In the Laboratory
A Physical Chemistry Lab Project: The Effect of Composition on Several Physical Properties of Binary Mixtures of Common Liquids Luther E. Erickson and Kevin Morris Department of Chemistry, Grinnell College, Grinnell, IA 50112 The effect of the composition of solutions on their physical properties has been an important focus of both experimental and theoretical investigations in physical chemistry for many years. For several years our physical chemistry laboratory program included a multipart project that involved the determination of the effect of composition on the viscosity and partial molar volume for a binary mixture and the construction of the vapor–liquid phase diagram for the same mixture. Based on the suggestion of Fung et al. (1), we recently expanded the assignment to include determining the effect of composition on the thermodynamics of mixing of the mixture. Appropriate selection of components for the mixtures insures interesting variations in these properties with composition. Comparison of the whole range of properties invites a consistent interpretation of the observed composition dependence of these properties at the molecular level. The entire project can be completed in three 3-hour laboratory periods with students working in pairs. An additional period is allocated to complete workup of the data and preparation of a formal report. Coming early in the first semester of the course, the workup of the data provides a good introduction to (or review of) the use of spreadsheet software and computer graphing of data. This year we added a poster presentation to encourage comparison of results among the groups and to provide opportunities for students to give oral reports on their investigations. Experimental Details
Effect of Composition on Density, Viscosity, and Molar Volume Students are instructed to prepare 25 or 50 mL of five mixtures and two pure liquids, a and b, and to determine the mean molar volume, density, and viscosity of each mixture and of the pure liquids at 25 °C. The mean molar volume and density of each solution can be obtained with satisfactory accuracy by preparing the solutions in 25- or 50-mL volumetric flasks, taking some pains to compensate for the heat of mixing and for the nonadditivity of volumes. After obtaining the mass (to nearest milligram) of the empty flask and the mass of the flask with one component added, the second component is added to within about 0.5 mL of the mark and the solution is mixed thoroughly and placed in a 25° water bath. After final dilution to the mark and mixing, the flask is dried carefully and the final mass is determined. From the masses of the two components, the mole fraction composition, Xb = n b/(na + nb), the density, ρ = m/V (where V is the volume of the flask), and mean molar volume, Vm= V/(na + nb), can be calculated. These solutions are then used for the viscosity determinations, using a standard Ostwald viscometer (2). For students working in pairs, one student can begin making viscosity determinations for the pure liquids while the other completes the preparation of solutions. Duplicate or triplicate determinations of the times required to
empty the viscometer bulb provide an indication of the precision in the viscosity determination.
Construction of a Temperature–Composition Boiling-Point Diagram Our students use the standard sidearm modified distillation flask with internal nichrome wire heater (3) to permit convenient sampling of both the vapor and the liquid with which it is in equilibrium at a particular boiling temperature. Analysis of the liquid and vapor fractions is most readily carried out by gas chromatography of samples of the liquid in the flask and the condensed vapor in the sidearm bulb. We have typically encouraged students to work out some of the details of the separation conditions, including the selection of the more appropriate of two chromatographic columns employed with a Hewlett-Packard Model 5750 gas chromatograph. Whether electronic integration or a strip chart recorder is employed to record the data, a calibration curve of relative response vs. mole fraction may be required to get reliable concentrations from relative peak areas (or heights) of the chromatograms. The solutions prepared earlier for molar volume and viscosity measurements can be used for this calibration. For liquids with quite different refractive indices, nD, refractive index measurements can be employed as an alternative technique for analysis of liquid and vapor fractions (3). A calibration curve of nD vs. Xb is also required for this approach, though the assumption of linear variation of nD with Xb is reasonably close. Enthalpy of Mixing We have employed the Parr 1451 solution calorimeter and the quantities of materials suggested by Fung (1) to determine the enthalpy of mixing for 6 compositions of mixtures. A simple Dewar flask equipped with an accurate thermometer or thermistor could also be used to get satisfactory data. The enthalpy of mixing can be either positive (endothermic) or negative (exothermic). The sign of ∆H can be determined easily by adding a dropper full of liquid a to a similar volume of liquid b in a test tube and noting the temperature change to guide the setup of the temperature recording device of the Parr calorimeter. A reasonable plot of ∆H vs. composition can be generated by determining the heat of mixing for about 5-6 compositions. To save material, the heat of dilution from one composition to another can be added to the heat of mixing for the initial solution, as described by Fung (1). Calculations and Results
Partial Molar Volume The partial molar volume of each component in each solution can be calculated from the mean molar volume, Vm, by plotting Vm vs. Xb and drawing a line tangent to the smooth curve at a particular concentration (4). The partial molar volumes Va and Vb for the two components
Vol. 73 No. 10 October 1996 • Journal of Chemical Education
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In the Laboratory
120 1 20
1.2
Cyclohexane
100
1.0
V/mL
Relative
Ideal
Viscosity
80 0.8
Ethanol
Experimental
60
0.6 0.0
40 0.0
0.2
0.2
0.4
0.6
0.8
1.0
Xb, mole fraction ethanol
0.4 0.6 0.8 1.0 Xb, mole fraction ethanol
Figure 1. Composition dependence of mean molar volume, Vm, and partial molar volumes of cyclohexane (a) and ethanol (b) for cyclohexane–ethanol mixtures at 25 oC.
