GROUP (11)
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6.4 Thermochemistry
 Standard State: it is the pure form of the substance at the
specified temperature and under 1 atmospheric pressure.
 The Reference State: it is the most stable state of an element
at the specified temperature and under 1 atmospheric
pressure.
 Standard Enthalpy of Transition: it is the enthalpy change
that accompanies the change of the substance from one phase
to another in their standard states.
There are many different types of transitions, each of which
has an associated change in enthalpy, examples of these
transitions are:
Phase transition: phase  → phase  , Hotrs
Fusion:
solid
→ liquid , Hofus
Vaporization:
liquid
→ gas
, Hovap
Sublimation:
solid
→ gas
, Hosub
Since the enthalpy is a state function, ∆HO of a phase change
is independent on path between the initial and final states.
Also, for forward and backward processes: ∆HO differs only in
sign.
 The Standard Enthalpy of a Reaction ∆HO(R): it is the
change in enthalpy when reactants in their standard states is
transformed to products in their standard states, thus for the
reaction:
aA+bB=cC+dD
H o R     (i ) H (i )    (i ) H (i )
  ( j ) H ( j )
prod.
react.
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where ( j ) is positive for products and negative for reactants.
 Hess' Law: the standard enthalpy of an overall reaction is the
sum of the standard change of enthalpies of the individual
reactions into which the overall reaction may be divides
(individual steps may not be real reactions, but must balance).
 Standard Enthalpy of Formation: it is the change in enthalpy
for formation of one mole of a compound from its constituent
elements in their reference states.
 Conceptual Reaction: decompose the reactants of a chemical
reaction into their elements, from these elements form the
products thus;
H o R    (i )H of (i )   (i )H of (i )
prod.
react.
H  R    ( j ) f ( j )
where (j) is positive for the products and negative for
reactants.
o
 Kirchoff's law: since H (i) T p  C p (i) ; thus,
(H o (i) T ) p  C p ( j )
integrating between the states: (T1, P) and (T2, P) gives:
T2
 R (T2 )   R (T1 )   C p ( R)dT
where:
T1
C p ( R ) 
 (i)c
p
prod.
(i ) 
 (i)c
p
(i )
react.
  ( j )c p ( j )
where (j) is positive for the products and negative for reactants.
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6.5 Temperature Dependence of Entropy
and the Third Law of Thermodynamics
 For a closed system undergoing a reversible process:

