The First Law of Thermodynamics

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Chapter 2 The First Law of Thermodynamics The
Concepts
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OUTLINE Definitions 2.1 The First Law of
Thermodynamics 2.2 Work 2.3 Heat 2.4
Enthalpy 2.5 Adiabatic changes 2.6 Stand
ard enthalpy changes 2.7 Enthalpies of
formation 2.8 Temperature dependence of
enthalpy changes 2.9
Atkins
HOMEWORK ASSIGNMENTS EXERCISES 2.4 - 2.44, Part
(a)s only PROBLEMS 2.2, 2.3, 2.12, 2.13, 2.27
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Definitions
THERMODYNAMICS

• Chemical thermodynamics is concerned with the
  equilibrium properties of substances or mixtures
  in so far as they are effected by temperature.

• Thermodynamics serves two functions-
• To decide how some process can be made to
  occur.
• If a process is spontaneous it can tell us how
  much work we can get from it. If not
  spontaneous whether it is worthwhile making the
  process occur.

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Definitions
SYSTEM AND SURROUNDINGS The system is the
part of the universe we are interested in. The
rest of the universe is the surroundings.
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Definitions
Classification of systems If matter and energy
can be transferred between the system and the
surroundings then the system is called
_______. If matter cannot be exchanged with the
surroundings, but energy can be, the system is
called ________. If neither energy nor matter
can be transferred the system is called
___________.
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Definitions
The State of a System A system is in a definite
state when each of its properties has a definite
value. The state of a system is uniquely
defined in terms of a few state properties that
may be linked by an EQUATION OF STATE.
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Definitions
PROPERTIES The properties of a system are those
physical attributes that are perceived by the
senses or are made perceptible by certain
experimental methods of investigation e.g.
pressure, temperature, etc. A state property
(a.k.a. state function, state variable) is one
which has a definite value when the state of the
system is specified.
The properties of a system may be
INTENSIVE Do not depend on the quantity of matter
EXTENSIVE Do depend on the quantity of matter
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Definitions
WORK Defined in physics as ____ ? ______ . It
represents something useful. Getting something
from one place to another we regard as
useful. ENERGY Energy is the capacity of a
system to do work. The more energy a system has
the more work it can do. Mathematically energy
and work are interconvertible something can be
given energy by doing work on it.
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Definitions
HEAT A system may gain or lose energy because of
a temperature difference between it and the
surroundings, we say "energy has been transferred
as heat". The first law of thermodynamics
relates HEAT and WORK.
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Definitions
Forms of energy Kinetic energy, the energy
associated with a moving body. Potential energy,
the energy associated with the position of a
body. Electrical energy, the energy associated
with the motion of electrons. Chemical energy,
the energy associated with chemical bonds. Heat,
the kinetic energy of molecular
motions. Internal energy The energy contained
within a system. It is an extensive state
property and given the symbol U. It is measured
in joules, J, where 1 J 1 kg m2 s-2
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Definitions
System enclosures/walls If a system cannot
receive or give energy to the surroundings in the
form of HEAT then it is said to be contained
within an ___________ enclosure. If a system can
receive or give energy to the surroundings in the
form of HEAT then it is said to be contained
within a ____________ enclosure.
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Definitions
PROCESSES, CHANGES IN STATE and PATHS (1)
A process is said to have occurred if any
macroscopic property of a system changes between
2 observations made on the system. A change in
state is completely defined when initial and
final states of a changed system are
specified. The path specifies the sequence of
intermediate states between the initial and final
states.
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Definitions
PROCESSES, CHANGES IN STATE and PATHS (2)
Any process that releases heat is called
______________, e.g. combustion. Any process
that absorbs heat is called ______________, e.g.
evaporation. A cyclic process (or
transformation) is one in which the initial state
and the final state is the same.
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THE FIRST LAW OF THERMODYNAMICS The first law
of thermodynamics is essentially the statement of
the principle of the conservation of energy for
thermodynamical systems. We will investigate the
validity of this statement. First, let ?U
represent the change in a systems internal energy
in going from state A to state B i.e.
?U UB - UA This change is independent of the
path of the change of state.
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THE FIRST LAW OF THERMODYNAMICS
A system gaining energy through a thermal process
absorbs a positive quantity of heat.
Let q represent the heat absorbed by the system
from the surroundings.
When the system gains energy by other methods a
positive quantity of work is done on the system.
Let w represent the work done on the system by
the surroundings.
For a change of state from A to B the first law
states ?U UB - UA q w
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Work and the First Law In order to use the first
law in a practical way it is convenient to switch
to infinitesimal changes. dU dq dw We
know that Work Force ? Distance.
Therefore dw F dz If the object
moves from zi to zf, the total work done is
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Work and the First Law
1. A system raises a mass m by a distance h.
What is w? w -mgh.
2. The system contains a spring which is
compressed by a distance x from the
equilibrium position, zi 0. What is w? The
force law (Hooke's Law) is F -kz (k
is the FORCE CONSTANT) so dw kz dz
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Work and the First Law
In many cases found in chemistry work is done by
the system when it expands against an external
pressure.
Consider an expansion
dw -F dz -pexA dz -pexdV
For a compression dV lt 0 and thus dw gt 0. FREE
EXPANSION pex 0 and w 0.
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Work and the First Law
Types of changes If the system is kept
continually in a state of equilibrium while a
change is carried out then that process is called
REVERSIBLE. Example Compressing a gas in a
cylinder (the system) by pushing in the piston
very slowly. Truly reversible processes are
ideal they are carried out infinitely slowly and
will be capable of doing the maximum amount of
work. If the piston were pushed in fast the gas
near the piston would heat up and/or currents
would form and the system would no longer be in
equilibrium. This would be an IRREVERSIBLE
process.
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Work and the First Law
Types of changes
If pex p we have equilibrium. If we increase
pex infinitesimally the gas contracts slightly
and vice versa. In either case the change is
reversible.
pex
If pex gtgt p then decreasing pex infinitesimally
will not cause the gas to stop contracting and
vise versa. Here infinitesimal changes in
conditions do not cause opposite changes in the
state of the system. The system is not in eqm
with its surroundings and the change described is
irreversible
p
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Work and the First Law
Consider the reversible, isothermal expansion of
1 mol of ideal gas.
Reversible, so p pex nRT/V. dw -pdV
-nRT/V dV
This is all of the area under the curve in the
indicator diagram. Irreversible Allow pex lt p
then V increases instantly from Vi to Vf. The
work is less. Max work performed is -wrev.
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Work and the First Law

