umetric expansion coefficient and βT = â(âV/âp)T/V is the isothermal compressibility. The kinetic pressure of the ideal gas is pk = RT/V, and that of a van der ...
Russian Journal of Physical Chemistry, Vol. 76, No. 6, 2002, pp. 903–905. Translated from Zhurnal Fizicheskoi Khimii, Vol. 76, No. 6, 2002, pp. 1016–1018. Original Russian Text Copyright © 2002 by Kartsev, Rodnikova, Bartel, Shtykov. English Translation Copyright © 2002 by MAIK “Nauka /Interperiodica” (Russia).
CHEMICAL THERMODYNAMICS AND THERMOCHEMISTRY
The Temperature Dependence of Internal Pressure in Liquids V. N. Kartsev*, M. N. Rodnikova**, I. Bartel***, and S. N. Shtykov* * Chernyshevskii Saratov State University, ul. Universitetskaya 42, Saratov, 410601 Russia ** Kurnakov Institute of General and Inorganic Chemistry, Russian Academy of Sciences, Leninskii pr. 31, Moscow, 117907 Russia *** Institute of Physical and Theoretical Chemistry, Regensburg, Germany Received July 11, 2001
Abstract—Internal pressures were calculated for a large variety of liquids in a wide temperature range from abundant experimental data on isothermal compressibility and thermal volumetric expansion coefficients obtained on a unique piesometric unit. The temperature coefficient of internal pressure was shown to be a structural characteristic of liquids. This coefficient was found to be positive for weakly associated liquids whose structure approximated close packing and negative for liquids with a spatial network of H-bonds. The largest negative temperature coefficient of internal pressure was obtained for water, whose spatial network of H-bonds was most perfect.
According to [1], the temperature dependence of internal pressure in liquids can be treated as a characteristic of their structure. A positive temperature coefficient of internal pressure is evidence of an openwork character of the structure and a possibility of the existence of a spatial network of H-bonds in the liquid [1]. Consider this conclusion in more detail; we will illustrate it using the available experimental data. The internal energy of one mole of a homogeneous system can be represented by the sum of two terms, id
mi
U = U +U , where Uid is the internal energy of the hypothetical ideal gas and Umi is the contribution of intermolecular interactions, which transforms an ideal system into a real system [2]. The partial derivative of internal energy with respect to the volume then takes the form ( ∂U/∂V ) T, x = ( ∂U /∂V ) T, x id
umetric expansion coefficient and βT = –(∂V/∂p)T/V is the isothermal compressibility. The kinetic pressure of the ideal gas is pk = RT/V, and that of a van der Waals gas is pk = RT/(V – b) [3]. The internal and kinetic pressures in the system are interrelated [3], pk + pi = p. Hence p i = p – p k = p – ( αT /β T ).
For most of the liquids, α > 0 and isothermal compressibility is an essentially positive value. At atmospheric pressure, p = patm Ⰶ pk; therefore, pi < 0. An exception is water, for which pk ≤ 0 and pi ≥ 0 in the temperature range 0–4°C. Internal pressure tends to draw structural units in condensed media closer together. For most of the liquids, we have patm /pk < 10–3 [3, 5, 6]. It follows that ignoring p = patm in calculating pi by (1) leads to errors smaller than 0.1%. Equation (1) can then be simplified to p i = – αT /β T .
+ ( ∂U /∂V ) T, x = ( ∂U /∂V ) T, x , mi
mi
because the internal energy of the ideal gas only depends on temperature. The pi = –(∂U/∂V)T, x value is called internal or static pressure [3]. It follows from this definition that internal pressure is caused by intermolecular forces and is determined by the reaction of these forces to volume deformation caused by equilibrium isothermal expansion. Internal pressure of the ideal gas equals zero, and that of a gas with van der Waals interparticle interactions is pi = –a/V2 [3]. In [4], internal pressure was related to the Laplace molecular pressure. Equilibrium thermodynamics also uses the kinetic pressure concept, pk = T(∂p/∂T)V = αT/βT; this pressure is caused by thermal motion of molecules [3]. Here, α = (∂V/∂T)p/V is the thermal vol-
(1)
(2)
The temperature dependences of pi for n-alkanes, n-alcohols, water, diols, and an aminoalcohol are shown in Figs. 1–3. These dependences were calculated by (2) from our experimental data obtained on a unique piesometric unit [7] and from the data reported in [5]. The temperature dependences of internal pressure in liquids differ in character. According to the form of these dependences, liquids can be divided into two classes. Liquids of the first class have positive temperature coefficients of internal pressure. They include n-alkanes, carbon tetrachloride, benzene, toluene, o-, m-, and p-xylenes, and acetone; that is, liquids with comparatively weak intermolecular interactions. Note that the first class also includes diamines (ethylenediamine, 1,2- and 1,3-diaminopropane, and 1,6-diamino-
903
904
KARTSEV et al. t, °C 20
40
60
20
80
40
60
80
200 (a)
(b)
pi × 10 –6, Pa
220
240
260
280
300
6 7 8 9 10 11 13 15
2 3 4 5 6 7
Fig. 1. Polytherms of internal pressure in liquids of homologous series of (a) n-alkanes and (b) n-alcohols. Numbers on the lines are the numbers of carbon atoms in hydrocarbon chains of molecules (n).
