2D_Course_Notes_-_Part_III

# 2D_Course_Notes_-_Part_III - 1 The Ideal Solution i id i ig...

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Unformatted text preview: 1 The Ideal Solution i id i ig i ig i i id i ig i ig i i ig i ig i i ig i ig i i i id i i ig i ig i H H H H V V V V x ln R S S y ln R S S x ln RT G G y ln RT G G = = = = & = & = + = + = ( ) i i id i id i i id i i i i id i i i id i i i i i i id i i i i i i id f x f f ln RT T H x H V x V x ln x R S x S x ln x RT G x G = + ¡ = μ = = & = + = ¢ ¢ ¢ ¢ ¢ ¢ Ideal gas mixture: Ideal liquid solution: 2 What happens in mixing ideal solution ? ( ) & & ¡ = ¡ = ¢ i i id i id i i id mix x ln x R S S x S ( ) H H y H id i id i i id mix = ¡ = ¢ & ( ) V V x V id i id i i id mix = ¡ = ¢ & ( ) & & & ¡ = ¡ = ¢ id i id i i id i i id i i id mix M M x M x M x M ( ) & & = ¡ = ¢ i i id i id i i id mix x ln x RT G G x G 3 What can we do if solution is nonideal? E E id mix mix E E id mix mix i i i i i i E id mix mix i i i i i i E id mix mix H H H H V V V V x R x x R S S S x RT x x RT G G G = + = = + = & & = + = + = + = ¡ ¡ ¡ ¡ ¢ ¢ ¢ ¢ £ ¢ ¢ £ ¢ ¢ ln ln ln ln ¡ ¡ ¡ ¡ ¡ £ = + ¢ = £ + = = ¢ = ¢ i i i E E id i i i i i i i i i i i i id ln x RT G G G ln x RT x ln x RT a ln x RT G x ln x RT G : Recall 4 Excess Properties Residual: Excess: ( ) ( ) & & ¡ = ¡ = ¡ = ¡ = i id i i i id E i ig i i i ig R M M x M M M M M x M M M 5 Activity and Activity Coefficient ( ) P y f P y f RT G i i i i i ig i i R i / / ln = = & = ¡ μ μ ( ) ( ) ( ) f / f x a f x / f f x / f ln RT G f x ln RT T f ln RT T i i i i i i i i i id E i i i i id i i i i = ¢ = = ¢ = μ & μ = + £ = μ + £ = μ ( ) [ ] ( ) [ ] ( ) [ ] j n , P , T i E i x , P E 2 E x , T E E n / RT / nG ln T / RT / G RT / H P / RT / G RT / V ¤ ¤ = ¢ ¤ ¤ & = ¤ ¤ = ( ) [ ] ( ) [ ] ( ) [ ] j n , P , T i R i x , P R 2 R x , T R R n / RT / nG ln T / RT / G RT / H P / RT / G RT / V ¤ ¤ = ¡ ¤ ¤ & = ¤ ¤ = 6 Activity coefficients from LVE Data fundamental criterion for phase equ. Coefficient definitions substituting definitions recall for a pure liquid l a v a f f = P y f a v a v a = & a a l a a f x f = ¡ a a a a a f x P y ¡ & = ¢ ¢ £ ¤ ¥ ¥ ¦ § = ¨ P P sat RT VdP exp sat a sat a P f & Vapor Liquid 7 From LVE data continued & completely rigorous - no approximations & can't usually apply - not enough information & ¡ ¢ £ ¤ ¥ = ¦ P P a sat a sat a a a a a sat a RT dP V P x P y exp § ¨ § Substitution of previous 2 gives P a sat T P T a & b a only v a sat a § x a ¨ a y a a § 8 Approximation 1- assume liquid incompressible ( ) & & ¡ ¢ £ £ ¤ ¥ ¦ = RT P P V P x P y sat a l a sat a sat a a a a a exp § ¨ § & ¡ ¢ £ ¤ ¥ = © P P a sat a sat a a a a a sat a RT dP...
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2D_Course_Notes_-_Part_III - 1 The Ideal Solution i id i ig...

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