In the Laboratory
Measurement of Evaporation Rates of Organic Liquids by Optical Interference Scott A. Riley, Nathan R. Franklin, Bobbie Oudinarath, Sally Wong, David Congalton, and A.M.Nishimura* Department of Chemistry, Westmont College, Santa Barbara, CA 93108-1099 The coherent light sources available through inexpensive He–Ne and solid-state lasers have allowed their more extensive use in undergraduate chemistry laboratories. Described here is a simple method by which evaporation of volatile organic liquids can be measured by monitoring the optical interference of spatially coincident light reflected from air–liquid and liquid–glass interfaces (1). As the liquid evaporates, the difference in the distances traveled by the beams changes, resulting in an intensity that oscillates. The frequency of this oscillation correlates to a rate expressed as the depth of the liquid layer undergoing evaporation per unit time. The basic apparatus can be assembled with materials found in undergraduate laboratories. Its response is fast and its sensitivity is very high. If the optical interference method is used in conjunction with a balance and a thermocouple thermometer, further insights into the evaporation process can be obtained.
Figure 1. Diagram of origin of optical interference used in this project.
beams must be equal to an integral multiple, m, of the laser wavelength, λ: m λ = 2y – x
Theory In the experiment, the laser beam is split at the airliquid interface: part of the beam is reflected, while most of it is refracted, as diagrammed in Figure 1. This refracted beam is reflected at the liquid–glass interface, as shown in the lower part of Figure 1, and travels a distance indicated by 2y, before recombining with the previously reflected beam. The reflected beam travels the distance x before converging with the refracted beam. Constructive interference will occur whenever the difference in the path lengths of the two split beams is an integral multiple of the laser wavelength. Because the difference in the distances that the two beams travel is a function of the thickness of the evaporating liquid layer, constructive and destructive interference is observed as a function of time. This difference can be calculated by simple geometry. Referring again to Figure 1, the reflected beam travels a distance given by
Substituting x and y from above into the previous equation yields m λ = (2d/ cosθ 2) – 2d tanθ 2 sinθ 1 Solving for d:
1 – tan θ sin θ 1 2 cosθ2
2
The rate of evaporation (in distance per unit time) is the same as the rate at which d decreases. The difference in d from one maximum in the signal intensity due to constructive interference to the next, in which m is incremented by one unit, is given by
x = ( 2 d tanθ 2 ) sinθ 1 in which d is the thickness of the liquid layer, θ1 is the incident angle, and θ2 is the refracted angle. In this equation, the factor in the parentheses is the horizontal displacement of the refracted beam, which can be determined by noting that one half of this displacement divided by d is equal to tanθ2. Now, the distance traveled by the other beam, which is refracted at the upper air–liquid interface and reflected from the lower liquid–glass interface, is given by
mλ
d=
λ
∆d = 2
The time taken for successive constructive interference is the frequency of oscillation, ν, which can be readily observed from a plot of the signal intensity due to interference versus time. Therefore, the product of ν and ∆d is the rate of evaporation:
y = d /cosθ 2 As stated above, the additional distance traveled by the refracted beam is 2y, whereas for the reflected beam, the additional distance is given by x. For constructive interference to occur, the difference in the optical paths of these two
*Corresponding author.
