Download Entropy, free energy and equilibrium

Entropy, free energy and
equilibrium
Spontaneity
Entropy
Free energy and equilibrium
Learning objectives
 Discuss what is meant by spontaneity
 Discuss energy dispersal and its relevance
to spontaneity
 Describe the concept of a reversible process
 Define entropy
Equilibrium
 At an equilibrium point, the system resists small
disturbances (not necessarily large ones)
unstable
Locally
stable
more
stable
 At equilibrium, the rates of the forward and
backward processes are equal
Spontaneity
 The tendency for a process to advance to
equilibrium without external influence
 Something that happens naturally is spontaneous
 Any process will be spontaneous in one direction
 The reverse is non-spontaneous
 If work needs to be done, it is not spontaneous
 A rock naturally rolls down a hill - spontaneous
 It must be pushed back up - nonspontaneous
 A hot object naturally cools - spontaneous
Indicators of spontaneity
 What is the indicator of spontaneity?
 Heat evolved?
 But…endothermic reactions occur spontaneously
as well (ice melting, salt dissolving)
 Enthalpy is not an indicator of spontaneity,
although most spontaneous processes are
exothermic – energy is conserved not created
 The amount of energy does not change in any
process – but it is redistributed...
Various spontaneities: dispersal
 Matter disperses – gas fills a container, two
liquids mix
 Heat disperses – hot object cools on cold
surface
 Motion disperses – a ball stops bouncing
 The reverses of these three well known
processes never occur spontaneously
Reversibility
 A reversible process is one where the
system and surroundings are changed to
original values without any change
 An irreversible process is one where the
system and surroundings cannot be
restored
 A reversible process produces the maximum
possible work
Reversibility and reality
 Reversibility only occurs when the system is
in or almost at equilibrium – at an
infinitesimal rate
 In reality this does not obtain
 Real processes produce less work than
ideal processes
 Spontaneous processes are irreversible
 The reverse of a spontaneous process is
nonspontaneous
Spontaneity and speed
 The speed of a reaction is not an indicator of
its spontaneity.
 Spontaneity is determined by the relative
positions of the initial and final states
(thermodynamic state functions)
 Speed is determined by the pathway
(kinetics)
 Two independent regimes
Entropy – the mixing (distributing) link
 entropy measures distribution of energy over
states
 The more states available, the more entropy
 It is a “state function” – depends only on initial and
final states, not the pathway.
 The entropy change for a process is
S  S final  Sinitial
 Systems move spontaneously to a state of greater
entropy – greater distribution of energy
 Disorder provides more states for energy
distribution than ordered systems
Why do crystals form at all?
 Entropy is distribution of energy over
microstates
 Crystals are highly ordered arrangements
 Crystals should spontaneously fly apart to
maximize disorder
 But...This view ignores energy of the lattice
 Energy input to break bonds corresponds to
entropy decrease (localization of energy)
Don’t let them fool you
 A popular argument against evolution is that the
formation of organized DNA molecules from a
random soup of atoms and molecules contravenes
Second Law
 Just as crystals appear in a dish spontaneously so
can DNA form from smaller units
 N.B. Order (energy concentration) can appear
spontaneously locally provided greater disorder
(energy dispersal) is occurring elsewhere
Entropy and solubility
 Hydration increases entropy of the ions in
the lattice
 Ions in solution have greater disorder
 but can decrease entropy of the solvent
 Solvent molecules now have greater order
 Excessive hydration by highly polarizing
ions can reduce entropy of solvent
 CaSO4 is only slightly soluble
What will these socks ne’er be
matched?
 Would you be stunned
if the tumble dryer
matched the socks?
 Okay, you never match
the socks anyway
 Chaos in the sock
drawer is natural
 The same principles
are applied to
chemical change (sort
of)
Chance meeting: entropy and
probability
 Ordered states are less likely because there are
fewer ways to obtain them
 Do our socks become matched spontaneously?
 No, only one of many possible arrangements
 With only a few molecules the ordered state
becomes massively less probable than a
disordered state
Boltzmann and disorder
S  k ln W
 W is the number of possible arrangements
of the state
 k is Boltzmann’s constant =
 R/NA = 1.38x10-23 J/K
 The entropy is proportional to the natural log
of the number of arrangements of the state
Entropy of a disordered system
 An ordered arrangement has W = 1, S = 0
 Entropy of one mole of disordered
molecules
S  k ln W  k ln 2
 S = 5.76 J/K
NA
 kNA ln 2  R ln 2
Entropy and gas expansion
 There is only one possible way for all the gas
molecules to fill A and leave B empty. There are
ways 2 N A for NA molecules to occupy A and B
 Entropy associated with gas mixing
 Entropy associated with gas expansion:
Doubling the volume doubles the number of
positions (microstates) for distribution of energy
S  R ln
V final
Vinitial
Making sense of units and definition
of entropy
 Units of entropy are J/K
 How do these units connect to disorder and
probability?
 Disorder is not entropy
 Disorder increases the number of microstates
available
 Clausius definition of entropy is:
Change in entropy = (heat supplied)/temperature
S sys
q

