In the Laboratory edited by
The Microscale Laboratory
Arden P. Zipp SUNY-Cortland Cortland, NY 13045
An Inexpensive Microscale Method for Measuring Vapor Pressure, Associated Thermodynamic Variables, and Molecular Weight Jason C. De Muro, Hovanes Margarian, Artavan Mkhikian, Kwang Hwi No, and Andrew R. Peterson* U. S. Grant High School, 13000 Oxnard St., Van Nuys, CA 91401; *
[email protected] Simply from measurements of vapor pressure one can learn thermodynamics, solution chemistry, intermolecular bonding, the chemistry of gases, and the determination of molecular weight (1). This versatility has led to the perennial publication, in these pages, of methods for measuring vapor pressure (2–16 ). However, even the simplest of these methods (2, 14 ) is too expensive for use in a large urban high school like ours, while existing microscale methods (17) are not sufficiently quantitative. We now present a microscale method, adapted from Levinson (2) and Russo (18), that is inexpensive, quantitative, and useful in many ways for teaching chemistry in secondary schools. Materials and Procedures Denatured alcohol (95% ethanol, 5% isopropyl alcohol), methanol (99.5%), Beral pipets, graduated 1-mL disposable glass pipets (Kimble), and 18 × 150-mm disposable Pyrex culture tubes were obtained from Flinn Scientific, Batavia, IL. Alcohol thermometers ({20 °C–100 °C ), centigram balances, hot-plates, 100-mL plastic graduated cylinders, distilled water, 250- and 50-mL beakers, and soda bottles were also used. An IBM clone computer (Pentium, 200 MHz) with a Hewlett-Packard Deskjet 870Cxi printer and the Graphical Analysis Program (Vernier Software, Portland, OR) were used for processing the data. Aqueous solutions of the alcohols were prepared by adding a known volume of alcohol to a graduated cylinder and then adding water to 100 mL. The mole fraction of water was calculated from the volume/volume concentration by correcting for the partial molar volume of the alcohols and water (19) and for the 5% impurity in the ethanol. The procedure for water was as follows. The end of a 1-mL disposable glass pipet was sealed in a Bunsen flame 3–4 cm from the beginning of the graduations. The pipet was then cut off and flame-polished 8 cm from the seal, leaving a graduated microtube. This microtube was weighed to 2 decimal places and its weight recorded as W1. The tip of a Beral pipet was drawn into a spout long and thin enough to reach into the sealed end of the microtube. This pipet was then used to fill the microtube to the 0-mL mark with distilled water at room temperature (20–23 °C). The microtube with this water was weighed again and the weight was recorded as W2. The difference in the weights, W2 – W1 , was recorded as V1, the volume of the ungraduated portion of the microtube. The microtube was emptied by shaking it like a clinical thermometer and then filled with water from the Beral pipet to
within 0.15 mL of the top. The microtube was closed with a finger and inverted, and the air bubble was shaken into the bottom of the tube. The inverted microtube was submerged in 20 mL of water in a culture tube in an ice bath at 4 °C. A thermometer was inserted into the culture tube so that its bulb was level with the bubble in the microtube. At 4 °C, the volume of the bubble was read from the graduations in the microtube. This volume was recorded as V2. The culture tube with its water and the immersed microtube and thermometer (see Fig. 1) were clamped in a 250-mL beaker half filled with water, which was heated slowly. With the thermometer held so that its bulb was level with the middle of the bubble, the volume of the bubble was read at 5 °C intervals as the temperature rose. These tem- Figure 1. The apparatus peratures were recorded as T (°C), used for these experiand the corresponding volumes ments: the culture tube its water and the imwere recorded as V3. For Raoult’s with mersed microtube and law, only this volume, at 45 or 50 thermometer. °C, was recorded for each solution. The vapor pressure, Pv, of the water was calculated as follows. In accordance with ref 2 we neglected the vapor pressure of water at 4 °C. In addition, we neglected the contribution of the inverted meniscus. The volume v, of air at 4 °C was v = V1 + V2
(1)
The volume of air, Vtotal , at temperature T was Vtotal = V1 + V3
(2)
The moles of air, nair, in the bubble were calculated from the ideal gas law (1), with P = the atmospheric pressure: nair = Pv/(277 K)R
(3)
The air pressure, Pair, in the microtube at temperature T was given by Pair = nair RT/Vtotal
JChemEd.chem.wisc.edu • Vol. 76 No. 8 August 1999 • Journal of Chemical Education
(4)
1113
In the Laboratory 0.55 -4
0.50 -6
Vapor Pressure / atm
R lnP / (J mol -1 K -1)
0.45 -8
-10
-12
-14
0.40
0.35
0.30
0.25
0.20 -16
0.15 -18
0.10 0.0
0.0027
0.0028
0.0029
0.0030
0.0031
0.0032
0.0033
0.4
0.6
0.8
1.0
Mole Fraction of Water
(1/T) / K-1 Figure 2. Clausius–Clapeyron plots of R times the logarithm of the vapor pressure vs the reciprocal of the absolute temperature from duplicate experiments with water (circles), ethanol (squares) and methanol (triangles). The lines were fitted by linear regression.
