You\'ve seen several Pxy diagrams already. Now, let\'s construct a Txy diagram.
ID: 535711 • Letter: Y
Question
You've seen several Pxy diagrams already. Now, let's construct a Txy diagram. Txy diagrams plot temperature on the y-axis vs. mole fraction of x_1 on the x-axis. Pressure is constant. Use Excel to create a graph illustrating a Txy diagram for Benzene (1) + Toluene (2) mixtures at 1 atm. You will need to use Raoult's Law and the Antoine Equation within Excel: 1 atm = p_B + p_T = x_B P*_B(T) + x_T p*_T(T) Because it is a 2-component system, Raoult's Law can be simplified to: 1 atm = p_B + p_T = x_B p*_B(T) + (1 - x_B)p*_T(T) From the appendix of the book, we know the normal boiling points of benzene and toluene are 80.1 degree C and 110.6 degree C, respectively. We also have the Antoine coefficients for each substance to help us calculate p*(T) for each component. So, if we use the above equation at 0.1 degree C increments between these temperatures, we can solve for a relationship between T and x_B. Of course, once we know x_B for each T, solving for y_B at each T is simply a matter of using this equation: p_B = y_B P = x_B p*_B(T) Use color and labels to illustrate the liquid, vapor and 2-phase regions. Play with the graph settings in Excel to make it look nicer than the default graph produced by Excel. Add your name as a text box somewhere to the graph. Save your graph as a jpg or png image and upload it here. DO NOT upload your entire Excel spreadsheet.Explanation / Answer
For benzene, logPsat(mmHg)= 6.87987-1196.76/(t(deg.c)+219.161
for toluene, logpsat(mmHg)= 6.95087-1342.31/(t (deg.c)+219.187)
Assume a temperature between 80.1 and 110.6 deg.c which are the boiling point of benzene and toluene respectively.
Calculate P1sat for Benzene, more volatile component, P2sat for toluene , less volatile component.
From Raoult’s law
P=x1p1sat+x2p2sat
P= x1p1sat+(1-x1)P2sat
P= x1p1sat+P2sat-x1p2sat
Hence x1*(P1sat-P2sat)= P-P2sat
Hence x1= (P-P2sat)/ (P1sat-P2sat) (2)
And also y1P=x1p1sat, y1= x1p1sat/P (3)
Calculate x1 from Eq.2 , x2=1-x1, y1 from Eq.3 and y2=1-y1
The plot of T,x,y is drawn and shown .
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