Transcript Entropy, Free Energy, and Equilibrium

Thermodynamics
Entropy, Free Energy, and Equilibrium
Chapter 18
3/e
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
_______________ Physical and Chemical Processes
• A waterfall runs downhill
• A lump of sugar dissolves in a cup of coffee
• At 1 atm, water freezes below 00C and ice melts above 00C
• Heat flows from a hotter object to a colder object
• A gas expands into an evacuated bulb
• Iron exposed to oxygen and water forms rust
spontaneous
nonspontaneous
18.2
18.2
Refresh your memory: What is enthalpy?
Enthalpy is a thermodynamic property that describes heat
changes taking place at constant _____________.
Enthalpy is an ___________property—its magnitude depends
on the amount of the substance present.
Enthalpy cannot be determined, so we measure H, the
change in enthalpy.
In earlier chapters, we examined Hrxn, Hsoln, and Hºf
Enthalpy is a _____________function…
Identify the following reactions as exothermic or
endothermic. Does a decrease in enthalpy mean
a reaction proceeds spontaneously?
These are all
reactions:
CH4 (g) + 2O2 (g)
CO2 (g) + 2H2O (l)
H+ (aq) + OH- (aq)
H2O (l)
H2O (s)
NH4NO3 (s)
H2O (l)
H2O
NH4+(aq) + NO3- (aq)
H0 = - 890.4 kJ
H0 = - 56.2 kJ
H0 = 6.01 kJ
H0 = 25 kJ
18.2
So we see that a decrease in enthalpy does not mean a
reaction proceeds spontaneously.
What do we need to know in order to predict if a reaction
is spontaneous? Two things (p.577).
______________________________________________
…AND…
______________________________________________
The greater the disorder or randomness of a system,
the ___________________ _____ ________________.
The more ordered a system is, the less its ___________.
Entropy (S) is a measure of the _____________________
of a system.
order
disorder
S
S
S = Sf - Si
If the change from initial to final results in an increase in randomness
S > 0
Sf > Si
For any substance, the ____________ state is more ordered
than the ____________ state, and the ____________ state
is more ordered than ____________ state
Ssolid < Sliquid << Sgas
H2O (s)
H2O (l)
S > 0
18.2
Thermodynamics
__________________ _________________ are properties that
are determined by the state of the system, regardless of how
that condition was achieved.
energy, enthalpy, pressure, volume, temperature , entropy
Standard Entropy Values (S º)
for Some Substances at 25ºC
Potential energy of hiker 1 and hiker 2
is the same even though they took
different paths.
18.7
Processes that
lead to an
______________
in entropy
(S > 0)
p.579
18.2
Look at page 580, Example 18.1.
Let’s work through it together.
Then, let’s look at the Practice Exercise below it.
How does the entropy of a system change
for each of the following processes?
Ex.18.1, p.580
(a) Condensing water vapor
Randomness _______________ Entropy _______________
(b) Forming sucrose crystals from a supersaturated solution
Randomness _______________ Entropy _______________
(c) Heating hydrogen gas from 600C to 800C
Randomness _______________ Entropy _______________
(d) Subliming dry ice
Randomness _______________ Entropy _______________
18.2
First Law of Thermodynamics
Energy can be converted from one form to another,
but energy cannot be created or destroyed.
Second Law of Thermodynamics
The entropy of the universe increases in a spontaneous
process and remains unchanged in an equilibrium process.
Spontaneous process:
Suniv = Ssys + Ssurr > 0
Equilibrium process:
Suniv = Ssys + Ssurr = 0
18.3
Entropy Changes in the System (Ssys)
The ____________ _____________ of rxn
reaction (S0 ) is the
entropy change for a reaction carried out at 1 atm and 250C.
aA + bB
cC + dD
S0rxn = [ cS0(C) + dS0(D) ]
S0rxn = S nS0(products)
—
—
[ aS0(A) + bS0(B) ]
S mS0(reactants)
Sn = the sum of the stoichiometric coefficients of the products
Sm = the sum of the stoichiometric coefficients of the reactants
What does the superscripted zero mean?
18.3
Look at the bottom of page 581 and top of page 582,
Example 18.2.
