends on the direction of the heat flow. –ΔH, +ΔSsurr
• The magnitude of ΔSsurr depends on the temperature.
• Why does ice freeze, but only at lower temperatures? Balance between energy randomness and positional randomness.
• Liquid Solid
Section 16.3
The Mole The Effect of Temperature on Spontaneity
Return to TOC
Copyright © Cengage Learning. All rights reserved 23
ΔSsurr = - ΔH enthalpy determines the sign T
Section 16.3
The Mole The Effect of Temperature on Spontaneity
Return to TOC
Copyright © Cengage Learning. All rights reserved 24
ΔSsurr = - ΔH temperature determines the magnitude T
Heat flow (constant P) = change in enthalpy = ΔH
Section 16.3
The Mole The Effect of Temperature on Spontaneity
Return to TOC
Copyright © Cengage Learning. All rights reserved 25
Interplay of Ssys and Ssurr in Determining the Sign of Suniv
ΔSuniv = ΔSsys + ΔSsurr
Section 16.3
The Mole The Effect of Temperature on Spontaneity
Return to TOC
Copyright © Cengage Learning. All rights reserved 26
Objectives Review
• To predict spontaneity of a process based on ΔS and ΔH
• To understand the effect of temperature on Spontaneity
Section 16.4
Free Energy
Return to TOC
Copyright © Cengage Learning. All rights reserved 27
Objectives
• To understand Gibbs Free Energy (ΔG) in relation to ΔS and ΔH
• To predict spontaneity based on Gibbs Free Energy
• To conceptually and mathematically use Gibbs Equation
Section 16.4
Free Energy
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Copyright © Cengage Learning. All rights reserved 28
Free Energy (G)
• ΔG = ΔH – TΔS (at constant T and P)
• Negative ΔG means positive ΔSuniv
• positive ΔSuniv means Spontaneous!
• Negative ΔG means Spontaneous!• ΔG < 0 means spontaneous
Section 16.4
Free Energy
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Copyright © Cengage Learning. All rights reserved 29
How to determine spontaneity based on ΔS and ΔH …
For a process to be considered spontaneous, it must be both :
exothermic (favor energy randomness (-ΔH) and
Favor positional randomness (entropy (+ΔS))
ΔG = ΔH – TΔS
If the opposite of the above conditions exist, we can conclude that the process is not spontaneous.
Spontaneous Not Spontaneous Don’t Know Don’t Know
ΔH - + + -
ΔS + - + -
Section 16.4
Free Energy
Return to TOC
Copyright © Cengage Learning. All rights reserved 30
Describe the following as
spontaneous/non-spontaneous/cannot tell, and explain.
A reaction that is:
a) Exothermic and becomes more positionally random
Spontaneous
b) Exothermic and becomes less positionally random
Cannot tell
a) Endothermic and becomes more positionally random
Cannot tell
a) Endothermic and becomes less positionally random
Not spontaneous
Explain how temperature affects your answers.
Section 16.4
Free Energy
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Copyright © Cengage Learning. All rights reserved 31
Effect of ΔH and Δ S on SpontaneityΔG = ΔH – TΔS
H S Result
+ spontaneous at all temps
+ + spontaneous at high temps
spontaneous at low temps
+ not spontaneous at any temp
Section 16.4
Free Energy
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Copyright © Cengage Learning. All rights reserved 32
Concept Check
A liquid is vaporized at its boiling point. Predict the signs of:
w
q
H
S
Ssurr
G
Explain your answers.
–
+
+
+
–
0
Section 16.4
Free Energy
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Copyright © Cengage Learning. All rights reserved 33
Exercise
Predict the spontaneity of: H2O(s) H2O(l)
Given: ΔH = 6.03 X 103 J/mol ΔS = 22.1 J/K*mol
5-Step with Gibbs!
ΔG = ΔH – TΔS
Try at -10 oC, 0 oC, and 10 oC
-10 oC, ΔG = +2.2 X 102 J/mol
0 oC, ΔG = 0 J/mol
10 oC, ΔG = -2.2 X 102 J/mol
Section 16.4
Free Energy
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Copyright © Cengage Learning. All rights reserved 34
Exercise
The value of Hvaporization of substance X is 45.7 J/mol, and its normal boiling point is 72.5°C.
Calculate S, Ssurr, and G for the vaporization of one mole of this substance at 72.5°C and 1 atm.
ΔSsurr = - ΔH T
S = 132 J/K·mol
Ssurr = -132 J/K·mol
G = 0 kJ/mol
Section 16.4
Free Energy
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Copyright © Cengage Learning. All rights reserved 35
Exercise
Find the normal boiling point of liquid Br2.
Br2(l) Br2(g)
ΔH = 31.0 KJ/mol ΔS = 93.0 J/K*mol
5-Step with Gibbs!
