2D_Course_Notes_-_Part_IV

# 2D_Course_Notes_-_Part_IV - Equilibrium and Stability Phase...

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1 Equilibrium and Stability Phase Diagrams of Binary Systems Second law for any change in chemical states says: (d S) total > 0 (d G) T,P < 0 This leads to fundamental requirement for equilibrium The equilibrium state of a closed system is that state for which the total Gibbs energy is a minimum with respect to all possible changes at a given T and P . Mathematically this is: (d G) T,P = 0 this equation is necessary but not sufficient for chemical equilibrium

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2 Criterion for Phase Separation This mixture with composition x 1 * will phase separate into two liquid phases, one with composition x 1 a and the other with x 1 b . The mathematical criterion for NO phase separation in a binary system at constant T and P is : 0 2 1 2 > ± ² ³ ´ µ dx RT G d mix const T,P Spinodal limit
3 Other criteria for phase stability ( ) 0 0 0 1 ln 1 1 1 1 1 1 1 1 1 1 2 1 2 1 2 > > > > > dx dy dx d dx f d x dx d x x dx RT G d E μ ±

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4 Regular Solution: Can It Predict Phase Separation If we have equations for free energy of a mixture we can calculate when For 1 constant Margules model, phase separation can occur if the constant A > 2 . Can you derive this? 0 2 1 2 > ± ² ³ ´ µ dx RT G d mix 2 1 2 1 1 1 2 1 ln ln x Ax x x x x RT G x Ax RT G E + + = =
5 Analysis of liquid/liquid mixtures Criterion for equilibrium, and ± are labels indicating a phase Substituting definition of activity coefficients Rearranging gives ± 1 1 f f = 1 1 1 1 1 1 f x f x ² = 1 1 1 1 f x f ³ 1 1 1 1 x x =

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6 LLE Calculation Consider a binary liquid system with two equilibrium phases. a) Write down all the variable required to describe the composition. b) Write down a family of equations to solve for variables assuming 1 constant Margules model. use x 1 ± 1 = x 1 ² 1 ² to describe equilibrium ²
7 The Simplest Case: A system that follows regular solution ( ) ( ) 1 1 1 1 1 1 1 1 2 1 2 1 1 1 2 1 2 1 2 2 2 2 1 1 1 1 2 2 2 2 1 1 1 1 2 1 2 1 2 2 1 2 2 1 2 1 1 ln ) 2 1 ( 1 ., . , 5 . 0 x about

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## This homework help was uploaded on 04/17/2008 for the course MATLS Matls 2D03 taught by Professor Zhu during the Fall '05 term at McMaster University.

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2D_Course_Notes_-_Part_IV - Equilibrium and Stability Phase...

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