Fundamental Property Relation,The Chemical Fundamental Property Relation,The Chemical potential as a Criterition for Equillibrium for Phase Equillibrium,Partial Properties,EquationRelating Molar & Partial properties. CHEMICAL-III,SCET BY.. DOBARIYA BHAVIK [130420105010] DONGA SAGAR [130420105011] GAMIT STEPHEN [130420105013]

Content Fundamental Property Relation The chemical Potential as Criteria for Phase Equillibrium Partial Properties Equation relating Partial & Molar properties Application Reference CHEMICAL-III,SCET

FUNDAMENTAL PROPERTY RELATION CHEMICAL-III,SCET

Gibbs Free Energy: dG= Vdp – SdT Or d(nG)=(nV)dp- (nS)dT 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 CHEMICAL-III,SCET

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. CHEMICAL-III,SCET

Where ni is the number of moles of species i. 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 : CHEMICAL-III,SCET

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. CHEMICAL-III,SCET

THE CHEMICALPOTENTIL AND PHASE EQUILIBRIA CHEMICAL-III,SCET

History of Chemical Potential 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 CHEMICAL-III,SCET

THE CHEMICAL POTENTIAL AND PHASE EQUILIBRIA 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. CHEMICAL-III,SCET

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, CHEMICAL-III,SCET

From mass transfer between the phases, and mass conservation requires: 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: CHEMICAL-III,SCET

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.” CHEMICAL-III,SCET

PARTIAL PROPERTIES CHEMICAL-III,SCET

PARTIAL PROPERTIES 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. CHEMICAL-III,SCET

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. CHEMICAL-III,SCET

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. CHEMICAL-III,SCET

Equation Relating Partial Property & Molar Property CHEMICAL-III,SCET

Equation Relating Partial & Molar Property Define the partial molar property of species i: the chemical potential and the particle molar Gibbs energy are identical: for thermodynamic property M:

and Calculation of mixture properties from partial properties The Gibbs/Duhem equation

Application of Fundamental Property Corelation & OPthers CHEMICAL-III,SCET

For ColligativeProperties: 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. CHEMICAL-III,SCET

Reference CHEMICAL-III,SCET

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