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CHEM 11132
Thermodynamics
Textbooks
P. W. Atkins
The Elements of Physical Chemistry (Third Ed., Ch. 10)
P. W. Atkins
Physical Chemistry
Any Physical Chemistry Text Book; Levine, Daniel &
Alberty, Barrow.
Thermodynamics
• Thermodynamics is the branch of physical chemistry
that provides a macroscopic description of systems at
chemical equilibrium, based on energy
transformations. [Thermodynamics: The science of energy]
• A macroscopic description is based on the properties
of bulk matter rather than individual atoms and
molecules.
• A microscopic description deals with the atomic and
molecular level, as in quantum mechanics.
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Approaches to studying thermodynamics
– Macroscopic (Classical thermodynamics)
• study large number of particles (molecules) that make up the
substance in question
• does not require knowledge of the behavior of individual
molecules
– Microscopic (Statistical thermodynamics)
• concerned within behavior of individual particles (molecules)
• study average behavior of large groups of individual particles
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What is Energy?
Energy is the capacity to do work
Energy is the capacity to do work
•
Radiant energy comes from the sun and is
earth‟s primary energy source
•
Thermal energy is the energy associated with
the random motion of atoms and molecules
•
Chemical energy is the energy stored within the
bonds of chemical substances
•
Nuclear energy is the energy stored within the
collection of neutrons and protons in the atom
•
Potential energy is the energy available by virtue
of an object‟s position
Energy Changes in Chemical Reactions
Heat is the transfer of thermal energy between two bodies that
are at different temperatures.
Temperature is a measure of the thermal energy.
Temperature = Thermal Energy
900C
400C
Thermochemistry is the study
of heat change in chemical
reactions.
Systems & Surroundings
In thermodynamics, the world is
divided into a system and its
surroundings
A system is the part of the
world we want to study (e.g. a
reaction mixture in a flask)
The surroundings consist of
everything else outside the
system
System and Surroundings

System - the part of the world, with
defined boundaries, in which we have a
special interest.

Surroundings - The area outside the
system. The surroundings are separated
from the system by boundaries..

Boundary - real or imaginary layer that
separates the system from its
surroundings
system
surroundings
Changes in a system are associated with the
transfer of energy

Unstable: falling or rolling

Stable: at rest in lowest energy
state

Metastable: in low-energy perch
Natural systems tend toward states of minimum energy
SYSTEM
OPEN
ISOLATED
CLOSED
Types of Systems

Open - exchanges matter
and energy with
surroundings.

Closed - exchanges only energy
with surroundings.

Isolated - no interchange with
surroundings.
Matter
Energy
Energy
open
Exchange: mass & energy
closed
isolated
energy
nothing
Getting Started
All of thermodynamics can be expressed in
terms of four quantities
Temperature (T)
Internal Energy (U)
Entropy (S)
Heat (Q)
These quantities will be defined as we progress
through the lesson
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Properties
Any characteristic of a system in equilibrium is called a
property.
Intensive property are independent of the amount of
material present:
e.g. Density (D), Pressure (P), Temperature(T)
Extensive property are dependent on the amount of
material present:
e.g. Volume (V), Mass (m), Total energy
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State & Equilibrium
State of a system
• system that is not undergoing any change
• all properties of system are known & are not changing
• if one property changes then the state of the system
changes
Thermodynamic equilibrium
• “equilibrium” - state of balance
• A system is in equilibrium if it maintains thermal (uniform
temperature), mechanical (uniform pressure), phase
(mass of two phases), and chemical equilibrium
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Processes & Paths
Process
• when a system changes from one equilibrium state to
another one
• some special processes:
• isobaric process
- constant pressure process
• isothermal process - constant temperature process
Path
• series of states which a system passes through during a
process
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Compression Process
DV = Vfinal - Vinitial
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State functions are properties that are determined by the state
of the system, regardless of how that condition was achieved.
energy, pressure, volume, temperature
DE = Efinal - Einitial
DP = Pfinal - Pinitial
DV = Vfinal - Vinitial
DT = Tfinal - Tinitial
Potential energy of hiker 1 and hiker 2
is the same even though they took
different paths.
Exothermic process is any process that gives off heat –
transfers thermal energy from the system to the surroundings.
2H2 (g) + O2 (g)
H2O (g)
2H2O (l) + energy
H2O (l) + energy
Endothermic process is any process in which heat has to be
supplied to the system from the surroundings.
energy + 2HgO (s)
energy + H2O (s)
2Hg (l) + O2 (g)
H2O (l)

