Bms

1. CHEMICAL-III,SCET
1
BY..
DOBARIYA BHAVIK [130420105010]
DONGA SAGAR [130420105011]
GAMIT STEPHEN [130420105013]

2.  Fundamental Property Relation
 The chemical Potential as Criteria for Phase
Equillibrium
 Partial Properties
 Equation relating Partial & Molar properties
 Application
 Reference
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3. 3
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4.  In thermodynamics, the fundamental
thermodynamic relation is generally expressed as
an infinitesimal change in internal energy in terms
of infinitesimal changes in entropy, and volume for
a closed system in thermal equilibrium.
 The basic relation connecting the gibbs energy to
the temperature and pressure in any closed
system:
Gibbs Free Energy: dG= Vdp – SdT
Or
d(nG)=(nV)dp-(nS)dT
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5.  This equation is applied on single phase fluid, For such a
system the composition is necessarily constant.
and
 The Subscript n indicates that the numbers of moles of
all chemical species are held constant
 Consider now the more general case of a single-phase
open system that can interchange matter with
surroundings.
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CHEMICAL-III,SCET

6. nG = g(P,T,n1,n2,…….,ni,…..)
 Where ni is the number of moles of species i.
 The total differential of nG is,
 By definition the chemical potential of species I in the
mixture is :
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7.  With this definition and with the first two partial
derivatives replaced by (nV) and –(nS), the preceding
equation becomes:
 This equation is the fundamental property relation for
single-phase fluid systems of constant or variable mass
and constant or variable composition.
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8. 8
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9.  Chemical potential was first described by the
American engineer, chemist and mathematical
physicist Josiah Willard Gibbs.
 If to any homogeneous mass in a state of
hydrostatic stress we suppose an infinitesimal
quantity of any substance to be added, the mass
remaining homogeneous and its entropy and
volume remaining unchanged, the increase of the
energy of the mass divided by the quantity of the
substance added is the potential for that substance
in the mass considered
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CHEMICAL-III,SCET

10.  Consider a closed system consisting of two phases in
equilibrium.
 Within this closed system, each individual phase is an
open system, free to transfer mass to the other.
Where, α & β = Phases.
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11.  The presumption is that at equilibrium T and P are
uniform throughout entire system.
 The change in total Gibbs energy of the two-phase
system is the sum of these equations.
And the sum is,
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CHEMICAL-III,SCET

12.  Since two-phase system is closes, comparison of the two
equations shows that at equilibruim;
 From mass transfer between the phases, and mass
conservation requires:
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CHEMICAL-III,SCET

13.  By successively considering pairs if phases, we may
readily generalize to more than two phases the equality
of chemical potentials; the result for ∏ phases is :
 Thus, “multiple phases at the same T and P are in
equilibrium when the chemical potential of each species
is the same in all phases.”
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14. 14
CHEMICAL-III,SCET

15.  It is Response function explained by detecting
property.
 A partial molar property is a thermodynamic
quantity which indicates how an extensive
property of a solution or mixture varies with
changes in the molar composition of the
mixture at constant temperature and pressure.
 Essentially it is the partial derivative of the
extensive property with respect to the amount
(number of moles) of the component of interest.
 Every extensive property of a mixture has a
corresponding partial molar property.
15
CHEMICAL-III,SCET

16.  Essentially it is the partial derivative of the
extensive property with respect to the amount
(number of moles) of the component of interest.
 This equation defines the partial molar property of
species i in solution.
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CHEMICAL-III,SCET

17.  Where the generic symbol Mi may stand for the Partial
molar internal energy Ui, the partial molar enthalpy Hi,
the partial molar entropy Si, the partial molar Gibbs
energy Gi.
 The Gibbs energy shows that the chemical potential and
the partial molar Gibbs energy are identical.
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CHEMICAL-III,SCET

18. 18
CHEMICAL-III,SCET

19.  Define the partial molar property of species
i:
 the chemical potential and the particle molar
Gibbs energy are identical:
 for thermodynamic property M:
j
n
T
P
i
i
n
nM
M
,
,
)
(









i
i G


,...)
,...,
,
,
,
( 2
1 i
n
n
n
T
P
M
nM 




















i
i
i
n
P
n
T
dn
M
dT
T
M
n
dP
P
M
n
nM
d
,
,
)
(

20. 



















i
i
i
n
P
n
T
dn
M
dT
T
M
n
dP
P
M
n
nM
d
,
,
)
(
 




















i
i
i
i
n
P
n
T
ndx
dn
x
M
dT
T
M
n
dP
P
M
n
Mdn
ndM )
(
,
,
0
,
,



































 
 dn
M
x
M
n
dx
M
dT
T
M
dP
P
M
dM
i
i
i
i
i
i
n
P
n
T
0
,
,



















 
i
i
i
n
P
n
T
dx
M
dT
T
M
dP
P
M
dM and 0

 
i
i
iM
x
M
Calculation of mixture
properties from partial
properties
0


i
i
iM
n
nM
0
,
,




















i
i
i
n
P
n
T
M
d
x
dT
T
M
dP
P
M

 

i
i
i
i
i
i dx
M
M
d
x
dM
The Gibbs/Duhem equation

21. CHEMICAL-III,SCET
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22. CHEMICAL-III,SCET
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•In chemistry, colligative properties are properties of
solutions that depend upon the ratio of the number of
solute particles to the number of solvent molecules in
a solution, and not on the type of chemical species
present.
•The word colligative is derived from the Latin
colligatus meaning bound together .
•Colligative properties include:
•1.Relative lowering of vapor pressure.
•2.Elevation of boiling point.
•3.Depression of freezing point.
•4.Osmotic pressure.
For ColligativeProperties:

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