T
Work and gas expansion
 Work associated with isothermal reversible
 V2 
expansion of gas
w  nRT ln  
rev
 V1 
 Isothermal means that ΔE = 0 = qrev + wrev
 But...
V 
qrev  wrev  nRT ln  2 
 V1 
Ssys
V 
nRT ln  2 
q
 V1   nR ln  V2 
 rev 
 
T
T
 V1 
 Equivalent to result obtained from consideration of
arrangements
Les Regles du Jeu
(Rules of the game)
Thermodynamics is the Law
 First Law: The total energy of a system and its
surroundings is constant in any process
Esys  q  w
 Second Law: In any spontaneous process, the
total entropy of a system and its surroundings
increases
Stot  0
Third Law of Thermodynamics
 The entropy of a perfectly ordered
crystalline substance at 0K is zero
 Increasing T causes increase in entropy through
molecular motion (rotational, vibrational and
translational), and changes of state
Entropy and temperature
 Disorder and motion
 Greater motion corresponds to greater number of
microstates – entropy increases with T
Entropy of a system increases with T
 Increasing T increases entropy through
greater molecular motion
 In a solid an increased number of vibrational
energy states – more ways to distribute energy
 Phase changes cause step change because
of increased number of microstates in less
condensed phase
Standard molar entropy
 S° The entropy of one mole of the pure
substance at 1 atm pressure and a specified
temperature, usually 25°C
 Determined experimentally from heat capacity
measurements
Comparison of different substances
 Gases have highest values
 Solids have the lowest values
Standard entropy of reaction
S  S
o
o
products
S
o
reactants
In the reaction N2O4 = 2NO2
o
o
S o  2S NO

S
N 2O4
2
 Products have more particles than reactants
 Predicting entropy change from chemical
equation by counting particles
Entropy: connecting the microscopic
to the macroscopic
 Microscopic:
 Measure of microstates and disorder
 Macroscopic:
 Indicator of spontaneous process
Three results

Stot  S sys  S surr
 Stotal > 0 the process is spontaneous
 Stotal < 0 the process is nonspontaneous
 Stotal = 0 the process is at equilibrium
Surroundings
 Entropy change for the system is obtained
from the entropies of the initial and final
states
 What about the surroundings?
 At constant pressure, the entropy change in
the surroundings is related to the enthalpy
change for the system
S surr   H
T
Enthalpy change of system determines
entropy change of surroundings
 Heat released by the system increases the
disorder of the surroundings.
 The effect of this is modulated by the
temperature:
 At low temperature the effect is much more
significant
 At high temperature, where there is already
considerable disorder, the effect is muted – the
difference between tossing a rock into a calm
pool (low T) and a storm-tossed ocean (high T)
Land of the Free... Energy
 Since Stotal is obtained from the Ssystem
and the ΔHsystem, everything can be written
in terms of the system:
 Gibbs free energy
G  H  TS
 State function, depends only on initial and final
states
G  H  TS
Significance of ΔG
Stot  S sys  S surr
 But from before,
Stot  S sys 
TStot
 So…
H sys
T
 TS sys  H sys
TStot  G
ΔG is indicator of spontaneity
G  TStot
1. ΔG < 0 reaction always spontaneous
2. ΔG > 0 reaction always nonspontaneous
3. ΔG = 0 reaction at equilibrium
The Gibbs Free Energy is a measure of the
total entropy change
Four possible conditions
ΔH
+
+
ΔS
ΔG
+
-
-
- Or
+
-
+
+
- Or
+
Spontaneity
Example
Spontaneous at all T
2NO2 = N2 + 2O2
Spontaneous at low T,
nonspontaneous at high T
N2 + 3H2 = 2NH3
Nonspontaneous at all T
3 O2 = 2 O3
Spontaneous at high T,
nonspontaneous at low T
2HgO = Hg + O2
Standard free energies
 Solids liquids and gases in pure form at 1atm
pressure
 Solution at 1 M concentration
 Standard temperature usually 25°C
 Standard free energy change:
ΔG°
Change in free energy that occurs when reactants in
standard states are converted to products in their
standard states
ΔG° as a predictor of reactions
 Consider the reaction
N 2 ( g )  3H 2 ( g )  2 NH 3 ( g )