• Q. What is w when 56 g of Fe(s) reacts with
  HCl(aq) to give H2(g)
• At fixed volume?
• In an open beaker?

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Work and the First Law

• From Atkins 2.7 (b) 2 mol of He is expanded
  isothermally at 22oC from 22.8 L to 31.7 L
• Reversibly
• Against constant pex equal to final pressure of
  the gas
• In a vacuum.
• For the 3 processes calc. w.

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Work and the First Law
Expansion/compression work is called "pV workand
in this context the First Law becomes
dU dq dw dq - pdV Constant volume
conditions (Heat and the First Law) dU dqV
( dqV dq at constant V ) and dV 0 so
?U U2 - U1 qV. The heat withdrawn from the
surroundings by a constant-volume system is equal
to the change of internal energy of the system.
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Measuring ??U Adiabatic Bomb Calorimeter
In practice we use a sealed CALORIMETER and
measure heat changes at constant volume (qV).
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Calorimetry
The calorimeter directly yields ?U (via qV ).
Again dU dqVdw
dqV -
pexdV
0 (V is constant)
dqV ?U qV
Step (1) Set up expt and wait for eqm. Measure
bath temperature, T. Perform reaction. Measure
rise in T ( ?T ). Step (2) Cool contents of
calorimeter back to T. Do electrical work on the
water bomb to reproduce ?T. Apply first law.
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Heat and the First Law Heat Capacities
The heat capacity, C, of any system is the amount
of heat required To raise the temperature of the
system by 1 K.
Define
It is useful to distinguish heat capacities at
constant volume and constant pressure.