at that concentration are the intercepts of the tangent line at Xb = 0 and 1.00, respectively. The data can be treated numerically by fitting a polynomial (typically second degree is sufficient) to the Vm vs. Xb data. Then the partial molar volumes, Va and Vb at Xb, where the mean molar volume is Vm, are given by: Va = Vm – Xb (∂Vm /∂Xb) (1) and Vb = Vm + (1 – Xb) (∂Vm /∂Xb) (2) where (∂Vm /∂Xb) is the slope of the Vm vs. Xb curve at that point. With a second-degree polynomial fit of the data, a general expression for the slope can be obtained and general expressions for Va and Vb can be formulated from eqs 1 and 2 for evaluation at each of the compositions examined. Typical student spreadsheet data for the cyclohexane (a)–ethanol (b) pair are summarized in Table 1; the mean and partial molar volumes for the pair are plotted in Figure 1. Deviations from ideality can be displayed most effectively by plotting Vm , Va, and Vb on the same graph. By also including a straight line connecting the molar volumes of the pure liquids, the direction of the deviation from ideality can be highlighted. Both the distinct positive curvature of the Vm curve and the increase in Va and Vb with dilution reveal the positive deviation from ideal behavior of this system.
Figure 2. Composition dependence of relative viscosity of cyclohexane(a)–ethanol(b) mixtures at 25 oC.
Viscosity Data The relative viscosity of each mixture, ηr, can be calculated from the densities (ρ) and flow times (t) for each solution by ηr = η/ηo = tρ/toρo (3) where the subscript “o” identifies one of the pure liquids designated as the reference material. Relative viscosity– composition data for the cyclohexane–ethanol pair, which are included in the Table 1 spreadsheet, are plotted in Figure 2. A straight line connecting the viscosities of the two pure liquids has been included in the graph to emphasize the direction and extent of deviation of the system from ideality. The deviation is sufficient, in this case, to lead to a minimum in the viscosity near Xb 0.30 (b = ethanol). The Vapor–Liquid Phase Diagram Ideal solutions are typically introduced by a discussion of Raoult’s Law and the associated vapor pressure– composition diagram (4). Extreme deviations from ideality can lead to a minimum or maximum in the vapor pressure–composition diagram and the resultant maximum or minimum in the corresponding boiling point–composition diagram. Binary mixtures assigned to students in the laboratory are typically chosen to show enough deviation from ideality to produce a minimum- or maximumboiling azeotrope (5). The temperature–composition phase diagram at atmospheric pressure, constructed from stu-
Table 1. Excel Spreadsheet: Composition Dependence of Molar Volumes and Relative Viscosity for Cyclohexane(a)-Ethanol(b) Mixtures at 25 °C mass fsk/g fsk+a/g fsk+a+b/g mass a/g mass b/g moles a
Vm/mL
t/sec
Vm/mL
Va/mL
0 0.418311
1
59.7641
117.6
0.770864
59.7641
110.951
59.151
1
1.9111
17.6586 0.022708 0.383299
0.94407
61.5753
110.5
0.782788
61.5753
110.594
59.161
0.955
20.4923 20.4923
39.7639
0
20.4925 22.4036
40.0622
21.1794
19.2716
moles b mole frac b
g/mL
Vb/mL
eta
27.152
40.5552
5.9726
13.4032 0.070967 0.290931
0.803903
69.0802
102
0.775032
69.0802
109.788
59.276
0.872
20.6831 30.6171
40.1072
9.934
9.4901 0.118037 0.205993
0.635722
77.1533
96.8
0.776964
77.1533
108.992
59.586
0.829
21.2831 34.8228
40.6084
13.5397
5.7856 0.16088 0.125583
0.438391
87.2712
92.4
0.773012
87.2712