We want to calculate ΔG°
Need ΔH° and ΔS°
ΔH° is equal to ΔH°(formation) for NH3
ΔS° comes from the S° values for the reactants and
product
ΔH° = 2 x -46.1 kJ/mol = -92.2 kJ/mol
ΔS° = -198.7J/mol K
ΔG°(25°C) = -92.2 – 298x-198.7x.001 kJ/mol
= -33.0 kJ/mol
Standard free energy of formation
 The free energy of formation of one mole of
the substance in its standard state from the
most stable forms of the elements in their
standard states
 Thus the ΔG°f for NH3 is given by
-33.0/2 kJ/mol = -16.5 kJ/mol
 Elements in the standard state have ΔG°f = 0
Standard free energy of formation of
some common compounds
Substance
Formula
ΔGfº/kJ
/mol
Substance
Formula
ΔGfº/kJ/
mol
NO2
51.3
H2O
-237.2
Acetylene
C2H2
209.2
Nitrogen
dioxide
Ammonia
NH3
-16.5
Water
Carbon
dioxide
CO2
-394.4
Diamond
C
2.9
Ethylene
C2H4
68.1
Graphite
C
0
The importance of the state
 Using reactants in different states will
require modification to calculation for ΔG°
 Consider graphite and diamond – two forms
of carbon. Is it perhaps surprising that
diamond is less stable than graphite?
ΔG°f (diamond) = 2.9 kJ/mol
 Free energy change for conversion of
diamond into CO2 is larger than for
conversion of graphite into CO2
ΔG°f and stability
 Many common compounds are unstable
with respect to their elements – NO2, C2H4
and C2H2
 They will spontaneously decompose to the
elements according to thermodynamics
 However, they are generally regarded as stable
 Kinetic barriers prevent rapid decomposition
Thermodynamic functions and
chemical processes
 The foolish man builds his process on a foundation without
ΔGfº
 ΔG°f calculations can save a lot of unnecessary work
 Indicates favourability of a reaction under standard
conditions
 If unfavourable, need to either modify the conditions or
explore alternative synthesis pathways
 Example:
 The formation of NO is not favoured from N2 and O2;
 but it is favoured by reaction of O2 with NH3
Accounting for actual conditions
 In most reactions, the reactants and products are
not in standard states
G  G  RT ln Q
o
Q is the reaction quotient – similar in form to K
 Pressures for gases
 Concentrations for liquids
N 2 ( g )  3H 2 ( g )  2 NH 3 ( g )
Q
2
NH 3
3
N2 H 2
p
p p
Free energy and equilibrium
 Q «1, ΔG < 0 Drives towards products
 Q » 1, ΔG > 0 Drives back towards reactants
 At equilibrium, ΔG = 0
ΔG° = -RT ln K
Relationship between ΔGfº and K
ΔGº Ln K
<0
>0
=0
>0
<0
=0
K
>1
<1
1
Comment
Mainly products
Mainly reactants
Even ratio of reactants and
products