Exothermic process –
to its surroundings

Endothermic process –
to its surroundings
24
Direction of
heat flow
Sign
Reaction
Type
Heat flows
OUT of the
system
Negative –
“Losing heat”
Exothermic
Heat flows
INTO the
system
Positive +
“Gaining heat”
Endothermic
© 2009 Brooks/Cole - Cengage
ΔH - change in heat content for a reaction at
constant pressure.
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Enthalpy (H) is used to quantify the heat flow into or out of a
system in a process that occurs at constant pressure.
DH = H (products) – H (reactants)
DH = heat given off or absorbed during a reaction at constant pressure
Hproducts > Hreactants
DH > 0
Hproducts < Hreactants
DH < 0
Thermodynamics States - state variables
A state variable describes the state of a system at
time t, but it does not reveal how the system was
put into that state.
Examples of state variables:
• P = pressure (Pa or N/m2),
• T = temperature (K),
• V = volume (m3),
• n = number of moles, and
• U = internal energy (J).
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Temperature is a measure of the thermal energy.
Temperature = Thermal Energy
Heat, q,
is energy in transit as a result of a temperature difference.
Temperature, T
is an intensive property that is used to define the state of a
system and determines the direction in which energy flows
as heat.
Diathermic
Walls that permit
the passage of
energy as heat are
called diathermic.
Eg. Metal container
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Adiabatic
Walls that do not
permit heat to pass
through even though
there is a difference
in temperature are
called adiabatic*.
Eg. Wall of a vacuum flask
(*from the Greek word for „not passing through‟)
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Internal energy (U)
Internal energy is defined as the energy associated
with the random, disordered motion of molecules.
The internal energy is the total energy contained in a
thermodynamic system.
Internal energy has two major components, kinetic
energy and potential energy.
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The internal energy is the grand total energy of the system.
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UNITS OF ENERGY
S.I. unit of energy is the joule (J)
Heat and work ( energy in transit) also measured in
joules
1 kJ (kilojoule) = 103 J
Calorie (cal): 1 cal is the energy needed to raise
the temperature of 1g of water by 1oC
1 cal = 4.184 J
Energy
Kinetic
energy
(EK)
Energy due
to motion
Potential
energy
(EP)
Energy due to
position (stored
energy)
Total Energy =
Kinetic Energy
+
E
EP
=
EK
+
Potential Energy
Kinetic energy & potential energy are interchangeable
Ball thrown upwards
slows & loses kinetic
energy but gains
potential energy
The reverse
happens as it falls
back to the ground
Energy and Its Conservation
Energy cannot
be created or
destroyed; it
can only
change forms
First law of thermodynamics – energy
can be converted from one form to another,
but cannot be created or destroyed.
DEsystem + DEsurroundings = 0
or
DEsystem = -DEsurroundings
C3H8 + 5O2
Conservation
of energy
3CO2 + 4H2O
Exothermic chemical reaction!
Chemical energy lost by combustion = Energy gained by the surroundings
system
surroundings
In chemistry, we are normally interested in the energy changes
associated with the system, not with its surroundings.
Therefore, a more useful form of the first law is:
(for DEsystem)
DE = q + w
q is the heat exchange between the system and the surroundings
w is the work done on (or by) the system
w = -PDV when a gas expands against a constant external pressure
Internal Energy
ΔU = Q + W
Heat Energy
(Conservation of Energy)
Work Done
Work and Heat
Example:
an example of energy leaving a
system as work
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System did work in
pushing the piston
upward
Dx
W = Fd
= (PA)∆x
W =-Pex ∆V
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Work
work can be defined as force F
multiplied by distance d :
System did work in
pushing the piston
upward
W = Fd
= (PA)∆x
W =-Pex ∆V
{const. external press.}
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Work Done On the System
w=Fxd
w = -P DV
DV > 0
-PDV < 0
wsys < 0
Work is
not a
state
function!
Dw = wfinal - winitial
initial
final
A sample of nitrogen gas expands in volume from 1.6 L to
5.4 L at constant temperature. What is the work done in
joules if the gas expands (a) against a vacuum and (b)
against a constant pressure of 3.7 atm?
w = -Pex DV
(a)
DV = 5.4 L – 1.6 L = 3.8 L
P = 0 atm
W = -0 atm x 3.8 L = 0 L•atm = 0 joules
(b)
DV = 5.4 L – 1.6 L = 3.8 L
P = 3.7 atm
w = -3.7 atm x 3.8 L = -14.1 L•atm
101.3 J = -1430 J
w = -14.1 L•atm x
1L•atm
Practice Exercise
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Work done by an expanding gas, constant pressure:
Isobaric
If the volume stays constant, nothing moves and no
work is done.
Isochoric
Reversible and irreversible processes
maximum work
w = -Pex DV
Maximum work is
obtained when the
external pressure is
only infinitesimally less
