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home / study / science / chemistry / chemical engineering / chemical engineering solutions manuals / introduction to chemical engineering thermodynamics / 7th edition / chapter 10
Introduction to Chemical Engineering Thermodynamics
Thermodynamics (7th Edition)
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Assuming the validity of Raoult’s law, do the following calculations for the benzene(1)/to
benzene(1)/toluene(2)
luene(2)
system:
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(a) Given x1 = 0.33 and T = 100&deg;C, ﬁnd y1 and P.
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(b) Given y1, = 0.33 and T = 100&deg;C, ﬁnd x1, and P.
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(c) Given x1, = 0.33 and P = 120 kPa, ﬁnd y1, and T.
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(d) Given y1, = 0.33 and P = 120 kPa, ﬁnd x1, and T.
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(e) Given T = 105&deg;C and P = 120 kPa, ﬁnd x1 and y1.
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(f) For part ( e), if the overall mole fraction of benzene is z1 = 0.33, what molar fraction of the twophase system is vapor?
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(g) Why is Raoult’s law likely to be an excellent VLE model for this system at the stated (or
computed) conditions?
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Step 1 of 12
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The given binary mixture system is benzene (1)/ toluene (2) system.
Write the mathematical expression of Raoult’s law as follows:
…… (1)
Here,
is the total pressure,
fraction,
is the vapor phase mole fraction,
is the liquid phase mole
is the vapor pressure of pure species.
Write the expression for total pressure by using Raoult’s law.
At
,
Then,
For binary species,
…… (2)
Write
Wri
te the exp
expre
ressi
ssion
on for the sat
satur
urati
ation
on pre
pressu
ssure
re
using
usi
ng Ant
Antoin
oine
e equa
equatio
tion.
n.
…… (3)
Here,
is in
, temperature is in
,
and
are constants.
26
218
26
From table B.2, the values of
and
for benzene and toluene is as follows:
Comment
Step 2 of 12
(a)
The given temperature is
bubble pressure as follows:
and the liquid phase mole fraction is
The mole fraction of benzene
in the liquid solution is
i n the liquid solution is
. Then, calculate the
and the mole fraction of toluene
.
Now, calculate saturation pressures of benzene and toluene in following manner:
Comment
Step 3 of 12
Calculate the total pressure of the system from equation (2) as follows:
Substitute the known values in equation (1) and calculate the value of
Therefore, the values of
and
are
and
.
respectively.
Comment
Step 4 of 12
(b)
The given vapor phase mole fraction is
dew pressure as follows:
The mole fraction of benzene
in the vapor phase is
and the temperature is
in the vapor phase is
. Then, calculate the
and the mole fraction of toluene
.
Now, calculate the saturation pressures of benzene and toluene from equation (3).
Comment
Step 5 of 12
To calculate liquid phase mole fraction, substitute the known values in equation (1).
Calculate the total pressure of the system from equation (2) as follows:
Therefore, the values of
and
are
and
respectively.
Comment
Step 6 of 12
(c)
The given liquid phase mole fraction is
and the total pressure of the system is
Then, calculate the bubble temperature as follows:
The mole fraction of benzene
in the liquid solution is
in the liquid solution is
.
and the mole fraction of toluene
.
Now, calculate the saturation pressure as follows:
To calculate the vapor phase mole fraction, substitute the known values in equation (1).
Calculate the total pressure of the system from equation (2) as follows:
Step 11 of 12
(f)
The overall concentration
of benzene is
fraction of vapor is equal to
.
. For the fraction of liquid be
and the
The expression for the overall balance is as follows:
Write the expression for the mole balance of benzene as follows:
Solve equations (6) and (7) and calculate the values of
.
The molar fraction of two phase system in vapor phase is
.
Comment
Step 12 of 12
(g)
Benzene and toluene are both non-polar and similar in shape and size. Therefore, there will be
very little interaction between them and more over high temperature and low pressure also favors
for the ideal behavior.
Comment
21
0
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