Download The Effect of Temperature on Spontaneity

Chapter 17
Spontaneity, Entropy,
and Free Energy
Section 17.1
Spontaneous Processes and Entropy
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.
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Section 17.1
Spontaneous Processes and Entropy
Spontaneous Processes and Entropy
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Thermodynamics predict the direction in which a process will occur but gives no
information about the speed of the process.
A spontaneous process is one that occurs without outside intervention.
It may be slow or fast.
A gas fills its container uniformly. It never spontaneously collects at one end of
the container.
Heat flow always occur from hot to a cooler one. The reverse process never
occurs spontaneously.
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Section 17.1
Spontaneous Processes and Entropy
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.
a) What should happen to the gas when you open
the valve?
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Section 17.1
Spontaneous Processes and Entropy
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 ΔH, ΔE, q, and w for the process you
described above.
All are equal to zero.
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Section 17.1
Spontaneous Processes and Entropy
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.
c) Given your answer to part b, what is the
driving force for the process?
Entropy
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Section 17.1
Spontaneous Processes and Entropy
The Expansion of An Ideal Gas Into an Evacuated Bulb
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Section 17.1
Spontaneous Processes and Entropy
Entropy
 Spontaneous processes is an increase in property
called entropy (s).
 The driving force for a spontaneous process is an
increase in the entropy of the universe.
 It is a measure of molecular randomness or
disorder.
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Section 17.1
Spontaneous Processes and Entropy
Entropy
 Entropy is a 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 highest probabilities of existing.
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Section 17.1
Spontaneous Processes and Entropy
The Microstates
That Give a
Particular
Arrangement
(State)
Section 17.2
Entropy and the Second Law of Thermodynamics
 Each configuration that gives a particular
arrangement is called microstate.
 Which arrangement is most likely to occur.
 Table 17.2 shows relative probabilities of finding
all the molecules in the left bulb.
Section 17.1
Spontaneous Processes and Entropy
Positional Entropy
 A gas expands into a vacuum to give a uniform
distribution because the expanded state has the
highest positional probability of states available to
the system.
 Therefore: Ssolid < Sliquid << Sgas
 Question 17.31, 32
Section 17.1
Spontaneous Processes and Entropy
CONCEPT CHECK!
Predict the sign of ΔS 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
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Section 17.2
Entropy and the Second Law of Thermodynamics
Second Law of Thermodynamics
 In any spontaneous process there is always an increase
in the entropy of the universe.
 The entropy of the universe is increasing.
 The total energy of the universe is constant, but the
entropy is increasing.
Suniverse = ΔSsystem + ΔSsurroundings
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Section 17.2
Entropy and the Second Law of Thermodynamics
ΔSuniv
 ΔSuniv = +; entropy of the universe increases
 ΔSuniv = -; process is spontaneous in opposite direction
 ΔSuniv = 0; process has no tendency to occur, and the
system is at equilibrium.
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Section 17.3
The Effect of Temperature on Spontaneity
CONCEPT CHECK!
For the process A(l)
A(s), which direction involves
an increase in energy randomness? Positional
randomness? Explain your answer.
As temperature increases/decreases (answer for both),
which takes precedence? Why?
At what temperature is there a balance between energy
randomness and positional randomness?
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Section 17.3
The Effect of Temperature on Spontaneity
CONCEPT CHECK!
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 17.3
The Effect of Temperature on Spontaneity
ΔSsurr
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There are two important characteristics of the entropy changes that occur in the
surroundings.
The sign of ΔSsurr depends on the direction of the heat flow. At constant temperature ,
an exothermic process in the system causes the heat flow into the surrounding. It
increases the random motions and the entropy of the surroundings. ΔSsurr is positive
The magnitude of ΔSsurr depends on the temperature. The transfer of a given quantity of
energy as a heat produces much greater percent change in the randomness of the
surrounding at a low temperature than it does at a high temperature. Thus depends
directly on the quantity of heat transferred and inversely proportional on the
temperature.
In other words, the tendency for the system to lower its energy becomes a more
important driving force at lower temperatures.
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Section 17.3
The Effect of Temperature on Spontaneity
ΔSsurr
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Section 17.3
The Effect of Temperature on Spontaneity
ΔSsurr
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Section 17.3
The Effect of Temperature on Spontaneity
ΔSsurr
We can express Δssurr in terms of the change in enthalpy ΔH
for a process occurring at constant pressure.
Heat flow (constant P) = change in enthalpy = ΔH
Questions 17.33, 17.34
Ssurr
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H
= 
T
21
Section 17.3
The Effect of Temperature on Spontaneity
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Section 17.4
Free Energy
Free energy (G)
 Free energy (another thermodynamic term) is
also related to spontaneity in dealing with
temperature dependence of spontaneity.