ΔG = ΔH – TΔS
Section 16.4
Free Energy
Return to TOC
Copyright © Cengage Learning. All rights reserved 36
Spontaneous Reactions
Section 16.4
Free Energy
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Copyright © Cengage Learning. All rights reserved 37
Objectives Review
• To understand Gibbs Free Energy (ΔG) in relation to ΔS and ΔH
• To predict spontaneity based on Gibbs Free Energy
• To conceptually and mathematically use Gibbs Equation
• Work Session: 27, 29, 30, 31
Section 16.5
Entropy Changes in Chemical Reactions
Return to TOC
Copyright © Cengage Learning. All rights reserved 38
Objectives
• To predict the sign of ΔS for a given chemical reaction.
• To calculate ΔS°reaction given ΔS° values for products and reactants
• To calculate ΔS°reaction , ΔH°reaction , ΔG°reaction
Section 16.5
Entropy Changes in Chemical Reactions
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Copyright © Cengage Learning. All rights reserved 39
ΔS changes in Chemical Reactions
• Entropy changes in chemical reactions are determined by positional probability.
• This means that the more molecules, the more possible configurations, the more disorder.
• Predict the sign of ΔS for the following reaction:
• H2 2H
• N2(g) + 3H2(g) 2NH3(g)
• 4NH3(g) + 5O2(g) 4NO(g) + 6H2O(g)
• CaCO3(s) CaO(s) + CO2(g)
• 2SOS(g) + O2(g) 2SO3(g)
Section 16.5
Entropy Changes in Chemical Reactions
Return to TOC
Copyright © Cengage Learning. All rights reserved 40
Concept Check
Gas A2 reacts with gas B2 to form gas AB at constant temperature and pressure. The potential energy of AB is much greater than that of either reactant.
Predict the signs of:
H Ssurr Suniv
Explain.
+ - +
Section 16.5
Entropy Changes in Chemical Reactions
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Copyright © Cengage Learning. All rights reserved 41
Third Law of Thermodynamics…there is a 3rd Law??
• So far, we’ve discussed the relative change in entropy, ΔS. Can we assign an absolute S?
• The entropy of a perfect crystal at 0 K is zero.• A perfect crystal represents the lowest possible
entropy.• Or in other words, everything is perfectly ordered, in
its place, just plain ducky….• Therefore, from 0 K, as the temperature increases, so
does the randomness of vibrational motion and, therefore, the entropy of the substance.
Section 16.5
Entropy Changes in Chemical Reactions
Return to TOC
Copyright © Cengage Learning. All rights reserved 42
Third Law of Thermodynamics…there is a 3rd Law??
• Oh, yeah, …• Since a perfect crystal at absolute zero is an
unattainable ideal, we take the Third Law as a standard although we have never actually observed it…….
• You are welcome….
Section 16.5
Entropy Changes in Chemical Reactions
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Copyright © Cengage Learning. All rights reserved 43
Standard Enthalpy Values (H°)
• Represent the increase in enthalpy of formation of a compound.
ΔH°reaction = ΣnpH°products – ΣnrH°reactants
n = moles (balanced coefficient)
H° = standard enthalpy (from a given list in problem # or on pages A20-A21)
See formula on AP reference sheet.
Section 16.5
Entropy Changes in Chemical Reactions
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Copyright © Cengage Learning. All rights reserved 44
Standard Entropy Values (S°)
• Represent the increase in entropy that occurs when a substance is heated from 0 K to 298 K at 1 atm pressure.
ΔS°reaction = ΣnpS°products – ΣnrS°reactants
n = moles (balanced coefficient)
S° = standard entropy (from a given list in problem # or on pages A20-A21)
See formula on AP reference sheet.
Section 16.5
Entropy Changes in Chemical Reactions
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Copyright © Cengage Learning. All rights reserved 45
Exercise
Calculate Δ S° for the following reaction:
2Na(s) + 2H2O(l) → 2NaOH(aq) + H2(g)
Given the following information:
S° (J/K·mol)
Na(s) 51
H2O(l) 70
NaOH(aq) 50
H2(g) 131
Δ S°= –11 J/K
Section 16.5
Entropy Changes in Chemical Reactions
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Copyright © Cengage Learning. All rights reserved 46
Exercise
Calculate Δ S° for the following reaction:
2NiS(s) + 3O2(g) → 2SO2(g) + 2NiO(s)
Given the following information:
S° (J/K·mol)
SO2(g) 248
NiO(s) 38
O2(g) 205
NiS(s) 53
Δ S°= –149 J/K
Section 16.5
Entropy Changes in Chemical Reactions
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Copyright © Cengage Learning. All rights reserved 47
Exercise
Calculate Δ S° for the following reaction:
Al2O3(s) + 3H2(g) → 2Al(s) + 3H2O(g)
Given the following information:
S° (J/K·mol)
Al2O3(s) 51
H2(g) 131
Al(s) 28
H2O(g) 189
Δ S°= 179 J/K
Section 16.6
Free Energy and Chemical Reactions
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Copyright © Cengage Learning. All rights reserved 48
Standard Free Energy Change (ΔG°)• The change in free energy that will occur if the
reactants in their standard states are converted to the products in their standard states.
