Finding VLE of Methyl Acetate & Methanol: Dew & Bubble T, Comp

[coso21]

(a) Find the dew temperature and composition for a mixture of y1 = 0.55 at 3.954 bar. (Answers. 371 K and x1 = 0.58)
(b) Find the bubble temperature and composition for a mixture of x1 = 0.50 at 3.954 bar.
(Answers. 371 K and y1 = 0.49)
(c) Using the Wilson equation and the constants listed, find the bubble pressure and vapour composition for a mixture of 30 mol% methyl acetate at 90C.
(Answers. 3.1 bar and y1 = 0.36)

Vc zcPc, bar Tc, K
Methyl acetate (1) 46.3 506.8 0.324 228.0 cc/mol 0.254
Methanol (2) 79.9 512.6 0.559 118.0 cc/mol 0.224

Antoine Constants (P is in torr)
CA B C Range,
Methyl acetate (1) 7.41791 1386.510 247.853 57 - 205
Methanol (2) 7.97010 1521.230 233.970 65 - 214

Constants A12 A21
Margules’ 0.8427 0.4043
Van Laar 0.8914 0.4718
Wilson 336.148 350.841

Vapour-Liquid Equilibrium Data at 3.954 bar Total Pressure,
Methyl acetate – Methanol
C x1Temperature, y1
104.40 0.0000 0.0000
100.50 0.0880 0.1540
98.60 0.1980 0.2730
97.30 0.2960 0.3680
97.20 0.3980 0.4370
97.10 0.5150 05220
97.00 0.5380 0.5380
97.30 0.6260 0.5980
98.10 0.7320 0.6840
98.90 0.7970 0.7500
99.60 0.8340 0.7950
101.30 0.9130 0.8950
103.80 1.0000 1.0000

How would i solve each question? I can't get the right answer.
I used Raoult's Law for the first two and didnt get close, is that right?

I need to use the antoine equation to find P1sat and P2sat right? But I don't know what value for Temperature I am meant to put in the equation (T is in celsius).

What do I use after I have worked that out?

 

[nate808]

To solve this problem, you will need to use a combination of the given equations and data. Here is a step-by-step guide to solving each question:

(a) To find the dew temperature and composition for a mixture of y1 = 0.55 at 3.954 bar, you will need to use the Wilson equation. Plug in the given values for y1, P, and the Wilson constants, and solve for T. This will give you the dew temperature, which is the temperature at which the vapor and liquid phases will be in equilibrium.

Next, you will need to use the given vapor-liquid equilibrium data for the mixture of methyl acetate and methanol at 3.954 bar. Find the data point closest to the dew temperature you calculated and record the corresponding value for x1. This will give you the composition of the liquid phase at the dew temperature.

(b) To find the bubble temperature and composition for a mixture of x1 = 0.50 at 3.954 bar, you will need to use the same process as in part (a), but with different given values. Use the Wilson equation to solve for T, and then find the data point closest to this temperature in the vapor-liquid equilibrium data. Record the corresponding value for y1, which will give you the composition of the vapor phase at the bubble temperature.

(c) To find the bubble pressure and vapor composition for a mixture of 30 mol% methyl acetate at 90C, you will need to use the given Antoine constants and the antoine equation. Plug in the given temperature (90C = 363.15K) and Antoine constants for methyl acetate, and solve for P1sat. This will give you the saturation pressure for pure methyl acetate at 90C.

Next, you will need to use the given Wilson constants to solve for P2sat, the saturation pressure for pure methanol at 90C. Once you have both saturation pressures, you can use the given Margules' equation to calculate the bubble pressure for the mixture. Plug in the saturation pressures, the given mole fraction of methyl acetate (x1 = 0.30), and the Margules' constants to solve for P. This will give you the bubble pressure for the mixture.

Finally, to find the vapor composition, you will need to use the given Wilson equation and the bubble pressure you just calculated. Plug in the given temperature (90C = 363

 

[Blueshift5]

To solve these questions, you will need to use a variety of equations and constants. Here are the steps to solve each question:

(a) To find the dew temperature and composition, you will need to use the Raoult's Law equation. This equation states that the vapor pressure of a component in a mixture is equal to its mole fraction multiplied by its vapor pressure at the given temperature. In this case, you will use the vapor pressure of methyl acetate and methanol at the given temperature of 371 K to solve for the mole fraction of methyl acetate (x1). Once you have x1, you can use the definition of mole fraction to solve for the mole fraction of methanol (x2). These two mole fractions will give you the composition of the mixture. Then, you can use the bubble point equation (also known as the dew point equation) to solve for the dew temperature at a given pressure. This equation can be found in most thermodynamics textbooks or online.

(b) The process for finding the bubble temperature and composition is similar to the one described above for the dew temperature and composition. The main difference is that you will use the bubble point equation to solve for the bubble temperature instead of the dew temperature. You will also use the vapor pressure of methyl acetate and methanol at the given temperature of 371 K to solve for the mole fraction of each component.

(c) To solve for the bubble pressure and vapor composition using the Wilson equation, you will need to first calculate the activity coefficients of each component using the Wilson equation. Then, you can use these activity coefficients to solve for the bubble pressure and vapor composition using the equations for the Wilson model. The constants listed in the problem (A12 and A21) can be used in these equations.

Overall, to solve these problems, you will need to use a combination of the Raoult's Law equation, the bubble point equation, and the Wilson equation. You will also need to use the given constants and data for the Antoine equation to calculate the vapor pressures of methyl acetate and methanol at the given temperatures. Make sure to double-check your calculations and units to ensure you get the correct answers.