(a) You have an equimolar mixture of ethanol (1) and 1-propanol (2) at atmospher

Question

(a) You have an equimolar mixture of ethanol (1) and 1-propanol (2) at atmospheric pressure (1 bar). Compute the dew point and bubble point of this mixture, making sure to think about what assumptions you can make and why they are valid.
(b) Plot the Txy diagram for this mixture (at a pressure of 1 bar) and label the bubble and dew lines. Include 11 points (or more if you wish) evenly spaced from x1=0 to x1=1 for both the bubble and dew lines, and make sure the plot is formatted so that the phase coexistence region is clearly visible.

a) You have an equimolar mixture of ethanol (1) and 1-propanol (2) at atmospheric pressure (1 bar. Compute the dew point and bubble point of this mixture, making sure to think about what assumptions you can make and why they are valid (b) Plot the Txy diagram for this mixture (at a pressure of 1 bar and label the bubble and dew lines. Include 11 points (or more if you wish) evenly spaced from x1 0 to x1 1 for both the bubble and dew lines, and make sure the plot is formatted so that the phase coexistence region is clearly visible

Explanation / Answer

Antoine equations for ethanol(1) and 1-propanol (2)

Ethanol : logPsat(mm Hg)= 7.68117-1332.04/ (t+199.3) , t in deg.c and the equation is valid in the temperature range of   77 to 243 deg.c

1-propanol log Psat (mm Hg) = 7.74416- 1437.686/ (t+198.463) , t in deg.c and the equation is valid for temperature range of 60 to 106 deg.c

First the temperature range of the mixture

At 1 bar= 0.9869 atm =0.9869*760 mm Hg=750 mm Hg

Ethanol, log 750= 7.68117- 1332.04/(t+199.2) , t= 77.95 deg.c

For 1-propanol log 750 = 7.74416- 1437.686/(t+198.463), t= 96.8 deg.c

The temperature lies between 77.9 deg.c amd 96.8 deg.c

Bubble point is the temperature at which first drop of liquid vaporizes.

Assuming validity of Raoult’s law, y1P= x1p1sat (1) and y2P= x2p2sat (2)

Where P is total pressure, y1,x1 are mole fractions of ethanol in vapor and liquid phase, y2,x2 are mole fractions of 1-propanol in the vapor and liquid phase.

Addition of Eq.1 and 2 gives

P= x1p1sat+x2p2sat

750= 0.5*P1sat+0.5*P2sat or P1sat+P2sat=1500 (3)

Assume a temperature. Calculate P1sat and P2sat to see that it matches with Eq.3 When solved in excel, this gives rise to a bubble point temperature of 85.79 deg.c

For Dew point calculations, y1=y2=0.5 and hence x1= y1P/P1sat and x2= y2P/P2sat

Hence x1+x2= 1= y1P/P1sat + y2P/P2sat

0.5*750/P1sat+0.5*750/P2sat= 1

Or 375/P1sat + 375/P2sat= 1, 1/P1sat +1/P2sat= 1/375= 0.002667

Assume a temperature and calculate P1sat and P2sat and see that it matched with the above equation. The calculations when done in excel gives a dew point is of 89 deg.c

For generating the T-x,y diagram, the following procedure needs to be adopted.

Hence P= x1P1sat+x2P2sat= x1P1sat+(1-x1)*P2sat,

Hence x1= (P-P2sat)/ (P1sat-P2sat)

Assume temperatures between 77.95 deg.c to 96.8 deg.c ( 11 points). Calculate P1sat and P2sat. Calculate x1 and x2=1-x1, y1 = x1p1sat/P and y2=1-y1

The calculations along with the plot are shown below

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