ds   q
rev
T

If the process is conducted at constant pressure,then:
ds  qrev T p  dH T p  c p T  dT
Thus, if the temperature of a closed system of fixed
composition that undergoes no phase transformation is
increased from T1 to T2 at constant pressure, then:
T2
T2
T1
T
T1
S (T2 , P)  S (T1 , P)   c p T dT   C p dnT
Generally:
ST  S0   c p dnT
0
where S0 is the entropy of the system at 0K .
 In 1906 , Nernest postulated that ‘for chemical reactions
between pure solid materials or liquid , the term
approaches zero as the absolute temperature T approaches
zero value; this is shown in figure (6.6).
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Figure (6.6): the variation of the change in The Gibbs free
energy for a reaction with temperature as the
temperature approaches absolute zero.
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 Also, he postulated that (∂∆H/∂T)p approaches zero as T
approaches zero.
 Since:
∆G=∆H-T∆S
thus: G T  p  H T  p  T S T  p  S
then:
 S  H T  p  T S T  p  S
and hence:
H
T  p  T S T  p  C p
Since (∂G/∂T)p and (∂H/∂T)p tends to zero as T0, and
(∂G/∂T)p = - ∆S and, (∂∆H/∂T)p =∆Cp , thus , For chemical
reactions between pure solids or liquids:
∆Cp0 as T0
Accordingly, Nernest postulated the following Nernest heat
theorem: "for all reactions involving substances in the
condensed state, ∆S is zero at the zero absolute temperature."
 The incompetence of Nernest's statement was pointed out by
Plank, who postulated that: "the entropy of any homogenous
substance, each is in complete internal equilibrium, may be
taken as zero at (0k)". This is the statement of the Third Law of
Thermodynamics.
 The statement of the Third Law of Thermodynamics must
include the requirement that the homogenous phase must be in
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complete internal equilibrium; this is illustrated by the following
examples:
1. glasses of noncrystalline solids properly regarded as
supercooled liquids in which the liquid-like disordered
atomic arrangement has been frozen into the solid state ;
its entropy at zero Kelvin "0K" is greater than zero by an
amount which depends on the degree of atomic disorder in
the glass which is not in internal equilibrium.
2. solutions are not fully ordered at 0K; consequently, a non
equilibrium degree of disorders is frozen, thus entropy will
not fall to zero at 0K.
3. pure elements are in fact mixtures of isotopes; thus, the
entropy of such elements will not fall to zero at 0K because
of the entropy of mixing which exists due to the mixing
between the different isotopes of the element.
4. nonequilibrium concentration of defects can be frozen
into the crystals giving rise to nonzero entropy at 0K.
5. random crystallographic orientation of molecules, such as
the case of solid CO, in the crystalline state can raise to
nonzero entropy at 0K.
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6.6 Experimental Verifications of the Third law of
Thermodynamics
 The Third Law can be experimentally tested by examining the
behavior of some simple phase transation of an element , e.g,
=
Where  and β are solid allotropes of the element.
consider the cycle shown in figure (6.7) for the  = β
transition between 0K and Ttrans , where Ttrans
equilibrium temperature of the phase transition reaction
unit pressure.
 Since the entropy is a state property , thus :
∆SIV =∆SII +∆SI + ∆SIII
 For the Third Law to be obeyed , ∆SIV = 0 , and hence:
∆SII = - (∆SI + ∆SIII )
thus:
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let us
phase
is the
under
Figure (6.7): the cycle used for the experimental verification of
the Third Law of Thermodynamics.
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
∆SII is termed "The Experimental Entropy Change", and
−(∆SI + ∆SIII ) is termed "The Third Law Entropy Change".
 The cycle has been examined for the reaction :
S (rhombohedra)  368.5K  S (monoclinic)
where it has been found that:
∆SII = 0.261 cal/deg-gm.atom (e.u.)
and : - ( ∆SI + ∆SIII ) = 0.23 cal/deg-gm.atom (e.u.)
As the difference is less than the experimental error, this is
taken as experimental verification of the Third Law of
Thermodynamics.
 Since the molar entropies are tabulated at 298 K ; Thus:
S298 =
and St is obtained as
ST  S 298 
Ttrans
 C d ln T  H T 
P
trans
298
taking into consideration the entropy of phase transition.
 Experimentally, it was found that: (∆Hm ∕ Tm) = 2 – 4 for number
of metals.
 The evaporation entropy, ( ∆Hevap. ∕ Tevap.) , has found to be 21
cal/deg-gm.atoms also for some metals. This known as
Trouten's law.
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 The entropy change of the reaction Pb +0.5 O2 = PbO at 298K
is given by the relation :
∆S(R) = S(PbO) – S(Pb) – 0.5 S(O2)
= 16.1 – 15.5 – (0.5 x 49)
= - 23.9 (e.u.) ~ 0.5 S(O2)

In other words, the change in the standard entropy of the
reaction is nearly equal to the entropy decrease resulting from
the disappearance of half mole of oxygen in reactions. Thus for
a gas that reacts with a condensed phase to produce a
condensed phase ; the entropy change of the reaction is that
corresponding to the disappearance of the gas.
6.7 Enthalpy and Entropy as Functions of Pressure
 For fixed-phase closed-system undergoing a change of
pressure at constant temperature:
dH = (∂H/∂P)T dP
since :
thus :
dH = TdS + VdP
(∂H/∂P)T = T (∂S/∂P)T +V
Using Maxwell's relation (∂S/∂P)T = - (∂V/∂T)p gives:
(∂H/∂P)T = - T (∂V/∂T)p + V = - TV +V = V (1- T)
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Integrating the previous equation yield for isothermal pressure
the following:
If temperature and pressure are changing at the same time:
T2
p2
T1
p1
   C p dT   V (1   )dp
 Also , for fixed-phase closed system undergoing a change of
pressure at constant temperature:
dS = (∂S/∂P)T dP
Since:
(∂S/∂P)T = - (∂V/∂T)T
and as:
= (1/V) (∂V/∂T)P
then:
(∂S/∂P) T = -
V
thus, for a change of a state from (P1, T) to (P2, T) we have:
p2
S    VdP
P1
If temperature and pressure are changing at the same time:
T2
p2
T1
p1
   c p d (nT )   Vdp
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