In the Laboratory
A Multipurpose Apparatus To Measure Viscosity and Surface Tension of Solutions
W
The Measurement of the Molecular Cross-Sectional Area of n-Propanol Xin Zhang,* Shouxin Liu, and Baoxin Li College of Chemistry and Material Science, Shaanxi Normal University, Xi’an, Shaanxi, China, 710062; *
[email protected] Na An College of Life Science, Shaanxi Normal University, Xi’an, Shaanxi, China, 710062 Fan Zhang Xi’an Dolphin Electric Technology Co. Ltd, Xi’an, Shaanxi, China 710068
The measurement of viscosity and surface tension of solutions is an important exercise in chemistry and chemical engineering. It is a common laboratory exercise in physical chemistry (1, 2). Articles describing these measurements can be found in this Journal (3–11). Some authors used commercial apparatuses for educational experiments, such as measuring the critical micelle concentration (CMC) of a surfactant (3), measuring the molecular cross-sectional area (MCSA) of a solute (4), measuring the molecular weight (MW) of a polymer (5), and assessing the shapes of macromolecules (6, 7). Other authors suggested corrections or new measurement methods for various parameters of the apparatus, such as the correction of the volume of the droplets (8), the optical measurement of the radius of the capillary (9), and the auto-timing instrumentation for the viscometer (10). Moreover, some new, convenient, and practical instruments
g
were designed (3, 11). However, there still remain some problems in the determination of viscosity and surface tension with these apparatuses. For instance, these apparatuses are not suitable to measure properties of solutions with surface foaming. Furthermore, the apparatuses cannot be used to measure of a set of solutions (obtained by dilution of initial concentration) without reloading each solution. In this article, we describe a multipurpose apparatus that can be used to measure the viscosity of solution by the Ostwald method and the surface tension of solution by the drop-weight method or by the capillary-rise method, and some basic experiments related to the two parameters, such as measuring the CMC, MCSA, and MW. The apparatus is convenient for in-situ preparation of solutions of different concentrations and avoids the error that frothing of the liquid surface introduces into measurements.
j
k Figure 1. Schematic of the comprehensive measuring apparatus:
f
p
(a) constant-volume bulb (V = 5 mL); (b) liquid-level controlling tube (with a stopcock p);
a
e1
(c) measuring tank (i.d. = 30 mm, h = 160 mm);
e2
(d) reservoir (i.d. = 30 mm, h = 65 mm); (e1) and (e2) liquid-level marks specifying beginning and end of the viscosity measurement; (f) ground-glass stopper (with a ventilating opening k);
b
(g) three-way stopcock (side is linked to a capillary j);
h
(h) measuring capillary (i.d. = 0.35 mm, o.d. = 3.5 mm, L = 90 mm) with attached graduated ruler;
i
(i) liquid-level controlling line;
c
(j) capillary; (k) small hole to relieve pressure; (p) tank-fill stopcock.
d
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In the Laboratory
Apparatus A schematic of the apparatus is shown in Figure 1. The apparatus consists of a measuring system and a liquid-level controlling system. The measuring system consists of a threeway stopcock (g), a constant-volume bulb (a), and a capillary (h) with graduation. The measuring system is the central tube welded to a ground-glass stopper (f ) with a small ventilating hole (k). The function of the hole (k) is to balance the pressure inside and outside the apparatus. The liquid-level controlling system consists of the storage tanks (c) and (d) (c and d are linked by a conical tube) and side tube (b) with a stopcock (p). The liquid level of tank (c) can be controlled by blowing gas into tube (b) or sucking gas from tube (b) to change the pressure of tank (d). Experimental Methods Capillary-rise method: The liquid level of tank (c) is adjusted to mark (i) by blowing gas to tube (b) with rubber ball via stopcock (p). The surface tension, γ, is determined by measuring the liquid column height in capillary. Ostwald method: The liquid in tank (c) is sucked into the central tube until the liquid level is above the mark (e1). The viscosity (η) is measured by determining the time for the liquid in bulb (a) to flow through the capillary. Drop-weight method: The liquid in tank (c) is sucked into the central tube until the liquid level is above the mark (e1). Closing the stopcock (g) and opening the stopcock (p) causes the residual liquid in tank (c) to flow back to tank (d) until the lower end of the capillary breaks away from the liquid level and hangs. The surface tension is measured by counting the number of drops as the liquid in bulb (a) is draining from the lower tip of the capillary. Detailed instructions for the methods are found in the Supplemental Material.W Measurement of MCSA of n-Propanol