108.295
60.187
0.788
21.4391 38.8279
40.7133
17.3888
1.8854 0.206616 0.040925
0.165325
100.994
91.6
0.770968
100.994
107.753
61.441
0.779
40.091
19.6489
0
107.08
95.5
0.785956
107.08
107.663
62.438
0.828
20.4421
972
40.091
0 0.233471
0
Journal of Chemical Education • Vol. 73 No. 10 October 1996
In the Laboratory 2000
T ∆S(ideal)
1500 1000
∆H(exp)
500 J/mol 0 −500 −1000
∆G(exp)
−1500
∆G(ideal)
−2000 0.0
0.2
0.4 0.6 0.8 1.0 Xb, mole fraction ethanol
Figure 3. Vapor–liquid phase diagram of the cyclohexane( a)– ethanol(b) system at atmospheric pressure (about 735 torr).
Figure 4. Composition dependence of thermodynamic quantities for cyclohexane(a)–ethanol(b) mixtures at 25 oC.
dent data for the cyclohexane–ethanol system used in the earlier illustrations, is shown in Figure 3. The minimum in the boiling point at 74 °C implies a maximum in the vapor pressure–composition diagram, which indicates a strong positive deviation from ideality; that is, each component in the mixture has a higher vapor pressure than predicted by Raoult’s Law, pi = Xi pi o.
large decrease in the relative viscosity of mixtures relative to values predicted by the linear dependence expected for an ideal solution (Figure 2). Finally, the weaker interactions between a and b permit a and b to get further apart on the average, so that the partial molar volumes of both a and b in mixtures exceeds the molar volumes of pure a and b, respectively (Figure 1). For the cyclohexane–ethanol pair, the assumption that the T∆S contribution to the ∆G of mixing is given by eq 5 is not particularly good. Fung (1) includes experimental data for ∆G, as reported by Stokes and Adamson (6) from vapor pressure data, and for T∆S = ∆H – ∆G. For this system, both a positive ∆H of mixing and a less positive than ideal ∆S of mixing contribute to making ∆G much less negative than expected for an ideal solution and also significantly less negative than calculated from the experimental ∆H and T∆S(ideal). In any case, the low-boiling azeotrope requires a maximum in the vapor pressure vs. composition curve with a large positive deviation from ideality; that is, for both components i, pi > Xi pio. Therefore, ∆G = RT[Xa ln(pa/pao) + Xb ln(p b/p bo)] > ∆G(ideal), and ∆H > 0 accounts for at least part of this non-ideality. Alger has recently called attention to the key role of the entropy contribution to the closely related solubility of water in aliphatic alcohols and hydrocarbons (7). The above explanation also nicely accounts for the data for other alcohol–hydrocarbon or alcohol–ester mixtures, such as ethanol–benzene or propanol–ethyl acetate, but other mixtures don’t behave quite so consistently. The chloroform–acetone mixture is the classic example of a high-boiling azeotrope, indicative of substantial negative deviations from ideality. However, the viscosity–composition curve for acetone–chloroform mixtures shows very little deviation from linearity, and the molar volume vs. composition curve resembles the curve for cyclohexane– ethanol mixtures. Surprisingly, for ethanol–acetonitrile mixtures, which show a positive deviation from ideality, and a low-boiling azeotrope such as typical alcohol–hydrocarbon mixtures, partial molar volumes of the two components in a mixture are, in fact, less than molar volumes of the pure components. In general, the molar volume is the least sensitive indicator of non-ideal behavior. Conversely, it is the best indicator of careful technique.
