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Chem 1310:
Introduction to physical chemistry
Part 1: Thermodynamics 2
Peter H.M. Budzelaar
The direction of chemical reactions
The total energy of the universe is constant, and so is
the energy of any isolated system.
But energy can change form, and this happens in
both chemical and physical changes.
Thermodynamics, in its more complete and
quantitative form, can tell you in which direction
such changes will go.
It will not tell you how fast they will go: you'll need
kinetics for that.
Free energy
The Gibbs free energy (DG) is the quantity that is
important for systems at constant T,p.
Free energy consists of enthalpy (see MSJ ch 6) and
entropy (will be explained here).
Reactions can happen whether they are endothermic
(DH > 0) or exothermic (DH < 0); they will not
happen when they are endergonic (DG > 0). This
has a lot of predictive power.
Energy, enthalpy and entropy
DE = energy change = q+w
At constant volume, no work done: DE = qV
For constant-pressure processes, enthalpy is more
appropriate:
DH = qP = heat transferred at constant pressure
(where work is done only to adjust the volume so
that p remains constant).
Energy, enthalpy and entropy
Enthalpy is not enough to predict the direction of a
reaction.
Dissolve NaOH and NH4Cl (separately) in water. Note the
temperature changes. One process is exothermic, the other
endothermic, yet both occur spontaneously!
To get any further, we need the idea of "entropy".
Entropy
Entropy is a somewhat diffuse concept. It is a
measure for the dispersion of energy (and matter)
over a system (or over its surroundings). If it is
defined in a proper, quantitative fashion, we have a
rule that says the entropy of the universe cannot
decrease ("second law").
Entropy and reversibility
The concept of entropy may be diffuse, but its
definition is not. For a reversible process, the entropy
change is defined as:
T in Kelvin! We are dividing
qrev
DS 
T
by an absolute temperature,
not a difference,
so the zero point matters.
Reversible: a process where a tiny change in
conditions would reverse the process.
During a reversible process, the system remains at
equilibrium. You disturb it a bit, then let it respond before
disturbing it further.
Reversibility
• Melting ice at 0°C is reversible: cooling a little bit
produces more ice, heating a bit yields more water.
• Melting ice at 10°C is not: if you cooled the
system a bit, ice would not re-form.
• Even if the process you are studying in a system is
irreversible, the change in the surroundings can be
carried out in a reversible manner (like adding
heat from something only slightly warmer than the
system).
Entropy
• Entropy can often be interpreted as "disorder", and
this "disorder" is zero (absent) for pure, crystalline
compounds at absolute zero (0K) ("third law").
• So, we can assign an absolute entropy S, not just a
relative value DS, to every compound under given
conditions:
Heat it from 0K to R.T. in small steps, and
measure the heat absorbed (at constant pressure)
 qrev  S.
Entropy
Entropy values can be (are) tabulated just like
enthalpies, and refer to standard conditions
(R.T., 1 bar). They have the dimension of
energy/temperature, or J K-1.
Note: energies are often tabulated in kJ; correct for the
factor 1000 differences when making comparisons!
Factors affecting entropy
• State: gas >> liquid > solid
(disorder between molecules)
• Rigidity: loose/floppy molecules > rigid molecules
(disorder within molecules)
• Solution > pure solid+solvent (usually!)
(but solute may enforce ordering of solvent)
• Solution < pure gas+solvent
Entropy does not decrease
("the arrow of time")
For any process, the entropy of a system may
increase or decrease, and same for surroundings, but
the entropy of the universe as a whole will never
decrease.
Calculating entropy changes
To use this idea, we need to be able to get/calculate
DSsystem and DSsurr for any process.
A spontaneous process happening in a system is not
reversible, so we cannot use eqn MSJ 18.3
(DS = qrev/T) directly.
Calculating entropy changes (2)
Trick: we assume the surroundings change
reversibly. That means:
DS surr
qrev ( surr ) DH ( surr )
DH ( sys )



T
T
T
So, we can calculate the change in entropy of the
surroundings from the change in enthalpy of the
system!
For the system itself we still need to get/measure
DSsys!
Entropy and free energy
Once we have DSsys and DSsurr:
DSuniverse = DSsys + DSsurr = DSsys - DHsys/T
We do not really want to work with the whole
universe all the time. And DSuniverse only depends on
properties of the system anyway. A useful definition
is:
DGsys = -T DSuniverse = DHsys - T DSsys
This is the "Gibbs free energy".