Theory The MCSA of n-propanol can be measured by the dropweight method. Detailed theory for this experiment can be found in the literature (12); only a brief discussion is given here. Surface tension measurements are used to calculate the surface adsorptive capacity, Γ, which is the amount of moles of solute present on unit surface area of solution. The relation between γ and Γ of the solution under different concentrations is shown by the Gibbs equation, Γ = −
C · RT
∂ γ ∂ C
(1)
T
where R is the gas constant, T is the adsorption temperature in Kelvin, and C is the concentration of solution. The Langmuir equation shows the relation between Γ and C,
C 1 C = + Γ Γ∞ K Γ∞
(2)
where K is adsorption equilibrium constant and Γ∞ is the ad-
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List 1. Drop Correction Factor, Φ, Φ, for the Drop-Weight Method (2) r/v1/3
Φ
0.300
1.378
0.325
1.405
0.350
1.426
0.375
1.457
0.400
1.464
0.425
1.481
0.450
1.499
0.475
1.517
0.500
1.534
0.525
1.550
0.550
1.572
0.575
1.583
0.600
1.600
0.625
1.624
sorptive capacity at saturation, which is the value of a monolayer of solute distributed completely on the unit surface of solution. Plots of C兾 Γ versus c can be examined and Γ∞ can be calculated from slope of the curve. Γ∞ is related to the molecular cross-sectional area of solute, So, by,
Sο =
1 Γ∞ NA
(3)
where NA is Avogadro constant. The crux of the experiment is measurement of the surface tension of solution. In the experiment, the surface tension can be measured by drop-weight method,
γ =
gV ρΦ ρΦ · = B 2π r n n
(4)
where B is the apparatus constant of drop-weight method, g is the gravitational constant, V is volume of a given liquid, r is the outer radius of the capillary, n is the number of drops, ρ is the density of the drop, and Φ is the correction factor of the drop. When the drop detaches from the capillary, a small part of solution is left attached to the tip of the capillary owing to the mechanical instability of the drop and its deformation. Very small drops tend to have substantial errors in their masses from this effect. Correction factors that take this into account are based on the ratio of the radius of the capillary to the cube root of the volume of the drop, r兾v1/3. The corrections are available in tabular form (List 1) and have been obtained by interpolation of the curve of best fit (2). The apparatus constant, B, can be calculated using the dimensions of the apparatus. The concentration of n-propanol is in the range of 0.1–0.6 mol L᎑1 in the measurement. The internal radius of capillary of the apparatus is 2.50 mm and volume of bulb a is 3.35 mL. Thus, B = 4.186 × 10᎑3 m3 s᎑2.
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In the Laboratory
Table 1. Measured Values of Parameters of Straight Chain Alcohol (aqueous solution, 20 ⬚C) Added Quantity of Water/mL
C/ (103 mol m᎑3)
n drop
r/v1/3
γ/ (10᎑3 kg s᎑2)
᎑(∂γ/∂C)T /(105 kg m3 mol᎑1 s᎑2)
Γ/ (10᎑6 mol m᎑2)
(C/Γ)/ (107 m᎑1)
00a
0.60
189.7
0.480
33.32
02.423
5.966
10.0600
02
0.50
180.7
0.472
34.90
02.884
5.917
8.450
03
0.40
167.3
0.458
37.62
03.573
5.864
6.821
05
0.30
148.7
0.443
41.96
04.713
5.802
5.171
05
0.24
138.3
0.432
44.90
---
---
---
05
0.20
128.3
0.421
48.21
06.781
5.565
3.594
10
0.15
118.7
0.411
52.20
08.820
5.429
2.763
10
0.12
113.7
0.405
54.11
---
---
---
---
0.10
---
---
---
12.770
5.240
1.908
10b
0.00
083.3
0.365
72.39
---
---
---
a
b
Only add 10 mL of solution (0.6 M).
Only add 10 mL of water.
Hazards The vapor of the reagents propanol and butanol is anesthetic to human nerves. The mixture of the vapor and air is easy to ignite or explode. Their respective explosion limits are 2.15–13.5 and 1.45–11.25% (by volume). Results The experimental data and the calculated results are shown in Table 1. The volume of a single drop, v, was calculated from n and V. The Φ can be found by substitution into r兾v1/3 of each solution. Thus, γ of each solution was calculated by substitution of n, ρ, and Φ in eq 4. From the curve of C versus γ (Figure 2), the values of ∂(γ)兾∂C at different concentrations were obtained by the graphical differentiation method (12). Thus, Γ of each solution was calculated by substitution of C, T, and ∂(γ)兾∂C into eq 1. The plot of C兾 Γ versus C was drawn (Figure 3) and fitted to a line with linear
correlation coefficient of 0.9891. From the slope of the curve the value of Γ∞ was calculated as 6.138 × 10᎑6 mol m᎑2. The molecular cross-section area of n-propanol can be calculated by the substitution of Γ∞ in eq 3. The value of So was calculated to be 27.07 × 10᎑20 m2 versus the literature value of 27.4 × 10᎑20 m2 (12). In the experiment, the average value of 10 student measurements is (27.62 ± 0.20) × 10᎑20 m2; thus, the requirement for a student’s one-time-measurements is So = (27.62 ± 0.60) × 10᎑20 m2.
