Potentially Useful Equations rev

Potentially Useful Equations rev - Potentially Useful...

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Unformatted text preview: Potentially Useful Equations (List to be furnished during examinations) GU CV H U PV A U TS PV TS H TS U T ; CP V A PV H T P dU TdS PdV dH TdS VdP dA dG fi f iVapor RT ln i SdT PdV SdT VdP fi yi i P RT dv RT ln zmix v m V m P ni y j Bij T , P ,n j ln i 2 v fi j1 3 2v 2 sat m y j yk Cijk j1k 1 P ln zmix liquid v liquid dP xi i Pi exp RT P sat i RT ln i g E i nT g E ni P T , P ,n j fi solid v solid dP Pi exp RT P sat sat i Gibbs-Duhem Equation m At Constant T, P: i1 xi d ln i 0 Liquid-Liquid Equilibria At Critical Solution Point: 2 G M / x 2 0; 3 G M / x 3 1-Term Margules: gE Ax1 x2 ; A / RTc 2 van Laar Equation: 0 T UCST A 2 x1 x2 UCST B ; x1 3 A R x1 x2 B Regular Solution Theory 2 2 x1 x2 v12 v2 2 1 2 3 2 A B 2 1 A 1 B A 1 B 2 A B RTc x1v1 x2 v2 ; x1 v1 2 v12 v2 v1 v2 v1v2 Solid Solubility 1 ln x2 h fusion Tm 1 RTm T ln 1 2 Equations of State Ideal Gas: Pv Virial EOS: z Pv RT 1 RT BC ... v v2 RT a van der Waals EOS: P v - b v2 aT RT Peng-Robinson EOS: P v-b v v b b v b hemical ΔH Cf(T), ln Equilibrium i ˆ fi / fi o K ; K exp G o / RT G If For Ideal Gas, For Liquid at low P; o d ln K Ho iG ; dT RT 2 K Ho 1 1 K' R T T' o i yi i P Po xi i K K i Some Excess Gibbs Energy Expressions MARGULES EQUATION: gE x1 x2 RT ln ln 2 1 2 B C x1 x2 3 3 D x1 D 2 x2 x2 2 ... 5 5 ... ... x2 B C 4x 2 2 x1 B 1 6 x2 C 4 x1 D 2 x1 1 6 x1 VAN LAAR EQUATION: gE RT ln A 1 ABx1 x2 Ax1 Bx2 2 ln B 2 Ax1 1 Bx2 Bx2 1 Ax1 2 REGULAR SOLUTION THEORY : gE x1v1 RT ln RT ln 1 2 x2 v 2 v1 v2 2 2 2 1 1 2 1 1 ( 1 2 2 2 )2 ( ( i )2 )2 2 i i i Multicomponent System : RT ln vi SCATCHARD-HAMER EQUATION: ln ln 1 2 A z2 B z3 2 3 B 2 v2 2 z1 v1 B v2 3 z1 v1 2 A WILSON EQUATION: gE RT where, ij N N xi ln i1 j1 xj ij ij vj exp vi N ii RT N ln i 1 ln j1 xj xk N ki kj ij k1 xj j1 NRTL EQUATION: g RT where G12 ln 1 E x1 x2 21 x1 g12 G21 x2 G21 12 G12 x2 x1 G12 21 12 exp x 2 2 21 12 g22 ; RT 12 ; G12 g12 g11 RT 12 12 exp 2 G21 x1 x2 G21 G12 x1 G12 x2 12 G12 x2 G 21 2 2 x1 G12 2 21 ln 2 2 x1 12 x1 x2 G21 ...
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This note was uploaded on 10/18/2009 for the course CHBE 3110 taught by Professor Staff during the Spring '08 term at Georgia Tech.

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