Lets derive these
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Constant pressure conditions
Often chemical systems are studied at constant
external pressure.
This makes it difficult to measure changes in U.
We invent a convenience function, H, the
ENTHALPY, defined by
H U pV
At constant pressure its use is seen from
dH dU pdV Vdp
dH dU dw dqp
so qP H2 - H1 ?H. ?H
is the heat transfer at constant pressure.
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Constant pressure conditions

• Notes about H
• H is an extensive state property.
• Even for non-constant p, ?H has a definite value.
  However, in such a case ?H ? q
• For processes involving solids and liquids ?H ?
  ?U usually.

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Constant pressure conditions
Self test 2.3 from Atkins Calculate the
difference between ?H and ?U when 1.0 mol of grey
tin (density 5.75 g cm-3) changes to white tin
(density 7.31 g cm-3) at 10.0 bar. At 298 K, ?H
2.1 kJ.
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Constant pressure conditions
In the reaction 2H2(g) O2(g) ?2H2O(l), 3 mol of
gas phase molecules is replaced by 2 mol of
liquid phase molecules. Calculate the difference
between the enthalpy and the energy taking place
in this system. (T298 K, assume perfect gas
behaviour).
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The Variation of Enthalpy with Temperature.
A few slides earlier we introduced
and
But recall
dH dU dw dqp
So it follows that
And so at constant pressure dH CpdT
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The relation between Cp and CV
If something is heated at constant p we generally
observe an expansion. So the system receives
energy in the form of heat but loses energy in
the form of pV work. Therefore the temp. rises
less than when heating at constant volume. The
rate of change of temp. w.r.t. heat is less at
constant p than at constant V.
Recall that C is a measure of the rate of change
of the systems heat w.r.t. temperature.
So, if the temp. of a system rises slower at
constant p compared to constant V, then it
follows that Cp gt CV
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The relation between Cp and CV
We will show now and in a later lecture that
Cp-CV nR
It may be shown by kinetic theory
that CV,m(3/2)R for a monatomic gas
CV,m(5/2)R for a
diatomic gas
Hence Cp,m(5/2)R
for a monatomic gas
Cp,m(7/2)R for a diatomic gas
If we put
? (5/3) for a monatomic gas ? (7/5)
for a diatomic gas
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The Adiabatic Expansion of a Perfect Gas
The change of a thermodynamical system is said to
be adiabatic if it is reversible and if the
system is insulated so that no heat can be
exchanged between it and its environment during
the change.
Expansion ? work is done by the system on the
surroundings.
Adiabatic enclosure ? no heat exchanged, q 0
? First Law tells us DU will be lt 0 and that it
will equal wad
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The Adiabatic Expansion of a Perfect Gas
Under constant volume conditions
For a perfect gas U depends only on T and so we
may write
So the change in internal energy is DU wad
CV(Tf-Ti)
The work done during an adiabatic expansion of a
perfect gas is proportional to the difference of
the initial and final temperatures.
For a reversible adiabatic expansion of a perfect
gas we may derive
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The Adiabatic Expansion of a Perfect Gas
Using the Heat Capacity Ratio, ? , we can address
the change in pressure that accompanies an
adiabatic reversible expansion of a perfect gas
Recall
We can show that
( c.f. the equation pV constant for an
isothermal expansion )
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A practical example of adiabatic
expansion/contraction If a body of air in the
atmosphere changes height, the pressure and hence
volume change, leading to a temperature
change. Let pressure be p at a height h. Molar
mass M 0.029 kg mol-1, g acceleration due
to gravity 9.81 m s-2. In the atmosphere,
dp/dh -pMg/RT. What is dT/dh ? This
is called the DRY ADIABATIC LAPSE RATE.
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Thermochemistry
Thermochemistry is the quantitative study of the
heat produced by a given chemical reaction.