Substituting for nair from eq 3, R canceled; and assuming that P is 1 atm, a reasonable assumption for most common weather conditions close to sea level, the vapor pressure Pv of the water in the microtube was given by Pv = 1 – (T /277 K) (v/Vtotal )
0.2
0.0034
(5)
For studies of Raoult’s law where T was constant at 318 K, the equation was
Figure 3. Raoult’s law plots of vapor pressure at 50 °C vs the mole fraction of water from duplicate experiments with aqueous solutions of ethanol (squares) and methanol (triangles). Our data (solid symbols), smoothed by the Graphical Analysis program, are compared with data from ref 22 (open symbols).
eq 9 and solving for Mr: Mr = W (Ptotal – P2°)/n(P1° – Ptotal )
(11)
Thermodynamic parameters of vaporization were determined using the Clausius–Clapeyron equation (1): R ln Pv = { ∆H (1/T ) + ∆S
(12)
The molecular weight of an alcohol was calculated as follows. Raoult’s law (20) for a solution of two volatile components, water = 1 and alcohol = 2, is
The enthalpy (∆H ) and entropy (∆S ) of vaporization were determined by linear regression of a plot of R ln Pv vs 1/T, where R = 8.31 J mol {1 K {1 and T is the absolute temperature in kelvin. The normal boiling point of the liquid was obtained by setting Pv equal to 1 atm so that
Pv = P1 + P2 = X1P1° + X 2 P2°
boiling point = ∆H /∆S
Pv = 1 – (1.15v/Vtotal )
(6)
(7)
where Pv is the vapor pressure over the mixture of the two components. The individual vapor pressures of the components in the mixture are P1 and P2. The mole fractions of the components are X1 and X2. The vapor pressures of the unmixed components are P1° and P2°. Since X 2 = 1 – X1, eq 7 can be rewritten Ptotal = X 1(P1° – P2°) + P2°
(8)
For an ideal solution a plot of Ptotal vs X 1 gives a straight line with slope P1° – P2° and intercept P2°. To calculate the molecular weight of component 2, eq 8 was rearranged: X1 = (Ptotal – P2°)/(P1° – P2°)
(9)
The mole fraction (20) is also given by X1 = nMr /(nMr + W )
where n is the moles of water, W is the mass of alcohol, and Mr is the molecular weight of alcohol. Substituting for X1 in 1114
Results Clausius–Clapeyron plots of water, ethanol, and methanol from duplicate experiments are compared in Figure 2. The heats of vaporization and entropies of vaporization calculated from the figure are on average within 10% of the published data, and the boiling points are on average within 11% of published values (Table 1). Table 1. Thermodynamic Parameters Determined from Clausius–Clapeyron Plots Parameter ∆H/kJ mol {1
(10)
(13)
Water
Ethanol
Methanol
Lit. (21) Exptl.a
Lit. (21) Exptl.a
Lit. (21) Exptl.a
41
44
39
∆S/J mol {1 K {1
110
120
bp/°C
100
94
aData
41
35
41
110
110
100
120
79
10 0
65
69
from Fig. 2.
Journal of Chemical Education • Vol. 76 No. 8 August 1999 • JChemEd.chem.wisc.edu
In the Laboratory
In the Raoult’s law plots (Figs. 3 and 4) the values of P1° at 50 °C and 45 °C were calculated from the data for water from Figure 2. The plots of the vapor pressure over aqueous solutions of ethanol and methanol agree with published data (22), giving positive deviations from Raoult’s law (Fig. 3). However, plots for 25%, 50%, and 75% v/v solutions of ethanol (X1 = 0.92, 0.79, and 0.52) and methanol (X1 = 0.87, 0.70, and 0.44) appeared linear (correlation coefficients of .99 and .98, respectively). The small error bars were obtained by averaging v/Vtotal for the duplicate experiments that were performed together. The molecular weights of the alcohols were averages of the molecular weights calculated from the vapor pressures of the three solutions and were not significantly different from the published molecular weights (Table 2).
