Given the adjacent Txy phase diagram, apply the Gibbs phase rule to calculate th

Question

Given the adjacent Txy phase diagram, apply the Gibbs phase rule to calculate the degrees of freedom. F =2- pi + N where pi is the number of phases present, N is the number of chemical species present and F is the number of degrees of freedom that the system has. Note that the pressure is constant. for a point inside the vapor phase for a point within the L+V region for the boiling point of toluene, i.e., 110.6degree C. State the number of species, phases, and you're your calculations in every case for full credit. (b) Consider a mixture with composition x_benz= 0.4 at 85 degree C. The mixture is heated slowly. Use the above phase diagram to determine the following: At what temperature does the first vapor bubble form? What is the composition of this vapor phase? At what temperature does complete vaporization of the initial mixture first occur? What is the composition of the last remaining liquid droplet prior to the complete vaporization?

Explanation / Answer

a) i) F = 2 - 1 + 2 = 3 Since only phase and two components

ii) F = 2 - 2 +2 = 2 Since two phases and two component

iii) F = 2 - 2 +1 = 1 Since two phases and only one component that is toluene

b) i) From the x=0.4 draw a perpendicular to the x-axis find the point of intersection of it witht he lower curve. This point gives you the at which first vapor bubble forms. Ans: T = 93 deg C

ii) From this point draw a line paralle to the x-axis. Find its intersection with the upper curve. This point gives you the vapor compositiom. Ans: x benzene = 0.6 x toluene = 0.4

iii) From x=0.4 draw a perpendicular to the x-axis. Find its point of intersection witht he upper curve. This point gives you the T of complete vaporzation. Ans: T = 102 deg C

iv) From this point draw a line parallel to the x-axis. Find its point of intersection with the lower curve. This gives you the composition of the last liquid droplet. Ans: x benzene = 0.2 x toluene = 0.8

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