gibbs duhem @bhagya.pptx

gibbs

1. GIBBS DUHEM EQUATION CHITCHALA BHAGYA SRI B220810CH

2. Thermodynamics of open system Partial molal quantities Chemical potential Gibbs Duhem equation Partial molal properties

3. PARTIAL MOLAL QUANTITIES Consider a system containing (Open system) ….

4. Partial definition of thermodynamic function ‘y’ with respect to the amount of component i of the mixture when T , P and other constituents are kept constant is know as Partial molal quantity of ith component .     =   i=   i=   Partial molal Internal energy Partial molal Enthalpy Partial molal Gibbs free energy Partial molal Work function

5. Gibbs free energy in the form of chemical potential ( open system)

6. GIBBS DUHEM EQUATION The relation between chemical potential and amount of components in the system is generally represented by Gibbs Duhem equation. According to the equations, the chemical potential is a relative property. RELATIVE PROPERTY: If chemical potential of one component increases then the chemical potential of other component will decrease in the system. Mathematically, the equation is represented as   Above expression can also written as  

7.   Mathematical proof of Gibbs Duhem statement +n2d   =- Where Other important Gibbs Duhem equation  

8. PROOF OF GIBBS DUHEM EQUATION  

9. Question on Gibbs Duhem Equation Q. A mixture of ethanol (C2H5OH) and water (H2O) is in equilibrium at a certain temperature and pressure. If the mole fraction of ethanol is 0.4, and the chemical potential of ethanol is -52.5 J/mol, find the chemical potential of water. Sol: The Gibbs- Duhem equation relates the chemical potentials of the components in a mixture. For a binary mixture of components A and B, it can be expressed as: xА· dµA+xв · dµв = 0 Where: xA ​ is the mole fraction of component A xB ​ is the mole fraction of component B μA ​ is the chemical potential of component A μB ​ is the chemical potential of component B

10. In your case, you have a mixture of ethanol (C2H5OH) and water (H2O) with a mole fraction of ethanol ( xA ​) equal to 0.4 and the chemical potential of ethanol ( μA ​) equal to -52.5 J/mol. You want to find the chemical potential of water ( μB ​). Using the Gibbs- Duhem equation: xA ​⋅ d μ A ​+ xB ​⋅ d μ B ​=0 Substituting the given values: 00.4⋅(−52.5)+ xB ​⋅ d μ B ​=0 Now, solve for d μ B ​: 0.4⋅(−52.5)+ xB ​⋅ d μ B ​=0 0.4⋅52.5 xB ​⋅ d μ B ​=0.4⋅52.5 xB ​⋅ d μ B ​=21

11. Now, you can find d μ B ​: d μ B ​= 21/ xB Since xB ​=1− xA ​, because it's a binary mixture, you can calculate xB ​: xB ​=1−0.4=0.6 Now, substitute this value into the equation: d μ B ​=21​/0.6 d μ B ​=35J/mol So, the chemical potential of water ( μ B ​) is 35 J/mol.