University College - Chemistry Chem 402 Lecture Notes - Lecture 31: Xband, Phase Rule, Distant Early Warning Line

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harlequinimpala978

28 Apr 2017

School

WUSTL

Department

University College - Chemistry

Course

University College - Chemistry Chem 402

Professor

Barnes Alexander

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Document Summary

L31: two component phase equilibria: 2 component phase equilibria, vapor pressures at fixed temperature, ideal solutions where both components obey raoult"s law. 10 april 2017: the left diagram shows the composition of the liquid phase and does not provide information about the gas phase composition, the gas phase is described by ya or yb. If t and xa are given, they ya and yb are fixed (by the gibbs phase rule) = (cid:3043)(cid:3251) (cid:3025)(cid:3250)(cid:3043)(cid:3250) +(cid:4666)(cid:3043)(cid:3250) (cid:3043)(cid:3251) (cid:4667) (cid:2869)(cid:3026)(cid:3250)= (cid:3043)(cid:3251) (cid:3025)(cid:3250)(cid:3043)(cid:3250) +(cid:3025)(cid:3250)(cid:4666)(cid:3043)(cid:3250) (cid:3043)(cid:3251) (cid:4667) (cid:3043)(cid:3250) (cid:3025)(cid:3250)(cid:3043)(cid:3250) (cid:4672)(cid:3026)(cid:3250)(cid:3026)(cid:3250)(cid:4673) (cid:3043)(cid:3251) (cid:3025)(cid:3250)=(cid:3043)(cid:3250) +(cid:3026)(cid:3250)(cid:4666)(cid:3043)(cid:3251) (cid:3043)(cid:3250) (cid:4667) (cid:3043)(cid:3251) (cid:3025)(cid:3250)(cid:3043)(cid:3250) = (cid:2869)(cid:3026)(cid:3250)(cid:4672)(cid:3043)(cid:3250) (cid:3043)(cid:3250) (cid:4673) (cid:3043)(cid:3250) (cid:3043)(cid:3251) (cid:3043)(cid:3250) (cid:3026)(cid:3250) Rearrange to find xa: (cid:1850)(cid:3002)= (cid:3026)(cid:3250)(cid:3043)(cid:3251) (cid:3043)(cid:3250) +(cid:3026)(cid:3250)((cid:3043)(cid:3251) (cid:3043)(cid:3250) , then substitute into =(cid:3043)(cid:3250)(cid:3026)(cid:3250)=(cid:3025)(cid:3250)(cid:3043)(cid:3250) (cid:3026)(cid:3250) (cid:3043)(cid:3250) +(cid:3026)(cid:3250)((cid:3043)(cid:3251) (cid:3043)(cid:3250) ) (cid:4672)(cid:2869)(cid:3026)(cid:3250)(cid:4673)= (cid:3026)(cid:3250)(cid:3043)(cid:3251) (cid:3043)(cid:3250) (cid:3043)(cid:3251) (cid:3043)(cid:3250) (cid:3043)(cid:3250) +(cid:3026)(cid:3250)((cid:3043)(cid:3251) (cid:3043)(cid:3250) , looks like a function of 1/x multiplied by some constant, using bubble and dew line diagrams (constant t, looking at the diagram:

Related Questions

Which of the following statements are true about an ideal solution of two volatile liquids?

A. The partial pressure of each component above the liquid is given by Raoult's law.

B.The liquid and gaseous phases can only coexist for a single value of the pressure at a given temperature.

C. An ideal solution of two volatile liquids can exist over a range of pressures that are limited by the pressure for which only a trace of liquid remains, and the pressure for which only a trace of gas remains.

D. The vapor phase is always depleted in the more volatile or higher vapor pressure component in comparison with the liquid phase.

Answer choices:

A and B

A and C

C and D

B and D

The liquid phase activity coefficients of the ethanol(1)+toluene (2) system at 55 C are given by the two-parameter Margules equation, where A12=1.869 and A21=1.654.
(a) Show that the pure saturation fugacity coefficient is approximately 1 for both components.

(b) Calculate the fugacity for each component in the liquid mixture at x1=0.0, 0.2, 0.4, 0.6, 0.8 and 1.0. Summarize your results in a table. Plot the fugacities for both components versus x1. Label your curves. For each curve, indicate the regions that may be approximated by Henryâs law and the ideal solution model.

(c) Using the results in part (b), estimate the total pressure above the liquid mixture at 55 C when a vapor phase coexists. Assume the gas phase is ideal for this calculation. Also estimate the vapor composition.
(d) Comment on the validity of the ideal gas assumption used in part (c).

Suppose the (1) + (2) system exhibits liquid-liquid immiscibility. Suppose we are at a state where G1/RT = 0.1 and G2/RT = 0.3. The Gibbs energy of mixing quantifies the Gibbs energy of the mixture relative to the Gibbs energies of the pure components. Suppose the excess Gibbs energy for the (1) + (2) mixture is given by: GE/RT = 2.5 x1 x2

a. Combine this with the Gibbs energy for ideal mixing to calculate the Gibbs energy of mixing across the composition range and plot the results against x1 to illustrate that the system exhibits immiscibility.

b. Draw a tangent to the humps to illustrate that the system is one phase at compositions greater than z1 = 0.854 and less than z1 = 0.145, but will split into two phases with compositions at any intermediate overall composition. Most systems with liquid-liquid immiscibility must be modeled with a more complex formula for excess Gibbs energy. The humps on the diagram are usually offcenter, as in Fig. 14.3 on page 545 in the text. The simple model used for the calculations here results in the symmetrical diagram.

c. When a mixture splits into two phases, the over-all fractions (of total moles) of the two phases are found by the lever rule along the composition coordinate. Suppose 0.6 mol of (1) and 0.4 mol of (2) are mixed. Use the lever rule to calculate the total number of moles which would be found in each phase of the actual system. Designate the (1)-rich phase as the Î² phase.

d. What is the value of the hypothetical Gibbs energy, (expressed as G/RT), of a mixture of 0.6 mol of (1) and 0.4 mol of (2) if the mixture were to remain as one phase? Calculate the Gibbs energy of the total system considering the phase split into two phases, and show that the Gibbs energy is less than the Gibbs energy of the single-phase system.

University College - Chemistry Chem 402 Lecture Notes - Lecture 31: Xband, Phase Rule, Distant Early Warning Line

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