Solution Thermodynamics : Theory

FUGACITY AND

FUGACITY COEFFICIENT:

SPECIES IN SOLUTION

� The definition of the fugacity of a species in

solution is parallel to the definition of the pure

species fugacity

where is the fugacity of species i in

solution, replacing the partial pressure yi P

� Thus, multiple phases at the same T and

P are in equilibrium when the fugacity of

each constituent species is the same in

all phases.

� For the specific case of multicomponent

vapor/liquid equilibrium:

� Also,

� For an ideal gas, is necessarily zero;

therefore , and

� Also,

� This equation demonstrates that is a

partial property with respect to G R / RT

� To get use virial equation only.

iiMxM Σ=

ii

R

i

R

xRT

Gx

RT

Gφ̂lnΣ=Σ=

iφ̂

THE IDEAL SOLUTION

Total property from

summability

Partial property

� Enthalpy change of mixing:

∆Hmix= = Hid – ƩxiHi = 0

� Entropy change of mixing:

∆Smix= = Sid – ƩxiSi = -RƩxilnxi

� Gibbs energy change of mixing:

∆Smix= = Gid – ƩxiGi = RTƩxilnxi

Fugacity of component in ideal solution

� The LewisIRandall Rule

� Division of both sides by Pxi

Px

fx

Px

f

i

ii

i

id

i =ˆ

EXCESS PROPERTIES

� an excess property is defined as the

difference between the actual property value

of a solution and the value it would have as

an ideal solution at the same temperature,

pressure, and composition, thus,

EXCESS PROPERTIES

� For example:

� Also,

The Excess Gibbs Energy and the Activity Coefficient

� As, [1]

� [2]

� [1]-[2]ii

iid

iifx

fRTGG

ˆ

ln=−

� The activity coefficient of species i in solution

� Thus,

� For an ideal solution, = 0, and therefore

� is a partial property with respect to GE/ RT :

� The following forms of the summability and

GibbsIDuhem equations:

� To get

Using virial equation assuming ideal solution

(ex 11.9)

iϕ̂

Sheet 2

10. Two kmol/hr of liquid n-octane are continuously mixed with four kmol/hr of liquid iso-octane. The mixing process occurs at constant T and P; mechanical power requirements are negligible

a) Use an energy balance to determine the rate of heat transfer

b) Use an entropy balance to determine the rate of entropy generation (W K-1)

Sheet 3

Sheet 3

Sheet 3

Sheet 3