HW8
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North Carolina State University *
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205
Subject
Chemistry
Date
Jan 9, 2024
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ChE 205
–
Fall 2023
Homework Set 8
Due: Friday, November 3 at noon.
This assignment is to be completed in your homework groups. Be sure to include the group number as
well as first and last names of all contributing group members in addition to the assignment number and
instructor name on the group cover sheet (see template in Moodle). Gradescope will ask you to associate
the names of all group members when you submit the assignment.
The entire (Gradescope) assignment
must be in
one person’s handwriting
. If you use an equation solving tool (calculator, APEx, Solver,
MATLAB), write out the equation(s) and note the tool that you used; otherwise, show all hand
calculations in equation solving.
In addition to the usual Gradescope submission, please have one team member submit the Excel file
that includes work from problem 4 as a separate document in Moodle.
1.
(
5 pts
) As a team, review the team expectations document on the Moodle site. Develop a list of the rules
and expectations you agree as a team to adopt. You should deal with any or all aspects of the
responsibilities outlined in the team document: preparation for and attendance at group meetings, making
sure everyone understands all the solutions, cooperating with the team effort, communicating frankly but
with respect when conflicts arise, etc. Submitting this as the response to Problem 1 indicates each team
membe
r’s acceptance of these expectations and intention to fulfill them. This should be typed out.
These expectations are for your use and benefit.
Note, however, that if you make the list fairly
thorough without being unrealistic you'll be giving yourselves the best chance. For example, "We will
each solve every problem in every assignment completely before we get together" or "We will never miss
a meeting" are probably unrealistic, but "We will try to set up the problems individually before meeting"
and "We will make sure that anyone who misses a meeting for good cause gets caught up on the work"
are reasonable.
2.
(5 pts)
State whether you would use Raoult’s law or Henry’s law to perform vapor–
liquid equilibrium
calculations for each component in the following liquid mixtures: (a) water and dissolved nitrogen;
(b) hexane, octane, and decane; and (c) CO
2
and water in club soda or any other carbonated beverage.
3.
(
10 pts
) Three moles of benzene and 7 moles of toluene are placed in a closed cylinder equipped with
a piston. The cylinder is immersed in a bath of boiling water that maintains the temperature at 100°C.
The force exerted on the piston can be varied to adjust the cylinder pressure to any desired value. The
pressure is initially 1000mm Hg and is gradually lowered to 600mm Hg. Use the
Pxy
diagram of
Figure 6.4-1 to convince yourself that the cylinder initially contains only liquid benzene and toluene
and to answer the following questions.
(a)
At what pressure does the first vapor bubble form? What is its composition?
(b)
At what pressure does the last droplet of liquid evaporate? What is its composition?
(c)
What are the liquid and vapor compositions in equilibrium with each other when the pressure
is 750mm Hg? What is the ratio (moles vapor/mole liquid) at this point?
(d)
Estimate the volume of the cylinder contents when the pressure is (i) 1000mm Hg, (ii)
750mm Hg, and (iii) 600mm Hg.
4.
(
20 pts
) Use an Excel spreadsheet to create a
Txy
diagram for the benzene-chloroform system at 1
atm. Once the spreadsheet has been created, it can be used as a template for vapor
–
liquid equilibrium
calculations for other species. The calculations will be based on Raoult’s law (
y
i
P = x
i
p
i
*
), although
we recognize that this relationship may not produce accurate results for benzene-chloroform mixtures.
(a)
Begin by establishing bounds on the system behavior. Look up the normal boiling points of
chloroform and benzene and, without performing any calculations, sketch the expected shape of a
Txy
diagram for these two species at 1 atm, with the x-axis representing the mole fraction of
chloroform.
(b)
Using APEx or Table B.4, estimate the normal boiling points of the two species and compare
them to the results in Part (a).
(c)
Make a Txy diagram in Excel
using Raoult’s Law
:
In Row 1, place the title
“
Txy
Diagram for Ideal Binary Solution of Chloroform and Benzene.”
In Row 2, place the label “
P
(mm Hg) =” and in the adjacent cell enter the system pressure, which
for this case is 760.
Below the title and pressure labels, place headings for columns:
x
C
,
x
B
,
T
,
p
C
*
,
p
B
*
,
p
C
,
p
B
,
P
,
y
C
,
y
B
, and
y
C
+y
B
. Not all of these columns are essential but help provide a complete picture of the
system and a final check of calculations. Use the following procedures to calculate the variables:
▪
x
C
: enter values for the liquid mole fraction chloroform from 0 to 1.00. Include at least 20
different values of
x
C
.
▪
x
B
: calculate the mole fraction of benzene for each corresponding value of
x
C
.
▪
T
: enter an estimate of the equilibrium temperature that is between the two pure-
component boiling points. This is the variable we will adjust using GoalSeek, so just
provide an initial guess.
▪
p
C
*
and
p
B
*
: calculate the vapor pressure corresponding to the estimated temperature
using APEx or Table B.4
(Antoine’s constants)
.
▪
p
C
and
p
B
: calculate partial pressures based on
Raoult’s law
(
p
i
=
y
i
P = x
i
p
i
*
).
▪
P
: Calculate pressure by summing partial pressures.
▪
Use GoalSeek to correct T
: Check whether the calculated pressure is equal to the known
pressure (760 mmHg)
–
the calculated pressure is likely not equal to 760 mmHg since the
temperature was an estimate. Adjust T to make the calculated pressure correct by using
GoalSeek.
▪
y
C
and
y
B
: calculate vapor phase mole fractions using partial pressures and
P
(
p
i
=
y
i
P
).
▪
y
C
+y
B
: sum the mole fractions to check the sum is 1.00.
Once you have completed a row for the first value of
x
C
, copy formulas into subsequent rows and
use GoalSeek to correct each temperature (GoalSeek must be done manually each time). When
the calculation has been completed for all rows (for all
x
C
values spanning 0 to 1), draw the
Txy
diagram by plotting two curves: one with
x
C
and
T
and one with
y
C
and
T
.
(d)
The calculations used in part (c) relied on Raoult’s Law, which assumes the
solution is an ideal
solution. We can check whether chloroform and benzene form an ideal solution by comparing the
Txy diagram constructed using Raoult’s Law with its Txy diagram constructed using
experimental data.
The following vapor
–
liquid equilibrium data have been obtained for mixtures of chloroform (C)
and benzene (B) at 1 atm.
Draw the Txy curves using these data as well as the Txy curves using values calculated in part (c)
on the same graph, making sure to distinguish the two sets of values (i.e. plotting the calculated
values in one color and the experimental values in another).
(e)
Estimate the percentage errors in the Raoult’s
law values of the bubble-point temperature and
vapor mole fraction for
x
C
= 0.44, taking the experimental values to be correct. Why does
Raoult’s law give poor estimates for this system?
A screenshot of your spreadsheet display and plots should be submitted as part of the homework set
with Problem 4 via Gradescope. Additionally, each group should upload ONE Excel file to Moodle
(name the file
group#_HW8.xslx
using your group number). Any individual in the homework
group can submit the Excel file.
(
60 pts
) The remainder of the assignment (6 problems) will be completed online
individually
using
WileyPLUS.
You do not have to turn in any paperwork with this portion of the assignment.
The due date
for the WileyPLUS completion is the same as for the homework assignment.
Note that the WileyPLUS
assignment cannot be submitted late.
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