Free energy and
the direction of reactions
If it is DGsys<0, a reaction is spontaneous (but might
still be slow!)
If DGsys>0, the reaction will not go without "help".
This "help" must be something that at least
compensates for the positive DGsys of the reaction
being helped.
Any "excess" DGcomp will probably be wasted and
contributes only to warming the universe as a whole.
Enthalpy and entropy contributions
What can we say about a reaction?
• DH < 0, DS > 0: spontaneous
• DH > 0, DS < 0: will not happen
• DH < 0, DS < 0: don't know,
• DH > 0, DS > 0: need a calculation
Enthalpy and entropy contributions
Entropy-driven reactions (DH > 0, DS > 0):
• Evaporation of a liquid
• Dissolution of a solid in a solvent (NaCl in H2O)
Enthalpy-driven reactions (DH < 0, DS < 0):
• Reaction of two gases to form a solid
NH3+HClNH4Cl
• Precipitation of an insoluble salt
Ag+(aq)+Cl-(aq)  AgCl
• Formation of a polymer
n C2H4  (-CH2CH2-)n
Using tabulated values
Enthalpies, entropies and free energies are tabulaed
for standard conditions (1 bar): DH°, S°, DG°.
DH° and S° are not too temperature-dependent, and
can be used to estimate DG for different conditions
by using DH°, S° and the new T.
For solutions/gases, DH°, S° and DG° are for
standard concentrations (1 mol/L)/pressures (1 bar).
Free energies of reaction mixtures
For a reaction mixture under non-standard
conditions, corresponding to a specific reaction with
a given DG° under standard conditions:
DG = DG° + R T ln Q
where:
Q = QC for solutions
Q = QP for gases
Free energies and
equilibrium constants
At equilibrium, Q = K and DG = 0, so
DG = DG° + R T ln K = 0
DG 

 DG° = - R T ln K or K  e RT
where
K = KC for solutions
K = KP for gases
Equilibrium constants
depend on the temperature
DH° and DS° do not vary too much with temperature,
DS  DH 
but DG° = DH°-TDS° does, and so does K  e R  RT
Endothermic reactions (DH° > 0) become more
favourable at high temperature.
Exothermic reactions (DH° < 0) become less
favourable at high temperature.
The entropy changes gives a kind of temperatureindependent, intrinsic preference.
Equilibrium constants
depend on the temperature
DS  DH 
K e
R

RT
At low temperature, DH° dominates strongly and the
equilibrium will be very one-sided.
At high temperatures, DH° becomes unimportant and
DS° determines the product distribution.
For chemical reactions, we are usually in an
intermediate region.
The crossover temperature
There will be a temperature where K = 1:
DG° = 0  DH°-TDS°  T = DH°/DS°
Gibbs free energy
and coupled reactions
The Gibbs free energy shows whether there is a
driving or opposing force for a reaction. It also
places a limit on the amount of work we could
extract from this reaction.
The work could be done by coupling physical action
to the chemical reaction (as happens in a coal-fired
power plant or a car battery).
Gibbs free energy
and coupled reactions
Chemical coupling is also common. Metabolism
depends on coupling oxidation of carbohydrate etc to
formation of useful chemicals in the body. The main
biological energy carrier is ATP.
Muscle movement depends on the energy released in
the hydrolysis of ATP to ADP. This is (again)
coupling of chemical energy to physical movement.
actin
filament
Muscle movement
release of phosphate
induces movement
myosin
thick
filament
ATP binding
causes release
of actin
myosin-ADP complex
reattaches to actin
ATP hydrolysis causes
conformational change
http://www.kent.ac.uk/bio/geeves/Research/myo.htm
Gibbs free energy
and coupled reactions
We can often write reactions as coupled systems of
individual, simpler reactions. All thermodynamical
conclusions reached from that will be valid, even if
the reaction does not really follow the coupled path
(see e.g. MSJ p654).
Gibbs free energy
and coupled reactions
CH4 + ½ O2  CO + 2 H2
CO + 2 H2  CH3OH
CH4 + ½ O2  CH3OH
It would be nice if we could do this as one (coupled)
reaction. In practice, the first one is spontaneous at
low temperature, the second requires energy, and we
lose a lot because we cannot use the energy liberated
in the first step effectively.
