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ECHE 311/SPRING 2015 Problem Set #8 VLE Calculations 1. The excess Gibbs energy of the binary liquid mixture at T and P is given by: GE/RT = (-2.6 x1-1.8 x2) x1x2 For the given T and P, a) Find expression for ln 1 and ln 2 . b) Show that when these expressions are combined in accord with Eq. GE xi ln i the given equation for GE/RT is recovered. RT i c) Show that these expressions satisfy the Gibs/Duhem equation xi d ln i 0 . d) Show that ( d ln 1 / dx1 ) x 1 =( d ln 2 / dx1 ) x 0 =0 1 1 i Hint: a) Substitute x2=1-x1 b) Apply Eqs. M 1 M x 2 dM dM & Eq. M 2 M x1 dx1 dx1 for M=GE/RT GE d( ) GE RT ln 1 (1 x1 ) RT dx1 ; define ln 2 GE d( ) RT Find dx1 Find ln 1 and ln 2 2. Plot values of GERT, ln 1 and ln 2 calculated by the given equation for GE/RT and by the equations developed in problem (a) vs x1 . 1 3. For a ternary solution at constant T and P, the composition dependence of molar property M is given by: M x1M1 x2 M 2 x3 M 3 x1x2 x 3 C where M1 , M2 and M3 are the values of M for pure species, 1, 2, and 3 and C is a parameter independent of composition. Determine the expression for application of equation Mi [ (nM ] P,T ,n j ni 4. Equations analogous to Eqs M 2 M x1 dM dx1 property with respect to written for ln 1 and M 1 M x2 and ln i is a partial G E / RT , these analogous equations can be ln 2 in a binary system. ln 1 A12 (1 ln 2 A21 (1 dM dx1 apply for excess properties. Since Write these equations, and apply them to that Eqs M 2 by GE A12 A21 x1x2 A12 x1 A21x2 A12 x1 2 ) A21x2 A21x2 2 ) A12 x1 and are indeed obtained. 2 to show 5. The following is a set of VLE data for the system methanol(1)/water(2) at 333oK ______________________________ P/kPa x1 y1 __________________________ 19.953 39.223 42.984 48.852 52.784 56.652 60.614 63.998 67.924 70.229 72.832 84.562 0.0000 0.1686 0.2167 0.3039 0.3681 0.4461 0.5282 0.6044 0.6804 0.7255 0.7776 1.0000 0.0000 0.5714 0.6268 0.6943 0.7345 0.7742 0.8085 0.8383 0.8733 0.8922 0.9141 1.0000 a) Basing calculations on Eq. i yi P yP i sat xi fi xi Pi find parameter values for G E / RT the Margules equation that provide the best fit of to the data, and prepare a Pxy diagram that compares the experimental points with curves determined from the correlation. 3