Let’s work through it together.
Then, let’s look at the Practice Exercise below it.
Entropy Changes in the System (Ssys)
What is the standard entropy change for the following
reaction at 250C? 2CO (g) + O2 (g)
2CO2 (g)
S0(CO) = 197.9 J/K•mol
S0(CO
2)
= 213.6 J/K•mol
Where do we
get these values?
S0(O2) = 205.0 J/K•mol
S0rxn = 2 x S0(CO2) – [2 x S0(CO) + S0 (O2)]
S0rxn = 427.2 – [395.8 + 205.0] = -173.6 J/K•mol
18.3
You should work through
the other parts of this
Practice Exercise.
Entropy Changes in the System (Ssys)
When gases are produced or consumed
•
If a reaction produces more gas molecules than it
consumes, S0 > 0.
•
If the total number of gas molecules diminishes,
S0 < 0.
•
If there is no net change in the total number of gas
molecules, then S0 may be positive or negative—
BUT S0 will be a small number.
18.3
Look at page 582f, Example 18.3.
Let’s work through it together.
Then, let’s look at the Practice Exercise below it.
Entropy Changes in the System (Ssys)
What is the sign of the entropy change for the
following reaction? 2Zn (s) + O2 (g)
2ZnO (s)
Practice Exercise 18.3, part (b), page 583
18.3
Entropy Changes in the System (Ssys)
What is the sign of the entropy change for the
following reaction? 2Zn (s) + O2 (g)
2ZnO (s)
Since the total number of
gas molecules goes down,
S is negative.
Practice Exercise 18.3, part (b), page 583
18.3
You should work through
the other parts of this
Practice Exercise.
Entropy Changes in the Surroundings (Ssurr)
Exothermic Process
Ssurr > 0
Endothermic Process
Ssurr < 0
You should keep studying this until you understand it!
18.3
Third Law of Thermodynamics
The entropy of a perfect crystalline substance is zero
at the absolute zero of temperature.
18.3
“How can we tell if a reaction is spontaneous?”
You will soon have an answer to this question!
Spontaneous process:
Suniv = Ssys + Ssurr > 0
Substituting —Hsys/T for Ssurr
Multiply by T
Multiply by —1
Hsys
Suniv = Ssys —
>0
T
TSuniv = —Hsys + TSsys > 0
—TSuniv = Hsys — TSsys < 0
This says that for a process carried out at constant P and T,
if the changes in enthalpy (H) and entropy (S) of the system
are such that Hsys — TSsys is less than zero, then the
process must be spontaneous.
But we can predict spontaneity more directly….
p.586
18.4
Gibbs Free Energy (G)
G = H — TS
All quantities in the above equation refer to the system
For a constant-temperature process:
The change in Gibbs free energy (G)
____________________________________
If G is negative,
there is a release of usable energy,
and the reaction is spontaneous!
If G is positive, the reaction is not spontaneous!
18.4
For a constant-temperature process:
G = Hsys — TSsys
G < 0
The reaction is ___________ in the forward direction.
G > 0
The reaction is ________________ as written.
The reaction is ___________ in the reverse direction
G = 0
The reaction is _____________________ .
18.4
The _____________________________________
rxn
is the free-energy change for a reaction
when it occurs under standard-state conditions.
aA + bB
cC + dD
0
Grxn
= [cG0f (C) + dG0f (D) ] - [aG0f (A) + bG0f (B) ]
0
Grxn
= S nG0f (products) - S mG0f (reactants)
Sn = the sum of the stoichiometric coefficients of the products
Sm = the sum of the stoichiometric coefficients of the reactants
The superscripted zero means ______________________
18.4
Conventions for
Standard States
________________________
(G0f ) is the free-energy change
that occurs when:
* 1 mole of the compound
* is formed from its elements
* in their standard states.
Gf0 of anyf element in ______________________ is zero.
18.4
Look at page 587f, Example 18.4.
Let’s work through it together.
Then, let’s look at the Practice
Exercise below it.
What is the standard free-energy change for the following
reaction at 25 0C?
