Download MathCAD for Physical Chemistry Phase Equilibrium

MathCAD for Physical Chemistry
Phase Equilibrium
Objectives
In this problem set you will learn the following.
1. How to determine heats of vaporization from vapor pressure-temperature data.
2. How to go beyond linear least squares fit by fitting data to a linear combination of
functions.
3. Illustrative application of symbolic integration.
4. How to apply the solve block (Given and Find block) to solve a set of equations.
Prerequisites
Knowledge of the Clausius-Clapeyron equation
MathCAD’s integration function for definite integrals
Graphing data and fitted functions on the same plot
Boiling temperature of fluid via equal area rule
Text: Physical Chemistry Using MathCAD by Joseph H. Noggle [Pike Creek Publishing,
1997] and
Web resource: http://www.monmouth.edu/~tzielins/mathcad/tjz/doc001.htm
Read and Do Assignment
Do this before coming to the computer lab meeting
Noggle's text, Chapter 4 "Phase Equilibrium"
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•
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Read section 4.1 (Clausius-Clapeyron Equation). Work examples 4.1, 4.2. 4.3
4.2 (Curve Fitting). Work exercises 4.4 and 4.4
(skip 4.3)
4.4 (Vapor Pressure from Gas Laws). Work exercises 4.8, (skip 4.9) 4.10 and 4.11.
Problems: The computer lab meeting will concentrate on working these.
1. Open a new worksheet. [Noggle Problem 4.2] The standard method for measuring the
enthalpy of vaporization of a substance is an indirect approach based on vapor pressure versus
temperature and the Clausius-Clapeyron equation. For instance, the measured values of the vapor
pressure of carbon tetrachloride at several temperatures are given in the table:
1
Vapor pressure of CCl4 at several temperatures
T (C)
P (torr)
30
142.3
50
314.4
70
621.1
100
1463
(a) Make a plot showing ln (P/P0) versus 1/T (points - not connected by lines). Here P0 is some
"standard" pressure such as 1 bar or 1 atm (or even 1 torr). Such a denominator has to be
included because the logarithm of units is not defined.
(b) Now fit a straight line through the data points. Add the linear fit function to the plot you
made in part (a).
(c) From the slope calculate the value of ΔHvap for CCl4. Compare with the accepted value 89.40
BTU/lb at 100F (from an Engineering Table of thermodynamic properties).
2. Open a new worksheet. [Noggle Problem 4.3] A linear fit of ln (P/P0) versus 1/T holds well
over a limited temperature range. For an extended temperature range, a more complicated fitting
function should be used. For instance, use the following data and fitting function for CCl2F2.
Find the values of A, B, C, D by performing a "multilinear" fit to the data. [Consult MathCAD
help for fitting functions to data; linear combination of functions.] ln(P/P0) = A + B/T + C ln(T)
+ DT
Vapor pressure of CCl2F2 for several temperatures
P (torr)
T (C)
1
-118.3
5
-104.6
10
-97.8
20
-90.1
40
-81.6
60
-76.1
100
-68.6
200
-57
400
-43.9
760
-29.8
(a) Make a plot of the data as ln (P/P0) versus 1/T.
(b) Fit the data to the given fitting function. What are the values of A, B, C, and D? Don't forget
2
to include units.
(c) Add the fitted function to the plot of part (a).
3. Open a new worksheet. Now copy your solution of problem #2 into the new worksheet.
Make a new plot showing the heat of vaporization of CCl2F2 versus temperature. For this, use the
fitting function with constants you found in prob. #2 and the Clausius-Clapeyron equation.
4. Create a txt file from the data given in the table below. Use Notepad or Word to create it
(e.g. XY.txt). Separate the columns by space or comma. Read the txt.file from your USB or the
harddrive (document folder) using the Insert menu and scrolling down to Data.
• Perform a linear regression analysis of the dependence of the enthalpy of solution of Lascorbic acid upon the mole fraction of L-ascorbic acid, X.
• Determine the regression parameters (intercept and slope) and their standard deviations,
the correlation coefficient, and the standard deviation of the fit.
• Estimate the enthalpy of solution when X = 0.1.
• Create a word document that includes the data (mole fraction, X and Enthalpy of
solution, ΔHsol combined in a table or in 2 separate columns) and the plot (data points and
fit). For this use copy and paste special when pasting in Microsoft word. No calculations
should be included in the document. Print the WORD doc with the MathCAD worksheet.
X (mole fraction)
0.00102
0.00526
0.00510
0.01034
0.01465
0.02127
0.02406
0.02891
0.03428
0.03910
0.04199
0.04654
0.05119
0.05377
0.05779
0.06309
ΔHsol kJ/mol
25.44
25.33
25.32
25.33
25.30
25.16
25.25
25.16
25.06
25.05
24.86
24.79
24.78
24.75
24.66
24.70
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