Gibbs free energy
and coupled reactions
With the right catalyst, we might eventually be able
to do this better, by following a different mechanism
that is more complex and directly produces the final
CH3OH product without actually going through the
CO and H2 intermediates. Conclusions about
equlibrium will not change, but our production of
CH3OH will be more efficient and produce less
waste heat.
Stability
Chemists talk about "stable" and "unstable"
compounds. These terms are not very welldefined.
"Stable" usually means you can put the compound in
a bottle, store it for a long time, study it.
But it is also used to denote compounds that are "low
in energy".
These two things are not equivalent.
Types of stability
CO2: would usually be called "stable"
CH4: all decomposition routes are endothermic, but
the reaction with oxygen is highly exothermic!
C2H2: decomposition to C(s) and H2 is exothermic,
but only happens on heating or compression.
CH3Na: stable under nitrogen, but inflames in air.
CH3Ag: decomposes explosively above -80°C.
Types of stability
Thermodynamically stable:
if no reaction can produce a compound that is
lower in free energy.
We would call CO2 thermodynamically stable.
Kinetically stable:
if every reaction that is exergonic has an
appreciable activation barrier.
We would call C2H2 kinetically stable.
Stability depends on environment
CO2 would not be called "stable" in an atmosphere
of ammonia. It would form urea or ammonium
carbonate.
H2O would not be stable in an atmosphere of
fluorine.
CH3Na would be called stable in a nitrogen
atmosphere.
Magnesium and lithium should not be!
Concentration of energy
Compounds that are high in energy (relative to
feasible reactions) provide a concentrated form of
energy, easy to use for coupling to (endergonic)
reactions.
C can be used to reduce CuO
Sn is a much weaker reductant
Just using "more" of a less "energetic" compound
doesn't work because most chemistry is
stoichiometric.
Not all forms of energy are the same
Mechanical and electrical energy can more easily be
"concentrated".
Use pulleys to switch between one weight high up or
many weights at lower height.
Use a transformer to switch between high and low
voltages.
Not all forms of energy are the same
Heat is the least useful form of energy. It is already
very "spread out". It can only be partially
converted into other forms, and then the remainder
becomes even more spread out.
When everything in the universe is at the same
temperature and in chemical equilibrium, nothing
can happen any more. This is called "heat death"
(although is will actually be quite cold).
Light - the "ultimate" energy source
Light is important as an energy source because of its
"quality".
Two photons of visible light (wavelength of 6000Å)
are enough to cleave a strong single C-C bond.
To do the same thing by heating would require a
temperature of thousands of K.
Light is "concentrated energy", with great potential
for conversion to "useful work".
Energy content of a photon
4000Å
e = hn = hc/l
= (6.6*10-34Js)*(3*108m/s)/(6000*10-10m)
= 3.3*10-19 J per photon
or 198 kJ/mol per NA photons.
A C-C bond is ca 356 kJ/mol.
Converting water back into H2 + ½O2 costs about
286 kJ/mol.
7000Å
Photosynthesis
The "challenge" of photosynthesis is to harvest
photons and convert their energy selectively into
things cells need:
• short-term energy carriers (ATP)
• useful chemicals: reduced species that can be used
to reduce other molecules, producing long-term
energy carriers (carbohydrates, lipids)
• oxygen is only a by-product!
Photosynthesis
We would like to do something like:
H2O + CO2 + light  CH2O + O2
But just shining light on a mixture of water and CO2
does not cause this to happen!
• light needs to be absorbed
• its energy needs to be channeled
Chlorophyll a
Photosynthesis
Light causes ejection of an electron from chlorophyll.
The electron eventually serves to reduce NADP+ to
NADPH.
This can then be re-oxidized in an exothermic reaction that
also produces ATP.
The positive charge eventually
oxidizes water to O2.
NADP+
Light - the "ultimate" energy source
Except for nuclear energy and "tidal" energy, we
depend entirely on (past and present) sunlight for
our energy needs.
The ultimate energy source for us would be direct
conversion of light into a concentrated, useful
form of energy, e.g. electricity.
This can be done now, although the cost is
significant and the efficiency not yet satisfactory.
Photovoltaic cells
semiconductor
Issues:
stability, yield, efficiency, (energy) cost of production.