The Enthalpy of Mixing The ∆H of mixing in J mol–1 is calculated from the measured temperature rise, ∆T, the molar heat capacities of the two liquids, Ca and Cb, and the heat capacity of the empty calorimeter, Ccal, by eq 4. ∆H = [(naCa + nbCb) + Ccal] ∆T/(na + nb) (4) The enthalpy–composition diagram for the cyclohexane–ethanol pair, constructed from student data, is shown in Figure 4. In addition to the experimental ∆H data, Figure 4 includes the T∆S vs. composition curve calculated for an ideal or regular solution by eq 5, T∆S(ideal) = –RT[Xa lnXa + Xb lnXb] (5) the ∆G vs. composition curve calculated from the experimental ∆H data and the ideal entropy curve [∆G(exp) = ∆H – T∆S(ideal)], and the ∆G vs. composition curve expected for an ideal solution for which ∆H = 0 and ∆G(ideal) = –T∆S(ideal). Since ∆H is positive for this system, ∆G is calculated to be less negative than it would have been for an ideal solution. Analysis of the Results The discussion portion of the student report should be devoted largely to an interpretation of the interrelation among the four phenomena that were investigated in the project. For the cyclohexane–ethanol examples shown in Figures 1–4, the minimum boiling azeotrope in the boiling point diagram (Figure 3) indicates relatively weaker a–b interactions than the average of a–a and b–b interactions, where a and b are cyclohexane and ethanol, respectively. This interpretation also accounts for the mixing process being endothermic (Figure 4), as stronger a–a or b–b interactions are disrupted by dilution with the other liquid. The weaker a–b interactions also permit molecules to slide past each other more readily, accounting for the
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Assignment of Liquid Pairs As the foregoing examples suggest, the whole project is more interesting if each pair of students is assigned a different liquid pair and if the class has an opportunity to compare results. Extensive data on properties of liquid pairs are available in the literature (5). For example, with six pairs of students, two pairs each might be given (i) relatively ideal mixtures, (ii) high-boiling azeotropes, and (iii) low-boiling azeotropes. We usually have two sections of the lab, so we assign the same set of mixtures to each lab. The students are asked to compare results with their counterparts in the other lab section and are expected to resolve discrepancies before submitting their final written report. A lunch-hour joint poster session facilitates such an exchange. Safety and Disposal of Hazardous Materials Although the alcohol–hydrocarbon and alcohol–ester pairs can be handled without any unusual precautions, several of the solvents suggested for investigation are sufficiently hazardous to require special handling. For these liquids, solution preparation, viscosity measurements, and distillation and calorimetry experiments should all be carried out in well ventilated hoods. By locating the gas chromatograph near the hood where the distillation is being carried out, students can simply use a 10-mL syringe to
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collect a sample of the liquid or condensed vapor from the distillation apparatus and quickly inject it into the inlet port of the gas chromatograph a few feet away. At the end of each experiment, the mixtures are added to the appropriate organic waste container—with a separate clearly labelled container for any mixture which contains a halogenated compound. Acknowledgments The authors wish to thank Richard Biagioni and Holly Harris, who introduced or modified some of the procedures employed in the projects, and the several dozen physical chemistry students who have provided useful criticism and feedback in the evolution of this set of experiments over several years. Literature Cited 1. Raizen, D.A.; Fung, B. M.; Christian, S. D. J. Chem. Ed. 1988, 65, 932–933. 2. Sime, R. J. Physical Chemistry: Methods, Techniques, and Experiments; Saunders: Philadelphia, 1990; Experiment 14, pp 522–527. 3. Sime, R. J. op. cit., Experiment 6, pp 449–460. 4. Atkins, P. W. Physical Chemistry, 5th ed.; Freeman: New York, 1994; Chapter 7, pp 207–237. 5. Timmermans, J. Physico-Chemical Constants of Binary Systems; Interscience: New York, 1959. This is a rich source of data to guide selection of appropriate mixtures. 6. Stokes, R. H.; Adamson, M. J. J. Chem. Soc., Faraday Trans. 1 1977, 73, 1232– 1238. 7. Alger, D, J. Chem. Educ. 1994, 71, 281.
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