2C6H6 (l) + 15O2 (g)
12CO2 (g) + 6H2O (l)
0
Grxn
= S nG0f (products) - S mG0f (reactants)
0
Grxn
= [12G0f (CO2) + 6G0f (H2O)] - [ 2G0f (C6H6)]
0
Grxn
= [ 12x–394.4 + 6x–237.2 ] – [ 2x124.5 ] = -6405 kJ
Practice Exercise 18.4 (b), p.588
Is this reaction spontaneous at 25 0C?
18.4
What is the standard free-energy change for the following
reaction at 25 0C?
2C6H6 (l) + 15O2 (g)
12CO2 (g) + 6H2O (l)
0
Grxn
= S nG0f (products) - S mG0f (reactants)
0
Grxn
= [12G0f (CO2) + 6G0f (H2O)] - [ 2G0f (C6H6)]
0
Grxn
= [ 12x–394.4 + 6x–237.2 ] – [ 2x124.5 ] = -6405 kJ
Is this reaction spontaneous at 25 0C?
G0 = -6405 kJ < 0
This reaction is spontaneous
18.4
G = H — TS
If both H and S are positive, then G will be
negative only when the TS term is larger than H.
This occurs only when T is large.
If H is positive and S is negative, G will always
be positive—regardless of the temperature.
If H is negative and S is positive, then G will
always be negative regardless of temperature.
If H is negative and S is negative, then G will
be negative only when TS is smaller in magnitude
than H. This condition is met when T is small.
p.588
G = H — TS
Factors Affecting the Sign of G in the Relationship G = H — TS
p.589
18.4
Temperature and Spontaneity of Chemical Reactions
CaCO3 (s)
CaO (s) + CO2 (g)
At what temperature will this reaction become
spontaneous? Or…at what temperature
does Gº become zero—or negative?
1. Use Eqn 6.16 to calculate Hº
2. Use Eqn 18.4 to calculate Sº
3. Substitute these into Gº = Hº — TSº
to calculate Gº (130.0 kJ)
4. Since this is a large positive number, we set
Gº = 0 and solve the equation for T
Follow along on pp.589f
Temperature and Spontaneity of Chemical Reactions
CaCO3 (s)
CaO (s) + CO2 (g)
“Two points are worth making….”
[Read quote p.590.]
First, we used Hº and Sº values at 25ºC to calculate
changes that occur at much higher temperatures. Both Hº
and Sº change with temperature, so the Gº value will not
be accurate—but it is a helpful, ballpark estimate.
Second, don’t think nothing happens below 835ºC, and then
suddenly, at 835ºC, CaCO3 begins to decompose.
Look at the graph on the next frame to see what happens.
Temperature and Spontaneity of Chemical Reactions
CaCO3 (s)
CaO (s) + CO2 (g)
H0 = 177.8 kJ
S0 = 160.5 J/K
G0 = H0 – TS0
At 25 0C, G0 = 130.0 kJ
G0 = 0 at 835 0C
p.590
18.4
The condition G = 0 applies to any phase transition.
At the temperature at which a phase transition occurs,
the system is at equilibrium, so G = 0.
Substituting and rearranging,
G = H — TS
0 = H — TS
S = H/ T
Gibbs Free Energy and Phase Transitions
G0 = 0 = H0 – TS0
H2O (l)
S =
H2O (g)
H
40.79 kJ
=
T
373 K
= 109 J/K
18.4
Gibbs Free Energy and Chemical Equilibrium
G0 describes a reaction in standard state conditions
G must be used when the reaction is not in
standard state conditions
So we derive this equation: G = G0 + RT lnQ
R is the gas constant (8.314 J/K•mol)
At ________________
G = 0
T is the absolute temperature (K)
Q is the reaction quotient
Q=K
0 = G0 + RT lnK
G0
= - RT lnK
Kp for gases
Kc for reactions in solution
pp.592ff
18.4
G0 < 0
p.593
G0 > 0
18.4
G0 = - RT lnK
Relation between G0 and K as Predicted by G0 = - RT lnK
p.593
18.4
18.5
Alanine + Glycine
G0 = +29 kJ
ATP + H2O + Alanine + Glycine
G0 = -2 kJ
Alanylglycine
K<1
ADP + H3PO4 + Alanylglycine
K>1
18.5