20
60
40
t, °C 20
80
40
60
80
450 (b)
(a)
100
2
pi × 10 –6, Pa
470 200
3 490
300 2 400
510 1
1 530
500
4 550
Fig. 2. Polytherms of internal pressure in liquids with spatial networks of H-bonds; (a) (1) H2O and (2) D2O; (b) (1) ethylene glycol, (2) 1,2-propanediol, (3) 1,3-propanediol, and (4) 1,2-aminopropanol.
hexane [8]), which can form networks of H-bonds. These networks are, however, unstable in diamines because the energy of H-bonds in them does not exceed 4 kcal/mol, and contain many defects because of the presence of hydrocarbon bridges in these molecules [1]. The second class includes liquids whose temperature coefficients of internal pressure are negative. These are liquids with spatial networks of H-bonds such as
water, ethylene glycol, 1,2- and 1,3-propanediols, monoethanolamine, and 1,2-aminopropanol [6, 9]. Like diamines, diols and aminoalcohols contain spatial network defects caused by the presence of hydrocarbon bridges in their molecules. The energy of H-bonds in these compounds is, however, ~2 times higher than in diamines; their spatial networks of H-bonds are therefore much stabler [1, 10, 11].
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THE TEMPERATURE DEPENDENCE OF INTERNAL PRESSURE IN LIQUIDS (∆pi /∆T) × 10 –6, Pa/ä
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structures of liquids into openwork structures. This leads us to conclude that the temperature coefficient of internal pressure is a structural characteristic of liquids.
1 1
ACKNOWLEDGMENTS This work was financially supported by the Russian Foundation for Basic Research (project no. 00-0332073) and the Russian–German Joint Project (WTZ mit Rußland: RUS 99/178).
2 0 3
6
10
14
18
n
–1 Fig. 3. Mean temperature coefficients of internal pressure of (1) n-alkanes, (2) n-alcohols, and (3) diols in the temperature range 10–50°C; n is the number of carbon atoms in the molecular hydrocarbon chains.
REFERENCES
Internal pressure in n-alcohols is independent of temperature in the temperature range 0−40°C; that is, their temperature coefficients of internal pressure are zero, ∆pi /∆T = 0 (Fig. 1b). Recall that the energy of H-bonds in alcohols is ~6 kcal/mol, but they cannot form spatial networks of H-bonds because their molecules contain a single proton donor center each [1]. Alcohols have layered structures: within each layer, molecules are linked by H-bonds, but interlayer interactions are van der Waals in character [12]. Within each series of molecules with similar structures (n-alkanes, n-alcohols, H2O and D2O, and diols), the temperature coefficient of internal pressure is a slightly varying function (Fig. 3). The temperature coefficient of internal pressure, however, substantially changes in passing from one class of liquids to another. For instance, for weakly associated n-alkanes, the ∆pi /∆T coefficient is positive and equals 1 × 106 Pa/K. In n-alcohol, this coefficient virtually decreases to zero, and, for aminoalcohols and diols, ∆pi /∆T = –(0.5–0.7) × 106 Pa/K. Water has the most perfect network of H-bonds (the only origin of defects is thermal motion of molecules), and its ∆pi /∆T coefficient has the largest negative value, –7 × 106 Pa/K. To summarize, changes in the temperature coefficient of internal pressure allowed us to trace the transformation of closely packed or almost closely packed
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1. Rodnikova, M.N., Zh. Fiz. Khim., 1993, vol. 67, no. 2, p. 275. 2. Smirnova, N.A., Molekulyarnye teorii rastvorov (Molecular Theories of Solutions), Leningrad: Khimiya, 1987. 3. Moelwyn-Hughes, E.A., Physical Chemistry, London: Pergamon, 1961. Translated under the title Fizicheskaya khimiya, Moscow: Inostrannaya Literatura, 1962. 4. Rusanov, A.I. and Krotov, B.V., Zh. Fiz. Khim., 1976, vol. 38, no. 1, p. 191. 5. Egorov, T.I., Gruznov, E.L., and Kolker, A.M., Zh. Fiz. Khim., 1996, vol. 70, no. 2, p. 216. 6. Kartsev, V.N., Rodnikova, M.N., Tsepulin, V.V., and Razumova, A.B., Zh. Fiz. Khim., 1994, vol. 68, no. 10, p. 1915. 7. Kartsev, V.N., Tsepulin, V.V., and Zabelin, B.A., Voprosy prikladnoi fiziki (Problems of Applied Physics), Saratov, 1997, issue 3, p. 23. 8. Kartsev, V.N., Tsepulin, V.V., Rodnikova, M.N., and Dudnikova, K.T., Zh. Fiz. Khim., 1988, vol. 62, no. 8, p. 2232. 9. Kartsev, V.N., Rodnikova, M.N., Tsepulin, V.V., and Markova, V.G., Zh. Fiz. Khim., 1988, vol. 62, no. 8, p. 2236. 10. Rabinovich, I.B., Vliyanie izotopii na fiziko-khimicheskie svoistva zhidkostei (Isotope Substitution Effects on the Physicochemical Properties of Liquids), Moscow: Nauka, 1968. 11. Millero, F.J. and Lepple, F.K., J. Chem. Phys., 1971, vol. 54, no. 3, p. 946. 12. Dorosh, A.K., Struktura kondensirovannykh sistem (Structure of Condensed Systems), L’vov: Vishcha Shkola, 1981.
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