If we perform this reaction HCl(aq)
NaOH(aq) ? NaCl(aq) H2O(l) We will note that
the vessel gets hot.
Alternatively, if we perform the following
reaction in a beaker Ba(OH)28H2O(s)
2NH4NO3(s) ? Ba(NO3)2(s) 2NH3 (aq)
10H2O(l) We will observe the spontaneous
formation of ice on the outside of the vessel as
the temperature of the system decreases rapidly.
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Thermochemistry
It is more convenient to measure enthalpy
changes, DH, (constant pressure) as opposed to
internal energy changes, DU, (constant volume).
Lets not lose sight of
H is an extensive state property.
H U pV
dH dU dw dqp
And so at constant pressure dH CpdT
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Thermochemistry
We dont (cant) measure a chemicals enthalpy.
What we measure is the change in enthalpy that
occurs during a transformation.
In order to report enthalpy changes, DH, for a
given transformation it is useful to discuss
changes between substances in their standard
states, we then use DH? to represent the standard
change in enthalpy.
The standard state of a substance at a specified
temperature is its pure form at 1 bar.
E.g. the standard state of oxygen at 298.15 K is
pure O2(g), ethanol at 158 K is pure C2H5OH(s), C
at 298.15 K is pure C(graphite).
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Thermochemistry
There are many enthalpies of transition. Some
examples are
H2O(l) ? H2O(g) enthalpy of
vaporization, Dvap H Reactants ? Products
enthalpy of reaction, Dr H Elements ?
Compound enthalpy of formation, Df
H Species (s, l, g) ? Atoms (g) enthalpy of
atomization, Dat H See Atkins Table 2.4
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Thermochemistry
Hess's Law Consider
The standard enthalpy, DH?, of an overall
chemical reaction is the sum of the standard
enthalpies of the individual reactions into which
a reaction may divided.
We can set up Hess cycles to calculate DH for
reactions which are difficult to measure directly.
In the above cycle Dc H?2 Dc H?3 Dr H?1
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Thermochemistry
Consider
Hydrogenation of propene, CH2CHCH3(g) H2(g) ?
CH3CH2CH3(g) Dr H? -124 kJ mol-1 Combustion
of propane, CH3CH2CH3(g) 5 O2(g) ? 3 CO2(g)
4 H2O(l) Dc H? -2220 kJ mol-1 Formation
of water, H2(g) 0.5 O2(g) ? H2O(l)
Df H? -286 kJ
mol-1 Calculate Dc H? for CH2CHCH3(g)
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Thermochemistry
The reaction enthalpy in terms of enthalpies of
formation Taking Hesss law to its logical
conclusion suggests that we may consider a
reaction as proceeding by first breaking the
reactants up into its elements and then forming
the products from those elements.
Elements
-Df H?
Df H?
Enthalpy, H
Reactants
Dr H?
Products
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Thermochemistry
At 298 K 0.5 H2(g) 0.5 I2(s) ? HI (g)
Df H? 26.98 kJ mol-1
H2(g) 0.5 O2(g) ? H2O (g) Df H?
-241.82 kJ mol-1 Determine Dr H? and Dr U?
for 4 HI(g)
O2(g) ? 2 I2(s) 2 H2O(g) (Assume the gases
behave perfectly)
4? 0.5 H2(g) 0.5 I2(s) O2(g)
-Df H?
Df H?
Enthalpy, H
4 HI (g) O2 (g)
Dr H?
2 I2(s) 2 H2O(g)
-591.6 kJ mol-1
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Thermochemistry
The dependence of Dr H on T Kirchoffs law
We know
dH CpdT
Heating a substance from T1 to T2 its enthalpy
changes from H (T1) to
This applies to each substance in the reaction,
therefore
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Thermochemistry
The dependence of Dr H on T Kirchoffs law
Example 2.7 At 298 K H2(g) 0.5 O2(g) ?
H2O (g) Df H? -241.82 kJ
mol-1 Given What is Df H? at 100oC?
(Assume all heat capacities, Cp,m? , are
independent of T)
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• Chapter 2 SUMMARY
• Systems may be open, closed or isolated.
• Definitions of work, internal energy (U) and
  work. First Law or dU dq dw.
• U, and enthalpy, H, are state functions. H U
  pV.
• pV work and reversible/irreversible volume
  changes for an ideal gas at constant volume or
  pressure.
• Calorimetry and the measurement of DH and DU.
• Thermochemistry Hess's Law, thermochemical
  cycles and standard enthalpies of formation.
• The heat capacities Cp and CV relation to
  temperature dependence of DH and DU for a process
  (Kirchoff's Law) and for adiabatic changes.