Determination of Enthalpy of Vaporization of Pure Liquids by UV Spectrometry Gustavo Marin-Puga,1 Miguel Guzman L, Francisco Hevia Universidad Catolica del Norte, Antofagasta, Chile
The concept of vapor pressure of liquids is discussed in most general chemistry and physical chemistry courses. The Clausius-Clapeyron equation integrated for liquidvapor equilibrium is introduced to describe the variation of vapor pressure with the temperature and to determine the enthalpy of vaporization. Several demonstrations involving the volatility of liquids (1-3) and methods of measuring the change in vapor pressure with change in temperature have been reported in this Journal (4-8). In all of them, the measurement of the vapor pressure was achieved by measuring the pressure of the vapors on liquids using several types of manometers. On the other hand, many organic liquids have significant vapor pressure at room temperature and present relatively high molar absorptivity in the UV region. For these materials the absorbance of the saturated vapors, which is proportional to the concentration of molecules in the vapor phase, may be used to monitor the vapor pressure of the
liquid. In the experiment described here, students test this hypothesis, and measuring the absorbance at several temperatures, they are able to determine the enthalpy of vaporization of the liquid. Using vapor pressure values reported in literature and the absorbance measured, they find the correlation between vapor pressure and absorbance. The molar absorptivity of the organic product in the vapor phase can be also estimated. This experiment is appropriate for a physical chemistry course and for undergraduate research.
1 x cm *), substrate concentration (c in (e in M and cell M), length (l in cm).
sorptivity
A
=
excxl
(i)
Although this relationship is used almost exclusively for dilute solutions of absorbing molecules, it is also applicable in the gas phase. Actually, in the last case the absorbance measurements are not affected by solvent background or intermolecular interactions typical of solutions. Because most organic vapors are heavier than air, in a nearly closed UV cell containing some drops of a liquid, an almost perfect liquid-vapor equilibrium can be reached near the surface of the liquid. In the cell, the vapor pressure of the liquid is proportional to the concentration of the molecules of the material in the vapor phase. Thus, both the absorbance (A) measured in a point of the vapor phase and the vapor pressure are proportional to the molecule concentration of the material in the vapor phase. Therefore, at a given wavelength and temperature, absorbance is expected to be proportional to vapor pressure
(*W-
Pvap
kA
=
(2) k
T)
We then integrate the Clapeyron equation, assuming that the vapor behaves as an ideal gas and the enthalpy of vaporization (AH.,) does not depend on the temperature. In Pvap =
-
Atfv RT
+ 1
Theoretical
(3)
I
The Beer-Lambert equation relates the absorbance (A) of a solution at a particular wavelength Oj with molar ab-
£,
=
Taking the logarithm of eq 2 and replacing In
=
constant
Pvap
in eq
3, we get
In A
=
In C
AHy -
'
RT
(4)
C
=
constant
According to eq 4, by measuring the vapor absorbance as function of the temperature, AHv can be obtained from the slope of a plot of In A vs. 1IT. The constant k that relates absorbance to vapor pressure can be evaluated by comparing eq 4 with eq 3 and fitting eq 3 with data of the vapor pressure as a function of the temperature reported in the literature (9-11) or measured with one of the earlier reported methods (4—8). Assuming ideal behavior for the vapor, we can estimate the molar absorptivity of the organic product in the vapor phase from the absorbance and vapor pressure values at a given temperature. a
Experimental Materials •
1/T Logarithm of absorbance vs. 11T (K-1) data obtained for saturated vapor of toluene at 259.4 nm.
standard UV spectrophotometer with digital display (0.001 A units accuracy) with
Author to whom the correspondence should be addressed. Volume 72
Number!