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1 – tan θ sin θ 1 2 cosθ2
νλ
rate = 2
(1)
1 – tan θ sin θ 1 2 cosθ2
θ2 is determined from the experimental θ1, using Snell’s law: n1 sinθ1 = n2 sinθ2, in which n2 is the index of refraction of the liquid. The index of refraction of air, n 1, is assumed to
Journal of Chemical Education • Vol. 74 No. 11 November 1997
In the Laboratory be unity. If λ is given in nanometers, eq 1 gives the rate expressed as the depth of liquid layer that undergoes evaporation in nanometers per second. Additional insight into the process is gained if the weight loss and temperature are monitored during the optical interference experiment. Measurements of the weight as the liquid evaporates as a function of time yields the rate of weight loss in grams per second. Dividing this by the molecular weight of the liquid gives the moles evaporated per second. Multiplying by the Avogadro number and dividing by the rate of evaporation in nanometers per second gives the number of molecules per nanometer. The inverse of this ratio is the effective depth of the monolayer in the liquid phase. For a simple liquid on a glass, the glass acts as a thermal reservoir for the vaporization process. Since air is a poor thermal conductor, as the liquid evaporates, the glass will gradually cool. If the temperature of the glass surface is measured along with the optical interference, the thermodynamic enthalpy of the process can be determined. Since evaporation in bulk solutions is a zero-order kinetic process, the rate constant is equal to the rate of evaporation. Assuming an Arrhenius model, a plot of the logarithm of the rate of evaporation versus the inverse of the temperature will yield the heat of evaporation. Experimental Procedure The beam from a laboratory He-Ne laser—or alternatively, a diode laser pointer—was directed at the glass surface, upon which a liquid film of about 0.5 mm was placed (see Fig. 2). The light from these inexpensive low-power lasers is red and is not absorbed by most organic liquids. Consequently, the effect of laser heating can be neglected. Optical alignment and identification of the various reflected beams from the glass were facilitated by the use of a thick glass plate. The reflected beams were directed onto a diode
Table 1. Rates of Evaporation by Optical Interference Liquid acetone
Evaporation Rate a (nm/s)
(kJ/mol)
(% Deviation)
1600
32.7
+5.2
Heat of Vaporization b
methanol
91 0
38.4
+2.5
ethanol
463
44.3
+4.7
20 °C. Calculated assuming an Arrhenius model. The percentage deviation was determined from literature values (2 ). aAt b
detector biased with a 9-volt battery. The detector signal was simply fed into an analog chart recorder, which yielded results with minimum cost. The two optional additions described above, a balance and a thermometer, were incorporated into the apparatus. If a personal computer equipped with a data acquisition card is available in the student laboratory, data gathering can be made less tedious. The diode signal can be connected to an analog-to-digital input channel, and in place of a digital thermometer, a simple chromel–alumel thermocouple can be connected to another channel of the acquisition card. Most top-loading balances come equipped with an RS-232 output that can be connected to a communication port of a computer. Data from all three inputs can be monitored simultaneously and stored for later analysis using a spreadsheet program. Aliasing should be avoided by ascertaining that the rate of acquisition is faster than the interference oscillations. Results Figure 3 shows representative oscillations due to optical interference for methanol on glass. For any two successive maxima, the frequency of oscillation, ν, can be determined. Plugging this ν into eq 1, the rate of evaporation can be calculated. This is shown in Table 1, along with data for two other liquids, acetone and ethanol. From the thermocouple readings, the average temperature between the maxima can be recorded. As the liquid evaporates, owing to the near adiabatic conditions, the liquid temperature gradually decreases. This is reflected in the concomitant decrease in the frequency of oscillation. As described above, assuming an Arrhenius model, plots of the logarithm of the rate versus the inverse of temperature yield the heats of evaporation. These are also shown in Table 1. Conclusion
Figure 2. Experimental setup for optical interference.
Figure 3. Observed interference signals with methanol on glass.
The optical interference method can provide insight into the process of evaporation, particularly if used in conjunction with weight loss and temperature measurements. Some advantages of this method are its sensitivity and fast response to subtle changes that can affect evaporation, such as temperature and air currents, and its potential use in the study of liquid–surface interactions—which become relatively important at the completion of evaporation when the final volume of liquid vaporizes (see Fig. 3). Here, the process deviates significantly from zero-order kinetics. This optical method is also an alternative in situations where the use of a balance might not be practical—for example, with very small sample sizes, samples undergoing very rapid evaporation, samples in water baths, or evaporation or condensation of volatile liquids in closed systems. Finally, this optical interference method is a very inexpensive addition to other existing methods, which can be used to study this fundamentally important process.
Vol. 74 No. 11 November 1997 • Journal of Chemical Education
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In the Laboratory Acknowledgments Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this project. B. O. was an ACS Project SEED and a Summer Youth Employment Training Program participant.
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Literature Cited 1. Haynes, D. R.; Tro, N. J.; George, S. M. J. Phys. Chem. 1992, 96, 8502–8509. 2. Majer, V.; Svoboda, V. Enthalpies of Vaporization of Organic Compounds; IUPAC Chemical Data Series No. 32; Blackball Scientific: Oxford, 1985.
Journal of Chemical Education • Vol. 74 No. 11 November 1997
