1. SUBJECT:-CHEMICAL ENGINEERING THERMODYNAMICS 2 TOPIC:- DISCUSS GIBSS DUHEM EQUATION CALCULATION OF PARTIAL PROPERTIES FROM BINARY EQATION. BRANCH :-chemical (Sem- 5)
Pushpa Gohil
Khushbu Mehta
Manali Mistry
Bhavika Nikum
Bhavika Parmar

2. GIBBS DUHEM EQUATION
The change in partial molar properties with composition at constant temp. & press. Can be explained will by the gibbs duhem equation.
Of the partial molar gibbs function is particularly useful in describing behaviour of mixture and solution.
Since the free energy of the system is a state function, it depend upon T,P and V. Now, if the system is of fixed composition then it can be written as G=f(P,T).

3. But in case of an open system where the quantities of the component vary the free energy will depend upon the quantities of the components.
For a multicomponent system the fee energy(G) is a function of T,P and the quantites of the component.
Deriving the Gibbs-Duhem equation from thermodynamics state equations is very easy. The Gibbs free energy G in equilibrium can be expressed in terms of thermodynamics as:

4. The free energy (G) of the system can be expressed as
G=f(P,T, )
If the variables undergo change then on total differentiation
At constant tem & pre.
(1)
.....from eq.

5. Integrating above equation,
……………………….(2)
The total derivative of G gives
………………………………….(3)
Substracting equation (1) from eqation (3),
……………………………(4)
The equation (4) is known as the Gibbs-Duhem equation.

6. 0n dividing by n, eq.(4) yields in terms of the mole fraction
Where = = Mole fraction of component i.
Eq. (2) (4) (8) are commonly known as GIBBS –DUHEM EQUATIONS.
For a binary solution containing two components, Eq. (5) can be expressed as
It is a binary solution in a closed system and the number of the moles is independent ,then
………………………………(5)

7. dividing by gives us,
We know that for a solution of component i, the chemical potential expressed in terms of fugacity as,

8. Applying in above relation,
Simplify above eqation,
………………………(6)

9. Applications of Gibbs-Duhem equation:
(i) Gibbs-duhem equation is helpful in calculating partial molar quantity of a binary mixture by measuring the composition of the mixture which depends on the total molar quantity.   (ii) Gibbs-duhem equation is helpful in calculating the partial vapor pressures by calculating the total vapor pressure. All these calculations require a curve-fitting procedure. Using tabulated experimental data the accuracy of the calculated quantities was found to be comparable to the accuracy of the original experimental data.

10. THANK YOU