than the pressure of the
gas in the system.
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A process that can be reversed by an
infinitesimal change in a variable—in this case, the
pressure—is said to be reversible.
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In contrast, an expansion against a fixed external pressure
Proceeds at a finite rate until the internal and external
Pressures are equalized.
Irreversible process
Spontaneous processes are inheretantly irreversible.
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Reversible processes
•
•
•
infinitely slow
at equilibrium
do maximum
work
Irreversible processes
(spontaneous)
•
•
•
go at finite rate
Not at equilibrium
do less than the
maximum work
Reversible processes are also called equilibrium processes
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The work of reversible isothermal expansion
If the temperature is constant, the
pressure varies inversely with the
volume.
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For a gas to expand reversibly, the external pressure must be
adjusted to match the internal pressure at each stage of the
expansion
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FOUR THERMODYNAMIC PROCESSES:
• Isochoric Process:
DV = 0
• Isobaric Process:
DP = 0
• Isothermal Process: DT = 0
• Adiabatic Process:
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DQ = 0
ADIABATIC PROCESS:
NO HEAT EXCHANGE, D Q = 0
DU
Work Out
DQ = 0
+DU
Work
In
Work done at EXPENSE of internal energy
INPUT Work INCREASES internal energy
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ADIABATIC EXAMPLE:
PA
A
B
PB
V1
Insulated
Walls: DQ = 0
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V2
Expanding gas does
work with zero heat
loss. Work = -DU
The measurement of heat
Temperature is a measure of the thermal energy.
When a
substance is
heated, its
temperature
typically rises.
Heating Curves
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The measurement of heat
reaction
reaction
Exothermic reaction, heat
given off & temperature of
water rises
Endothermic reaction, heat
taken in & temperature of
water drops
Heat
↔
Temperature
For a specified energy, q, transferred by heating,
the size of the resulting temperature change, ΔT,
depends on the „heat capacity‟ of the substance.
The heat capacity, C, is defined as:
J K-1
Heat
↔
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Temperature
Extensive property
(a property that depends on the
amount of substance in the sample)
2 kg of iron has twice the heat capacity of 1 kg
of iron, so twice as much heat is required to
raise its temperature by a given amount.
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A brief illustration
If the heat capacity of a beaker of water is 0.50 kJ K-1,
and we observe a temperature rise of 4.0 K, then we can
infer that the heat transferred to the water is:
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It is more convenient to report the heat capacity of a substance as an
intensive property
(a property that is independent of the amount of substance in the sample).
specific heat capacity, Cs,
molar heat capacity,Cm,
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Cs = C / m
J K-1 g-1
Cm = C / n
J K-1 mol-1
Differential forms
So far we have written the First Law as,
ΔU = Q + W
where the Δ implies a finite change in U.
We could just as well have written it for an infinitesimal
change in U, using the language of calculus:
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w = -Pex DV
if this is the only kind of work done, the First Law can
be written
{pV work only}
Work due to gas expansions is sometimes called "pV work".
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Unless we say otherwise, we will assume that the
only kind of work done is that due to gas expansions,
and so use the form of the First Law as:
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Constant volume processes
If we imagine a process taking place
in a sealed container,
at constant volume, then no work can be
done as the gas cannot expand
0
{constant volume}
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If we want to measure ΔU ……………?
all we have to do is measure the heat change under
constant volume conditions.
Heat capacities (re-visit)
For infinitesimal quantities this relationship becomes
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For chemical substances it is convenient to use the molar
heat capacity, Cm,
which is the amount of heat needed to raise one
mole of the substance through one degree.
Cm = C / n
m
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J K-1 mol-1
For a process taking place at constant volume,
,m
where CV,m is the molar heat capacity at constant volume.
Writing this in the differential form,
,m
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{constant volume}
where we are now assuming that dU is the change
in internal energy per mole (i.e. n = 1).
Mathematically, this can be expressed as a partial
derivative:
{definition of CV,m}