Accuracy Two parameters, γ and η, of some solutions were measured to evaluate the accuracy of the apparatus. We compared the experimental values to literature values (13). The results are shown in Table 2. The maximum deviation by the dropweight method is 1.4‰; the maximum deviation by the Ostwald method is 1.7‰; and the maximum deviation by the capillary-rise method is 3.5‰. The values listed in Table 2 are the average of five measurement.
80
12
75 10
(C / Γ) / (107 mⴚ1)
γ / (10ⴚ3 kg sⴚ2)
70 65 60 55 50 45
8
6
4
40 2
35 30
0
0
1
2
3
4
2
5
ⴚ3
C / (10 mol m
Journal of Chemical Education
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0
1
2
3
4
2
)
Figure 2. The curve of γ versus C.
852
6
C / (10 mol m Figure 3. The curve of C/Γ versus C.
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ⴚ3
)
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In the Laboratory
Table 2. Comparison of Experimental Versus Literature Values for Surface Tension and Viscosity Measurements Surface Tension Liquid
Viscosity
Lit. Values (103 N m᎑1)
Cap-Rise (103 N m᎑1)
Rel. Error (‰)
Drop-Wght (103 N m᎑1)
Rel. Error (‰)
Lit. Values (103 N m᎑1)
Ostwald (103 kg m᎑1 s᎑1)
Rel. Error (‰)
Methanol
22.61
22.68
3.1
22.64
1.3
0.584
0.585
1.7
Toluene
28.50
28.60
3.5
28.53
1.1
0.590
0.589
1.7
Acetone
23.70
23.77
3.0
23.68
0.8
0.322
0.322
0.0
Acetic acid
27.80
27.89
3.2
27.84
1.4
1.220
1.218
1.6
Literature Cited
Conclusion • This apparatus can be used to measure both the viscosity and the surface tension of solution. • The apparatus is convenient for the in-situ preparation solutions of different concentration, because tanks (c) and (d) are installed in the liquid level controlling system. • The apparatus can avoid the interference of surface froth during measurements. Since liquid is sucked into the central tube through the tip of the capillary tube, which is inserted below the liquid level of the tank (c), the suction of surface froth can be avoided. • The precision of the apparatus is mainly dependent on the inner and outer radius of the capillary. WSupplemental
Material
The construction and the method of operation of the apparatus, the essential theory, the data and tables of the two educational experiments are available in this issue of JCE Online.
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1. Shoemaker, D. P.; Garland, C. W.; Nibler, J. W. Experiments in Physical Chemistry, 6th ed.; McGraw-Hill: New York, 1996; Experiment 29, p 324. 2. Kogasahara, O.; Seo, M.; Tada, A.; Tomobe, E. New Compiled Experiment of Physical Chemistry, 2th ed.; Sankyo Publishing Company: Tokyo 1998; pp 46–49, 92–95. 3. Castro, M. J. L.; Ritacco, H.; Kovensky, J.; Cirelli, A. F. J. Chem. Educ. 2001, 78, 347–348. 4. Mever, E. F.; Wyshel, G. M. J. Chem. Educ. 1986, 63, 996–997. 5. Mathias, L. J. J. Chem. Educ. 1983, 60, 422–424. 6. Rosenthal, L. C. J. Chem. Educ. 1990, 67, 78–80. 7. Richards, J. L. J. Chem. Educ. 1993, 70, 685–689. 8. Worley, J. D. J. Chem. Educ. 1992, 69, 678–680. 9. Munguia, T.; Smith, C. A. J. Chem. Educ. 2001, 78, 343–344. 10. Urian, R. C.; Khundkar, L. R. J. Chem. Educ. 1998, 75, 1135–1136. 11. Diagnault, L. G.; Jackman, D. C.; Rillema, D. P. J. Chem. Educ. 1990, 67, 81–82. 12. Cai, Xian’e; Xiang, Yifei; Liu, Yanguang. Experiments in Physical Chemistry, 2nd ed.; Higher Education Publishing House: Beijing, China, 1993; pp 161–165. 13. CRC Handbook of Chemistry and Physics, 60th ed.; Weast, R. C., Ed.; CRC Press: Boca Raton, FL, 1979–1980; pp F51– F57, F41–F46.
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