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Introduction to Chemical Engineering Thermodynamics Thermodynamics (7th Edition) Chapter 10, Problem 7P

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A single-stage liquid/vapor separation for the benzene(1)/ethylbenzene(2) benzene(1)/ethylbenzene(2) system must produce phases of the following equilibrium compositions. For one of these sets, determine the T  and  and P in the separator. What additional information is needed to compute the relative amounts of liquid and vapor leaving the separator? Assume that Raoult’s law applies.

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(a)  x 1 = 0.35,  y 1 = 0.70. (b)  x 1 = 0.35,  y 1 = 0.725. (c)  x 1 = 0.35,  y 1 = 0.75.

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(d )  x 1 = 0.35,  y 1 = 0.775. Manufacturi ng Processes

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The Antoine equations for vapor pressures of pure benzene (1) and ethylbenzene (2) are as follows:

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Step 2 of 12

Here, and

and

are the saturated pressures,

is the temperature temperature,,

are Antoine constants.

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Step 3 of 12

(a) The mo mole le fr fract action ion of ben benze zene ne in liq liquid uid

and vap vapor or

are

and

According to Raoult’s law, the expression for total pressure is as follows:

 …… (1)

,

26

218

26

Similarly, for benzene, the equation for Raoult’s law is as follows:

 …… (2) Now, substitute equation (2) in equation (1) and solve for temperature

On solving the temperature is

in following method:

.

Comment

Step 4 of 12

Now, substitute manner:

Thus, the pressure

in equation (2) and calculate the value of

is

in following

.

Comment

Step 5 of 12

(b) The mole fraction of benzene in liquid

and vapor

are

and

According to Raoult’s law, the expression for total pressure is as follows:

 …… (1) Similarly, for benzene, the equation for Raoult’s law is as follows:

 …… (2)

Now, substitute equation (2) in equation (1) and solve for temperature

On solving the temperature is

in following method:

.

Comment

Step 6 of 12

Now, substitute manner:

Thus, the pressure

in equation (2) and calculate the value of

is

in following

.

Comment

Step 7 of 12

(c) The mole fraction of benzene in liquid

and vapor

are

and

According to Raoult’s law, the expression for total pressure is as follows:

 …… (1) Similarly, for benzene, the equation for Raoult’s law is as follows:

 …… (2)

Comment

Step 8 of 12

Now, substitute equation (2) in equation (1) and solve for temperature

On solving the temperature is

in following method:

.

Comment

Step 9 of 12

Now, substitute

Thus, the pressure

in equation (2) and calculate the value of

is

in following manner:

.

Comment

Step 10 of 12

(d) The mole fraction of benzene in liquid

and vapor

are

and

According to Raoult’s law, the expression for total pressure is as follows:

 …… (1) Similarly, for benzene, the equation for Raoult’s law is as follows:

 …… (2) Now, substitute equation (2) in equation (1) and solve for temperature

in following method:

On solving the temperature is

.

Comment

Step 11 of 12

Now, substitute

Thus, the pressure

in equation (2) and calculate the value of

is

in following manner:

.

Comment

Step 12 of 12

Here, we just know only the mole fraction of benzene (1) and ethyl benzene (2). To determine the relative amounts of liquid and vapor leaving the separator, we need either mole rate or mass rate of the initial mixture.

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