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Constant pressure processes – enthalpy
Processes taking place under constant pressure conditions are
more common, especially in chemistry, where open apparatus
"on the bench" can be considered to be at constant pressure.
If we heat a gas at constant
external pressure it will expand
and by doing so it will do work
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For a given amount of heat, the increase in the
internal energy will be less in a constant pressure
process than in a constant volume one on account of
part of the heat being converted to work.
It will be convenient to have a state function whose
value is equal to this heat supplied at constant
pressure;
Enthalpy (H) ~ heat content (q) @ constant pressure
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The function we need is called the enthalpy, H and it
is defined as
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86
Properties of Enthalpy
• Since P, and V are all state
functions, enthalpy H must be a
state function also.
• Enthalpy changes have unique
values. DH = qP
Enthalpy change depends
only on the initial and
final states.
• Enthalpy is an extensive property.
– It depends on how much of the
substance is present.
Prentice Hall © 2005
Two logs on a fire give
off twice as much heat
as does one log.
Chapter Six
Enthalpy change (dH)
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Enthalpy change (dH)
(p + dp)
(V + dV)
(U + dU)
As a result of the changes in p, V and U, it is clear that H
will also change by a small amount, dH
(H + dH)
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Multiplying this out gives
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from the First Law
Now we substitute in the First Law, in the form of the
expression for dU,
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Finally, we impose the condition of constant external pressure,
Heat change measured under conditions of constant pressure.
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Constant-Pressure Calorimetry
Coffee-cup calorimeter
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Heat capacity at constant pressure
{constant pressure}
where Cp is the constant pressure molar heat capacity.
{definition of Cp,m}
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Variation of enthalpy with temperature
Suppose we know the (molar) enthalpy, H(T1), of a
substance at a particular temperature, T1,
but we want to know its (molar) enthalpy, H(T2), at another
temperature T2.
Heat capacities are the key to finding how H varies with T.
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Heat capacities are the key to finding how H varies with T.
rearrange this to give
{constant pressure}
Both sides of the Eq. can be integrated. First the left-hand side
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Both sides of the Eq. can be integrated. First the left-hand side
The right-hand side of Eq. is also integrated,
and we make the additional assumption that Cp does not vary
with temperature,
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Putting the left- and right-hand sides together we have
This is a practical relationship:
if we know H at one temperature and the heat capacity, we
can work out H at any other temperature (assuming that it is
valid to consider Cp as constant in this range).
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Second law of thermodynamics
Second Law:
The entropy of the Universe increases in a
spontaneous process.
Spontaneity
Reaction will occur ―naturally‖
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Spontaneous Physical and Chemical Processes
• A waterfall runs downhill
• A lump of sugar dissolves in a cup of coffee
• At 1 atm, water freezes below 0 0C and ice melts above 0 0C
• Heat flows from a hotter object to a colder object
• A gas expands in an evacuated bulb
• Iron exposed to oxygen and water forms rust
spontaneous
nonspontaneous
spontaneous
nonspontaneous
The Second Law states that the entropy of the Universe must
increase in a spontaneous process.
Entropy (S) is a measure of the randomness or disorder
of a system.
The entropy change of the Universe can
then be calculated from
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Entropy (S) is a measure of the randomness or disorder
of a system.
More ordered
Less random
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Less ordered
More random
Solids
Highly ordered
⇒ low entropy
Liquids
Less ordered
⇒ medium entropy
Gases
Highly disordered
⇒ high entropy
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Entropy
State functions are properties that are determined by the state
of the system, regardless of how that condition was achieved.
energy, enthalpy, pressure, volume, temperature , entropy
Potential energy of hiker 1 and hiker 2
is the same even though they took
different paths.
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We saw that the entropy of a substance increases as it is
heated.
Formally, entropy is defined as
