Partial Molar Quantities, Activities, Mixing Properties - PowerPoint PPT Presentation

About This Presentation
Title:

Partial Molar Quantities, Activities, Mixing Properties

Description:

Partial Molar Quantities, Activities, Mixing Properties Composition (X) is a critical variable, as well at temperature (T) and pressure (P) Variation of a ... – PowerPoint PPT presentation

Number of Views:2042
Avg rating:3.0/5.0
Slides: 29
Provided by: Alexand167
Category:

less

Transcript and Presenter's Notes

Title: Partial Molar Quantities, Activities, Mixing Properties


1
Partial Molar Quantities, Activities, Mixing
Properties
  • Composition (X) is a critical variable, as well
    at temperature (T) and pressure (P)
  • Variation of a thermodynamic parameter with
    number of moles of one component, all other
    compositional variables, T, P held constant

2
(No Transcript)
3
(No Transcript)
4
Partial Molar Volume
5
Example - spinel solid solution
6
Spinel volumes
7
(No Transcript)
8
(No Transcript)
9
Activity Composition Relations
10
The Entropy of Mixing in Solid Solutions   Contrib
utions vibrational magnetic and
electronic configurational   For the random
mixing of a total of one mole of species over a
total of one mole of sites,   ?Smix -RxA
ln xA xB ln xB   and   ?s(A) -R ln
xA , ?s(B) -R ln xB  
11
(No Transcript)
12
The thermodynamic activity is defined as   ?µº(A)
RT ln a(A) and ?µº(B) RT ln a(B)
The changes in chemical potential on
mixing can be related to partial molar enthalpies
and entropies of mixing   ?µºT(A) ?hºT(A) -
T?sºT(A) , ?µºT(B) ?hºT(B) - T?sºT(B)
13
Chemical Potential Partial Molar Free Energy
14
If the enthalpy of mixing is zero, then the
simple ideal solution results,  ?Gºmix RT xA
ln xA xBln xB   ?µº (A) RT ln xA ,
?µº (B) RT ln xB   a(A) xA , a(B)
xB. Raoults Law holds only when one mole
total of species being mixed randomly, so always
introduces a microscopic meaning you can not get
away from. Thus Raoults Law applies directly to
BaSO4-RaSO4 solid solutions, FeCr2O4-NiCr2O4
spinel solid solutions if one assumes Ni and Fe
mix on tetrahedral sites only, and UO2-PuO2 solid
solutions if there is no variation in oxygen
content.
15
Regular, Subregular and Generalized Mixing
Models   Starting point useful but inherently
contradictory assumption that, though the heats
of mixing are not zero, the configurational
entropies of mixing are those of random solid
solution.   ?Gºmix, ex ?Hºmix-T?Sºmix, ex
  For a two-component system, the
simplest formulation is  ?Gexcess ?Hmix
?xAxB WH xAxB
16
Generalization
  • For a binary system, the Guggenheim or
    Redlich-Kister based on a power-series expression
    for the excess molar Gibbs energy of mixing
    which reduces to zero when either x1 or x2
    approach unity
  • where the coefficients ?r are called
    interaction parameters. Activity coefficients can
    be obtained by the partial differentiation of
    over the mole fraction x1 or x2


17
Systematics in Mixing Propertieszz (Davies and
Navrotsky 1981)
18
Size Mismatch and Interaction Parameter
19
Henrys Law Regions
20
IMMISCIBILITY Immiscibility (phase separation)
occurs when positive WG terms outweigh the
configurational entropy contribution. For the
strictly regular solution, the miscibility gap
closes at a critical point or consolute
temperature. T WH/2R Conditions for
equilibrium between two phases (a and ß)
simultaneous equalities of chemical potential
or activities   µ(A, phase a) µ(A, phase
ß) µ(B, phase a) µ(B, phase
ß)   a(A, phase a) a(A, phase
ß) a(B, phase a) a(B, phase ß)
21
(No Transcript)
22
(No Transcript)
23
RESULTS
  • FREE ENERGY CURVES
  • Complete miscibility
  • Solvus- phases derived from same structure and
    one free energy curve
  • Immiscibility resulting from different structures

24
Phases with Different Structures   Partial
solid solution can exist among end members of
different structureA with structure a and B
with structure ß.   µ(A,a) µº(A,a) RT ln
a(A,a)   µ(A,ß) µº(A,a) ?µ(A,a?ß) RT
ln a(A,ß) µ(B,a) µº(B,ß) ?µ(B,
ß?a) RT ln a(B,a) µ(B,ß) µº(B,ß) RT
ln a(B,ß) The limiting solubilities are
given by equating chemical potentials   µ(A,a)
µ(A,ß) µ(B,a) µ(B,ß) The
miscibility gap can not close and is not a
solvus.
25
ZnO CoO solid solutions
If the surface energy in wurtzite phase is
smaller than in rocksalt, wurtzite will be
favored at the nanoscale. Solid solubility of ZnO
in rocksalt will decrease while that of CoO in
wirtzite will increase
Relevant to Chencheng Ma thesis work
26
Spinodal
27
Spinodal
28
References
  • Guggenheim, E.A., Thermodynamics An advanced
    treatment for chemists and physicists. 5th edn.
    Amsterdam North-Holland 390,1967
  • Thompson, J.B., Thermodynamic properties of
    simple solutions. In Researches in geochemistry.
    Edited by Abelson PH. New York John Wiley and
    Sons 1967 340-361.
  • Thompson, J.B., Chemical reactions in crystals.
    Amer. Mineral., 54 (1969) 341-375.
  • Eriksson, G., Rosen, E., Thermodynamic studies of
    high temperature equilibria. VIII General
    equations for the calculation of equilibria in
    multiphase systems. Chemica Scripta, 4(4) (1973)
    193-194.
  • Pelton, A. D., Bale, C. W., Computational
    techniques for the treatment of thermodinamic
    data in multicomponent systems and the
    calculation of phase equilibria. Calphad, 1(3)
    (1977) 253-273.
  • Wood, B.J., Nicholls, J., The thermodynamic
    properties of reciprocal solid solutions.
    Contributions to Mineralogy and Petrology 66
    (1978) 389-400.
  • Nordstrom, D.K., Munoz, J.L., Geochemical
    thermodynamics. 2nd edn. Boston Blackwell
    Scientific Publications (1994) 483.
  • Ott, J.B., Boerio-Goates, J., Chemical
    thermodynamics Advanced applications. San Diego
    CA Academic Press, 438 (2000).
  •  Ott, J.B., Boerio-Goates J., Chemical
    thermodynamics Principles and applications. San
    Diego CA Academic Press, 664 (2000).
  • Ganguly, J., Thermodynamic modelling of solid
    solutions. In EMU Notes in Mineralogy Solid
    solutions in silicate and oxide systems of
    geological importance. Edited by Geiger CA.
    Budapest Eotvos University Press, 3 (2001)
    37-69.
  • Geiger, C.A., Solid solutions in silicate and
    oxide systems of geological importance. In
    European mineralogical union notes in mineralogy.
    Edited by Papp G, Weiszburg TG. Budapest Eotvos
    University Press, 3 (2001) 458.
Write a Comment
User Comments (0)
About PowerShow.com