solutions
DESCRIPTION
Physical ChemsitryTRANSCRIPT
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Chemical Potential
inTPj
jn
G
,,
= Potential Chemical Diffusion from high to low potential.
Chemical potential is a Partial Molar Quantity
)jnT,f(P,G :components-multiFor =
Sum of moles of components
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Chemical Potential of a Binary (A & B) Mixture
)n , n , T , f(P G BA=
BnTPB
AnTPAnnPnnT
dnn
Gdnn
GdTTGdP
PGdG
ABBABA
+
+
+
=
,,,,,,,,
dPV dTS
ij
nTPjdn
n
G
i,,
iiii nSVj
nSPjnVTjnTPjj
n
Un
Hn
An
G
,,,,,,,,
=
=
=
=
Chem. Potential applied to other variables:
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Measures of Composition s = solute ; A = solvent; V = Tot. Vol. of solution. Weight %:
Mole Fraction:
100% xww
ww
As
s
s +=
s
snn
n
+=
Molarity:
Molality:
Ass
nn +=
VnM s
s=
Akgn
m ss
=
Different Composition Equations for different Laws
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Partial molar Quantities Let us suppose that a solution is formed by
mixing n1,n2, moles of substances 1,2,.. havingmolar volumes V*m,1, V*m,2,. at temp T andpressure P. Let V* be the total volume of theunmixed (pure) components at T and P.unmixed (pure) components at T and P.
V* = n1V*m,1 + n2V*m,2+.. nrV*m,r= niV*m,i After mixing, we find that volume V of solution is
not in general equal to the unmixed volume : V V*. e.g., 50 cm3 of ethanol added to 50 cm3 of water
gives 96.5 cm3 at 20C and 1 atm RANJANRANJANRANJANRANJAN DEYDEYDEYDEY
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(1) Difference betweenintermolecular forces in
the solution and those in
The difference between V of solution and V* results from:
the solution and those in
the pure component
(2) Diff between the packingof molecules in solution andpacking in pure components
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Other Partial Molar Quantities
jnTPii
n
VV,,
=
Partial Molar Volume:
jnTPii
n
HH,,
=
jnTPii
n
SS,,
=
Partial Molar Enthalpy:
Partial Molar Entropy:
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Solution Volume and Partial Molar Volume V = n f(T,P, x1,x2,) where n = ni and f is some
function of T, P and mole fractions. Differentiation of above equation gives : d V = f(T,P, x1,x2,) dn = Vidni xi = ni/n or ni = xin dV = x V dn for constant T, P, x dV = xiVidn for constant T, P, xi Comparison of expressions for dV gives: V = niVi for one phase system Where the V on the LHS is sometimes referred
to as the mean molar volume, Vm of the solution.
Change in volume of mixing, is given by:mixV =V-V*
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Calculation for Partial Molar Volumes
BnTPAA
n
VV,,
=
AnTPBB
n
VV,,
=
V = f(nA , nB) @ constant P & T
dnVdnVdV
+
= BnTPB
AnTPA
dnn
Vdnn
VdVAB
+
=
,,,,
BBAA dnVdnVdV +=
BBAA VnVnV +=
Integrate @ constant composition
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Slope of V vs nB curve at any composition gives VB for that comp.mixV = V V* = i ni ( Vi V*m,i )
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Ideal Solution Ideal solution will be one where the molecules of
the various species are so similar that replacing molecule of one species with another will not change the spatial structure or intermolecular interaction energy in the solution.
For this the molecules must be essentially of same For this the molecules must be essentially of same size and shape.
mixG = G G* = nii ni*i For an ideal solution : mixG = RT ni ln xi Equating : nii = ni(*i + RT ln xi ) i = *i (T,P) + RT ln xi (#1)
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Last eqn on previous slide is adopted as definition of an ideal solution
As xi0, i - . As xi increases, i increases at fixed T and P, reaching chemical pot of the pure i, *i in the limit xi =1
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Thermodynamic properties of Ideal Solutions
Standard state of each component i of the ideal liquid solution is defined to be pure liquid i at the temp T and pressure P of the solution.
G = RT n ln x mixG = RT ni ln xi mixV = 0 mixS = -R ni ln xi mixS = -( mixG / T)P,ni mixH = 0
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