Section 17.4
Free Energy
Free Energy (G)
Suniv
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G
= 
(at constant T and P )
T
A process carried out at constant T and P is spontaneous if the ΔG is negative.
Negative (-ΔG) means positive (+Δsuniv).
So we have two functions that can be used to predict spontaneity.
i) Entropy of universe, which apply to all processes.
Ii) Free energy which can be used for processes carried out at constant temperature
and pressure.
Question 17.37
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Section 17.4
Free Energy
Free Energy (G)
 ΔG = ΔH – TΔS (at constant T and P)
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Section 17.4
Free Energy
CONCEPT CHECK!
A liquid is vaporized at its boiling point. Predict the signs of:
–
w
+
q
+
ΔH
+
ΔS
–
ΔSsurr
0
ΔG
Explain your answers.
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Section 17.4
Free Energy
EXERCISE!
The value of ΔHvaporization of substance X is 45.7 kJ/mol,
and its normal boiling point is 72.5°C.
Calculate ΔS, ΔSsurr, and ΔG for the vaporization of one
mole of this substance at 72.5°C and 1 atm.
ΔS = 132 J/K·mol
ΔSsurr = -132 J/K·mol
ΔG = 0 kJ/mol
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Section 17.4
Free Energy
Spontaneous Reactions
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Section 17.4
Free Energy
Effect of ΔH and ΔS on Spontaneity
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Section 17.5
Entropy Changes in Chemical Reactions
CONCEPT CHECK!
Gas A2 reacts with gas B2 to form gas AB at constant
temperature and pressure. The bond energy of AB is much
greater than that of either reactant.
Predict the signs of:
ΔH
ΔSsurr
–
+
ΔS
ΔSuniv
0
+
Explain.
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Section 17.5
Entropy Changes in Chemical Reactions
Entropy changes in the system are determined by positional probability.
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Fewer molecule means fewer possible configurations.
Gases molecules generally possess more entropy than solid.
So whenever the products contains more moles of gases than reactant the entropy
change is probably positive.
Question 17.41, 42
Section 17.5
Entropy Changes in Chemical Reactions
Third Law of Thermodynamics: In thermodynamics change in a certain function is
usually important.
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The change in enthalpy determines if the reaction is exothermic or endothermic at
constant temperature.
The change in free energy determines if a process is spontaneous at constant
temperature and pressure.
A perfect crystal represents the lowest possible entropy.
Law: The entropy of a perfect crystal at 0 K is zero.
The entropy of a substance increases with temperature.
Since S is zero for a perfect crystal at 0 K, the entropy value for a substance at a
particular temperature can be calculated by knowing the temperature dependence
entropy.
The standard entropy values (S0) of many common substances at 298 K and 1 atm. are
listed in appendix 4.
Because the entropy is a state function of the system , the entropy change can be
calculated by the following equation.
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Section 17.5
Entropy Changes in Chemical Reactions
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.
 Question 17.45,46
ΔS°reaction = ΣnpS°products – ΣnrS°reactants
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Section 17.5
Entropy Changes in Chemical Reactions
EXERCISE!
Calculate ΔS° 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
ΔS°= –11 J/K
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Section 17.6
Free Energy and Chemical Reactions
Standard Free Energy Change (ΔG°)
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For a chemical reaction we are interested in the 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.
It is important to note that the ΔG° for a reaction is not measure directly.
ΔG° values for several reactions allow us to compare the relative tendency of these
reactions . More negative the value of ΔG°, the further a reaction will go to the right
to reach the equilibrium.
Question:17.53, 57, 59
ΔG° = ΔH° – TΔS°
ΔG°reaction = ΣnpG°products – ΣnrG°reactants
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Section 17.6
Free Energy and Chemical Reactions
CONCEPT CHECK!
A stable diatomic molecule spontaneously
forms from its atoms.
Predict the signs of:
ΔH°
ΔS°
–
–
ΔG°
–
Explain.
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Section 17.6
Free Energy and Chemical Reactions
CONCEPT CHECK!
Consider the following system at
equilibrium at 25°C.
PCl3(g) + Cl2(g)
PCl5(g)
ΔG° = −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.
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Section 17.7
The Dependence of Free Energy on Pressure
Free Energy and Pressure
G = G° + RT ln(P)
or
ΔG = ΔG° + RT ln(Q)
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Section 17.7
The Dependence of Free Energy on Pressure
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)
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Section 17.7
The Dependence of Free Energy on Pressure
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.
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Section 17.8
Free Energy and Equilibrium
 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)
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Section 17.8
Free Energy and Equilibrium
Change in Free Energy to Reach Equilibrium
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Section 17.8
Free Energy and Equilibrium
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Section 17.9
Free Energy and Work
 Maximum possible useful work obtainable from a
process at constant temperature and pressure is equal
to the change in free energy.
wmax = ΔG
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Section 17.9
Free Energy and Work
 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.
 As we use energy, we degrade its usefulness.
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