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Langmuir 1992,8, 602-603
Adsorption of n-Alkane Vapors on Water F. Hauxwell ICI Colours, P.O. Box 42, Hexagon House, Blackley, Manchester M9 3DA, England
N. R. Pallas BP Research, 4440 Warrensville Center Road, Cleveland, Ohio 44128
B. A. Pethica' Langmuir Center for Colloids and Interfaces, Henry Krumb School of Mines, Columbia University, New York, New York 10027 Received November 9,1990. I n Final Form: October 9, 1991 The standard free energies, enthalpies, and entropies for the adsorption of the vapors of four normal alkanes (C5 to Cg) at the surface of water are derived from experimental data on the surface pressure as a function of vapor pressure. The loss of entropy on adsorption is close to that expected from the loss of one of translational mode and all the chain configuration degrees of freedom. As part of the analysis of data on the formation of crystalline n-pentadecanoic acid from an ideal twodimensional vapor,' it was desirable to know the thermodynamic functions for the adsorption of n-alkane vapors at the air-water interface. It appears that only Jones and Ottewil12have published such results. However, a later doctoral thesis by Hauxwel13tabulates the surface pressure (r)as a function of the alkane vapor pressure @) for four alkanes (Cgto Cg) at 5 "C temperature intervals from 5 to 25 "C. The surface pressure and vapor pressure range studied goes well below the experimental range reported by Jones and Ottewil12 and the later results are correspondingly more reliable for calculations of standard heats and entropies. For example, the results for n-pentane at 15 "C in Figure 1show that an estimate of the initial slope of the isotherm would be midleading with the earlier data. The data in the thesis have been used to calculate disjoining pressures and Hamaker constants4but the heats and entropies of adsorption for several standard states have not been published. While interconversion of the standard states is straightforward, it was decided to recalculate the standard thermodynamic functions directly in the units of the data tables by estimating the initial slopes (a)of the r-p isotherms at each temperature. The results were fitted to a second-order polynomial over the lower pressure ranges only, arranged to give zero intercept. There was no significant change in the initial slopes using higher order polynomials and the results of manual plotting also gave good agreement. Only minor variations between the values reported in the thesis and those given here were found, the largest being about 7 5% for the initial slope for octane. The initial slopes were then plotted in the form
In a = A - BIT (1) The initial slopes are illustrated for n-pentane in Figure 2. The reciprocal temperature plots for all four alkanes aregiven in Figure 3. These plots are linear. The standard heats of adsorption were then calculated from - A H 0 = (1) Pallas, N.R.; Pethica, B. A. Submitted for publications in J . Phys. Chem. (2) Jones, D. C.; Ottewill, R. H. J. Chem. SOC.1955, 4076. (3) Hauxwell, F. The Adsorption of Hydrocarbons on Water. Ph.D. Thesis, University of Bristol, 1969. (4) Hauxwell, F.; Ottewill, R. H. J.Colloid Interface Sci. 1970,34,473.
2
oc
I
00
50 0
100 0
250.0
200.0
1500
Prmssure
300.0
3500
Ha)
(mm
Figure 1. Surface pressure of water as a function of the vapor pressure of n-pentane at 15 "C: 0,data of Jones and Ottewill (ref 2); D, data of Hauxwell (ref 3).
d 1
1
>.O Pressure
(mm
Hg)
Figure 2. Initial slopes of the surfacepressure-vapor pressure
isotherms for n-pentane.
RB, where R is the gas constant. The standard free energies are given by -AGO = R T In a
(2)
Table I gives the enthalpies, free energies, and entropies for adsorption of the alkanes at 25 "C, using as standard states unit vapor pressure (1 mmHg) and unit surface pressure (1 mN m-l) corresponding to the experimental units. The enthalpies and entropies are also shown in
0743-746319212408-0602$03.00/0 0 1992 American Chemical Society
Adsorption of n-Alkane Vapors on Water
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Langmuir, Vol. 8, No. 2, 1992 603
1 0 0034
Inverse
0 0035
Temperature
.o
0 0035
Carbon
(K”)
Figure 3. Reciprocal temperature plots of the initial slopes of the surface pressure-vapor pressure isotherms for the four nalkanes c5 t0 Cs: A, cg; 0,c6;0,c7; 0 , cs.
Chain
Number
Figure 4. Standard enthalpies of adsorption for the four nalkanes CSto Cs. 250.0
Table I. Thermodynamic Functions for the Adsorption of n-Alkane Vapors on Water at 25 chain length 5 6 7 8 40.8 51.1 30.3 40.9 -A?&, kJ mol-’ 11.3 10.2 8.6 AGO,kJ mol-’ 13.3 175 171 200 -A&,, J mol-’ K-l 146 a Standard states: 1 mmHg pressure; 1 m N m-l surface pressure.
Figures 4 and 5. An alternative method of calculating CY was also used, taking the experimental values of ~ l aspa function of p and estimating the limiting value as p goes to zero. The scatter in the estimates of CY so obtained gave no more than a 6 75 spread in the estimates of the entropies and enthalpies of adsorption for the Cg, CS, C7 alkanes, and about 10%for the CScompound, for which the vapor pressures are low. The results are seen to be consistent and to yield useful new information differing significantly from the results published by Jones and OttewiL2 Their heats are all lower than those shown in Table I, and their entropies show little variation with chain length, unlike the progression seen in Table I. Figures 4 and 5 show the expected characteristic “zigzag” variation of the enthalpies and entropies of adsorption with chain length. The even and odd carbon number chain lengths show separate trends, both probably being essentially parallel. For each of the alkanes, the loss of entropy on adsorption of the vapor to the water surface is close to the sum of the entropy changes calculated for the loss of one degree of translational freedom and for the loss of the configurational entropy of the chain (R In 3 for each C-C bond). This is illustrated in Figure 5 , which includes the calculated loss
0.0
10 0
5.0 Carbon
Chain
1
.o
Number
Figure 5. Standard entropiesof adsorption at 25 O C for the four n-alkanes C5 to CS. Also shown is the calculated entropy of adsorption for the loss of one degree of translational freedom from the Sackur-Tetrode equation for methane (0).The line shown is a linear regression for the odd-numbered fatty acids, including the calculation for methane.
of translational entropy from the Sackur-Tetrode equation for methane. A linear regression line is shown for the odd-numbered alkanes, to include the calculation for methane. The slope of the regression line is 0.98R In 3. This confirms that within experimental error, and neglectingthe small variation of the Sackur-Tetrode entropy with chain length, the entropies of adsorption of n-alkane vapors to the water surface can be explained by the loss of one translational mode and all the chain configurational freedom when the adsorbed layer is dilute.
Acknowledgment. We wish to thank Professor R. H. Ottewill for useful discussions. Registry No. Cg,109-66-0;c6,110-54-3; (27,142-82-5; Cs,11165-9.