ΔG° = ΔH° – TΔS°
ΔG°reaction = ΣnpG°products – ΣnrG°reactants
ΔH°reaction = ΣnpH°products – ΣnrH°reactants
ΔS°reaction = ΣnpS°products – ΣnrS°reactants
A20-A21 for ΔS°, ΔH°, ΔG° data…
Section 16.6
Free Energy and Chemical Reactions
Return to TOC
Copyright © Cengage Learning. All rights reserved 49
Concept Check
A stable diatomic molecule spontaneously forms from its atoms.
Predict the signs of:
H° S° G°
Explain.
– – –
Section 16.6
Free Energy and Chemical Reactions
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Copyright © Cengage Learning. All rights reserved 50
Predict the sign of:H° S° G°
Explain
Section 16.5
Entropy Changes in Chemical Reactions
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Copyright © Cengage Learning. All rights reserved 51
Objectives
• To predict the sign of ΔS for a given chemical reaction.
• To calculate ΔS°reaction given ΔS°values for products and reactants
• To calculate ΔS°reaction , ΔH°reaction , ΔG°reaction
• Work Session # 33, 34, 37, 39, 40, 41, 43, 45, 47, 51 (like Hess’s Law!) A20-A21 for ΔS°, ΔH°, ΔG° data…
Section 16.6
Free Energy and Chemical Reactions
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Copyright © Cengage Learning. All rights reserved 52
Concept Check
Consider the following system at equilibrium at 25°C.
PCl3(g) + Cl2(g) PCl5(g)
G° = −92.50 kJ
What will happen to the ratio of partial pressure of PCl5 to partial pressure of PCl3 if the temperature is raised? Explain. The ratio will decrease.
Section 16.7
The Dependence of Free Energy on Pressure
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Copyright © Cengage Learning. All rights reserved 53
Free Energy and Pressure
G = G° + RT ln(P)
or
ΔG = ΔG° + RT ln(Q)
Section 16.7
The Dependence of Free Energy on Pressure
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Copyright © Cengage Learning. All rights reserved 54
Concept Check
Sketch graphs of:
1. G vs. P
2. H vs. P
3. ln(K) vs. 1/T (for both endothermic and exothermic cases)
Section 16.7
The Dependence of Free Energy on Pressure
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Copyright © Cengage Learning. All rights reserved 55
The Meaning of ΔG for a Chemical Reaction
• A system can achieve the lowest possible free energy by going to equilibrium, not by going to completion.
Section 16.8
Free Energy and Equilibrium
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Copyright © Cengage Learning. All rights reserved 56
• The equilibrium point occurs at the lowest value of free energy available to the reaction system.
ΔG = 0 = ΔG° + RT ln(K)
ΔG° = –RT ln(K)
Section 16.8
Free Energy and Equilibrium
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Copyright © Cengage Learning. All rights reserved 57
Change in Free Energy to Reach Equilibrium
Section 16.8
Free Energy and Equilibrium
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Copyright © Cengage Learning. All rights reserved 58
Qualitative Relationship Between the Change in Standard Free Energy and the Equilibrium Constant for a Given Reaction
Section 16.9
Free Energy and Work
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Copyright © Cengage Learning. All rights reserved 59
• Maximum possible useful work obtainable from a process at constant temperature and pressure is equal to the change in free energy.
wmax = ΔG
Section 16.9
Free Energy and Work
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Copyright © Cengage Learning. All rights reserved 60
• Achieving the maximum work available from a spontaneous process can occur only via a hypothetical pathway. Any real pathway wastes energy.
• All real processes are irreversible.• First law: You can’t win, you can only break
even.• Second law: You can’t break even.
Section 16.1
Spontaneous Processes and Entropy
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Copyright © Cengage Learning. All rights reserved 61
Concept Check
Consider 2.4 moles of a gas contained in a 4.0 L bulb at a constant temperature of 32°C. This bulb is connected by a valve to an evacuated 20.0 L bulb. Assume the temperature is constant.
b) Calculate H, E, q, and w for the process you described above.
All are equal to zero.
Section 16.1
Spontaneous Processes and Entropy
Return to TOC
Copyright © Cengage Learning. All rights reserved 62
Concept Check
Consider 2.4 moles of a gas contained in a 4.0 L bulb at a constant temperature of 32°C. This bulb is connected by a valve to an evacuated 20.0 L bulb. Assume the temperature is constant.
b) Given your answer to part a, what is the driving force for the process?
Entropy
Section 16.1
Spontaneous Processes and Entropy
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Copyright © Cengage Learning. All rights reserved 63
The Microstates That Give a Particular Arrangement (State)
Section 16.4
Free Energy
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Copyright © Cengage Learning. All rights reserved 64
Free Energy (G)
• A process (at constant T and P) is spontaneous in the direction in which the free energy decreases. Negative ΔG means positive ΔSuniv.
univ = (at constant and ) G
S T PT