January 1995
91
thermostated cell holder standard quartz cell with cup (1 cm) (about 4 mL in volume) • standard thermostated circulator (0.1 °C accuracy) two Pasteur pipets toluene (Merck, p.a.) as the organic liquid
In Pvap
•
=
18.87
-
4627.8/7’(r = 0.999)
•
• *
Procedure Toluene (0.2 mL) was carefully deposited on the bottom of the UV cell using a Pasteur pipet. The cup of the cuvette was loosely closed, and the cuvette was inserted in the thermostated cell compartment of the UV spectrophotometer. The absorbance was monitored (259.4 nm) until it reached a constant value (about 10-15 min). A better UV spectrum may be recorded if another wavelength is required to read the absorbance. The possible condensation of the vapor on the walls of the cell must be avoided. This was not detected in the range we measured (20-35 °C), but it may be observed at
higher temperatures as a result of an inefficient thermostated cell holder. In our setup the light path is about 1 cm on the surface of the liquid. The complete procedure for each data point takes about 30 min. A small bottle with a polypropylene screw cup may be used to collect the small residues of organic liquids. Use ethanol to rinse the UV cell.
Results and Discussion The data obtained are shown in the figure. The plot In A vs. 1/T shows a good linear correlation in the range of temperature studied (In A = 14.83 4790.5/7)). The correlation coefficient is better than 0.99 for four degrees of freedom (t of student = 36.95, which corresponds to greater than 99% confidence). The slope of this graph results in -
Affv = 39.83 ± 1.8 kJ/mol
for the range 20-35 °C. Even with the crude approximations made, this result is reasonably close to those reported in the literature at 25 °C: 38.00 (9) and 38.37 kJ/mol ( TO). The values of vapor pressure and temperature reported for toluene (9) at 6.4, 18.4, 31.8, and 40.3 °C result in MI.,
=
38.48 kJ/mol
from the slope of
92
Journal of Chemical Education
(See eq 3.)
Using the result from eqs 3 and 4, for the constant of eq
2, we get £
£4
_
04 + 162.7/2*
Using eq 2 for 18.4 and 31.8 °C, we get vapor pressures of 19.9 and 39.9 mm of Hg, which are within less than 1% of the experimental values reported (20 and 40 mm of Hg) (9).
Conclusions •
•
•
The In A of the vapor is inversely proportional to the absolute temperature in the range studied. Through absorbance measurements of the vapor it is possible to measure the heat of vaporization of a volatile liquid. The proportionality constant that relates the absorbance of the vapor with vapor pressure results in
k(T)
•
=
ec+B'T
where C and B depend on the nature of the liquid and the wavelength used for the measurements. Once this constant is known, it is possible to estimate the vapor pressure of a liquid by measuring the vapor absorbance at a given temperature. The method may be applied to many other organic liquids having reasonably high molar absorptivity and vapor pressure. Using our setup, we tested nitrobenzene, anisole, xylenes, and benzaldehyde at their maxima absorption. Measurements in other regions of the spectra may be run for compounds having a very high vapor pressure or molar absorptivity. The thickness of the cell may be increased to read appropriate absorbance for compounds of low vapor pressure or low molar absorptivity.
Literature Cited 1. Dehunyea R. D. J. Chem. Educ. 1992, 69, 321-322. 2. Sears, J. A. J. Chem. Educ. 1990, 67, 427. 3. Koubek, E. J. Chem. Educ. 1983, 60,1069. 4. Van Hecke, G. R. J. Ckem. Educ. 1992, 69, 681-683. 5. Schaber, P. M. J. Chem. Educ. 1985, 62, 34. 6. Long, J. W. J. Chem. Educ. 1982,59, 933. 7. Levinson, G. S, J. Chem. Educ. 1982, 59, 337-338. 8. Borrel, P.; Nyburg, S. €. J. Chem. Educ. 1965, 42, 551-552. 9. Chemical Engineers Handbook, 5th ed.; Perry, R. H.; Chilton, C. H., Eds.;
Hill: New York, 1973; 3-115 and 3-60. 10. CRC Handbook of Chemistry and Physics, 67th ed; Weast,
McGraw-
R. C.; CRC Press: Ohio, 1987-1988; D-215. E. In Sciences Elsevier Science PublishFried, Vr; Hala, Data; Physical ers: Amsterdam, 1984; Vol. 17,
11. BoubHk, T.;