independent experiments, result from the volume of water in the meniscus, from residual water or alcohol in the microtubes, and from the subtraction step in eq 6. The first of these errors was minimal at temperatures high enough (≥45 °C) that bubble volumes were at least 0.10 mL. The second was reduced by rinsing the microtube with the solution that was to be measured. The third was minimized by calculating standard deviations from the raw data, namely, the ratio v/Vtotal . The errors notwithstanding, the data agree very well with published data for vapor pressures above aqueous solutions of the alcohols (Fig. 3). The positive deviation from Raoult’s law, which is surprising in view of the hydrogen bonding between the alcohols and water (23), can be explained as being the result of the breakdown, by the alcohols, of water clusters (19, 24 ). Because of the aforementioned positive deviation, the molecular weights calculated from the vapor pressures of the solutions varied with the concentration. However, the average of the molecular weights calculated from the vapor pressures over 25%, 50%, and 75% v/v aqueous solutions of ethanol and methanol were accurate within the 2-significant-figure precision of the method (Fig. 4, Table 2). For a class experiment, microtubes and Beral pipets were prepared ahead of time and the water and solutions were cooled in ice overnight. The experiment then took two days, (2 lab periods each 56 minutes in length). On the first day, the vapor pressure of water was measured first at 4 °C and then at five temperatures between 45 and 65 °C. The ratios v/Vtotal were calculated and entered into the computer, which calculated the mean and average deviation of the ratios, transformed the ratios into ln Pv and the temperatures into 1/T, produced the Clausius–Clapeyron plot, calculated the regression line, and gave, by interpolation, the vapor pressure of water at 45 °C. On the second day, the vapor pressure of pure ethanol and 75%, 50%, and 25% v/v aqueous ethanol solutions was determined at 45 °C, ethanol being chosen because it is the least toxic of the alcohols (Flinn Scientific). These data were entered into the computer, which calculated the mean and average deviation of v/Vtotal for ethanol and the solutions of ethanol. The students calculated the molecular weight of ethanol from these means and the vapor pressure of water at 45 °C. In their reports, they were required to explain their results in the light of the published positive deviation from Raoult’s law (22) and the evidence of water clusters (24).
Discussion
Literature Cited
Our method produced results similar in accuracy and precision to more elaborate procedures (13), but with the advantage that it is inexpensive and simple enough to be done by all the students in a high-school class. Another feature of the Table 2. Molecular Weight method is that students can see for themselves, directly, of Ethanol and Methanol Molecular Weight the effects of increasing presAlcohol sure on the bubble size. The Lit. Calcd a advantage of direct observaEthanol 46 50 ± 5 tion has been exploited in the Methanol 32 32 ± 3 design of laboratory demonaData from Fig. 4. The error is strations (7, 8). the sum of the errors of the vapor Errors, which can be as pressure of the solution, pure high as 30% in the means of water, and pure alcohol.
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
0.35
Vapor Pressure / atm
0.30
0.25
0.20
0.15
0.10
0.05 0.0
0.2
0.4
0.6
0.8
1.0
Mole Fraction of Water Figure 4. Raoult’s law plots of vapor pressure vs mole fraction of water from duplicate experiments with solutions of ethanol (squares) and methanol (triangles) at 45 °C. The error bars give the average deviation (3%) of the data from the means. Data for pure water (X1 = 1) at 45 °C were calculated from Figure 2.
Pauling, L. General Chemistry; Dover: New York, 1988; pp 386, 461. Levinson, G. S. J. Chem. Educ. 1982, 59, 337–338. Koubek, E.; Elert, M. L. J. Chem. Educ. 1982, 59, 357–359. Koubek, E.; Paulson, D. R. J. Chem. Educ. 1983, 60, 1069. Long, J. W. J. Chem. Educ. 1982, 82, 933. Schaber, P. M. J. Chem. Educ. 1985, 62, 345. Hall, P. K.; Wollaston, G. J. Chem. Educ. 1987, 64, 969. Richardson, W. S.; Jones, R. F. J. Chem. Educ. 1987, 67, 968. Hambly, G. F. J. Chem. Educ. 1990, 67, 278. Mundell, D. W.; Dreisbach, J. H. J. Chem. Educ. 1990, 67, 426. Sears, J. A.; Grieve, C. T. J. Chem. Educ. 1990, 67, 427. Van Hecke, G. R. J. Chem. Educ. 1992, 69, 681–683. Berka, L. H.; Kildahl, N. K.; Bergin, S. S.; Burns, D. S. J. Chem. Educ. 1994, 71, 441–445. 14. Kildahl, N. K.; Berka, L. H. J. Chem. Educ. 1995, 72, 258–260. 15. Burness, J. H. J. Chem. Educ. 1996, 73, 967–970. 16. Krieger, A. G.; Henderson, J. W. J. Chem. Educ. 1996, 73, 1039.
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In the Laboratory 17. Russo, T. Microchemistry 2; Kemtec: West Chester, OH, 1989; pp 33–35. 18. Russo, T. Microchemistry 1; Kemtec: West Chester, OH, 1986; p 2b. 19. Freifelder, D. Physical Chemistry for Students of Biology and Chemistry; Science Books International: Boston, 1982; p 194. 20. Oxtoby, D. W.; Nachtrieb, N. H. Principles of Modern Chemistry; Saunders: New York, 1986, pp 113–114. 21. CRC Handbook of Chemistry and Physics, 78th ed.; Lide, D. R.,
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Ed.; CRC: Boca Raton, FL, 1997–1998; pp 5-18–5-31, 6-8–6-71, 6-105–6-107. 22. CRC Handbook of Thermophysical and Thermochemical Data; Lide, D. R.; Kehiaian, H. V, Eds.; CRC: Boca Raton, FL, 1994; pp 213–214. 23. Whitten, K. W.; Gailey, K. D.; Davis, R. E. General Chemistry; Saunders: New York., 1992; p 530. 24. Liu, K.; Cruzan, J. D.; Saykally, R. J. Science 1996, 271, 929–933.
Journal of Chemical Education • Vol. 76 No. 8 August 1999 • JChemEd.chem.wisc.edu