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The direction of spontaneous change
The apparent driving force of spontaneous
change is the tendency of energy and matter to
become disordered.
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Dispersal of matter
Dispersal of energy
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In summary, we have identified two basic types of spontaneous
physical process:
1. Matter tends to become disordered.
2. Energy tends to become disordered.
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2nd Law of Thermodynamics
113
A reaction is spontaneous if ∆S for the universe is positive.
∆Suniverse = ∆Ssystem + ∆Ssurroundings
∆Suniverse > 0 for spontaneous process
First calc. entropy created by matter dispersal
(∆Ssystem)
Next, calc. entropy created by energy
dispersal (∆Ssurround)
Entropy change of the system
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Entropy change of the surroundings
Now, the heat that the surroundings absorbs comes from
the system so:
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Entropy change of the Universe
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Measuring entropy
Entropies can be evaluated from measurements of heat
capacities in the following way.
The definition of entropy is, in differential form
a process at constant pressure,
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Next we use the definition of the constant pressure heat capacity
to express dH in terms of Cp :
Substituting this into above Eq. gives
{const. pressure}
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To find the entropy at temperature T* both sides are
integrated from T = 0 up to T*
Measuring heat capacities right down to absolute zero is not a
particularly easy task.The entropy values determined in this
way are called absolute entropies.
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Converting entropies from one temperature to another
It will therefore be convenient to have a way of converting
the value of the entropy from one temperature to another,
just as we did for enthalpies
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This is a practical relationship for converting entropies from
one temperature to another.
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Second law states:
• Entropy of the Universe must increase
in a spontaneous process
DSuniv  0
spontaneou s
DSuniv  0
equilibrium
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The spontaneity of chemical reactions
Do we have to keep calculating ∆Suniv ?
Not necessarily!
A convenient way of using second law……
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at constant pressure,
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Multiplying through by –T , we obtain
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Gibbs Free Energy
The Gibbs Free Energy is a new
state function, defined as:
G  H  TS
Sometimes the Gibbs energy is
called "the Gibbs free energy", "the
Gibbs function "or simply "the free
energy".
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Josiah Willard Gibbs
(1839-1903)
At constant T and P, consideration of ∆G will answer the
question ―Will a given reaction be spontaneous?‖
DG < 0
DG > 0
DG = 0
process is spontaneous
reverse process is spontaneous
Equilibrium
The Gibbs Free Energy is a direct measure of spontaneity
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Starting from the definition of G, we can form the
complete differential as we did before,
Now, we consider a process at constant temperature,
so that the SdT term is zero.
DG  DH  TDS
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DrH = H (products) – H (reactants)
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ΔrS and ΔrG are defined in the same way:
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The Master Equations
We are almost in a position to derive the key
relationship between the standard Gibbs energy
change and the equilibrium constant:
A key idea in thermodynamics is that of a standard state.
The standard state of a substance is the pure form
at a pressure of one bar and at the specified temperature
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where
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The Third Law of Thermodynamics
Entropy is related to the dispersal of energy (degree
of randomness) of a substance. Entropy is directly
proportional to the absolute temperature. Cooling the
system decreases the disorder.
At a very low temperature, the disorder decreases
to 0 (i.e., 0 J/(K mole) value for S).
The most ordered arrangement of any substance is
a perfect crystal!
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The Third Law of Thermodynamics
The entropy of any perfect crystal is 0 J /(K mole) at 0 K
(absolute 0!)
Due to the Third Law, we are able to calculate
absolute entropy values.
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The Zeroth Law of Thermodynamics
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