Adsorption of Solutes at the Liquid-Gas Interface as Measured by Gas Chromatography and Gibbs Equation SIR: Adsorption of solutes a t the liquid-gas interface recently was found to affect markedly the elution orders and retention volumes in gas chromatography ( 7 ) . I n several cases, such adsorption was shown to be a larger contributor t o retention volume than solution in the bulk liquid, Two goals remained after the original work. One was to measure adsorption by a second method that would corroborate the measurements made by gas chromatography and thus verify the original postulate of adsorption a t the liquid surface in gas chromatography. The other was to develop equations for calculating solute concentrations at liquid surfaces from the gas-chromatographic measurements. The Gibbs adsorption equation (2, S), which describes solute concentrations a t liquid-gas interfaces, provides the corroborating means for measuring adsorption. A common form of this equation (3) for dilute solution is:
where z is the mole fraction of solute in the bulk liquid, R is the gas constant, T is temperature, dy/dx is the rate of change of liquid surface tension n-ith solute concentration, and r is the excess of solute at the surface, in moles per square centimeter, over that in an imaginary system in which the liquid retains the bulk composition up t o an infinitely sharp interface. To compare adsorption measured by Gibbs equation and gas chromatography, an equation has been developed for gas chromatography that also allows calculation of r.
DEVELOPMENT OF EQUATION T O MEASURE ADSORPTION BY G A S CHROMATOGRAPHY
I n gas chromatography, the contributions to retention volume from both solution in the bulk liquid and adsorption a t the liquid surface are expressed by (7):
where V k is the corrected retention volume, k is the partition coefficient in the bulk liquid. V L is the volume of liquid phase, k , is the adsorption coefficient, and A L is the area of the liquid surface. The first term, IZVL, accounts for the retention volume from solution in the bulk liquid; the second, k , l L ,
116
ANALYTICAL CHEMISTRY
The numerator of Equation 7 clearly is identical to r in Equation 1; it is the "excess" moles of solute per unit area of liquid surface. The denominator can be expressed as the mole fraction of solute in the bulk liquid multiplied by M L , the moles of liquid per unit volume of the liquid. These substitutions, after rearranging, give:
/
~~
/ __ H3.EE
~"M'x
-~
3 " B V G L C L3RCKLTCGRACHY
Figure 1. Adsorption on l-chloronaphthalene by gas chromatography and Gibbs equation
accounts for the additional retention volume resulting from adsorption a t the interface. Both k and k , can be obtained from Equation 2 because both A L and T i L can be measured, and V L systematically varied. The partition coefficient, k , for dilute solutions a t equilibrium is:
k =
moles of solute per unit volume of bulk liquid moles of solute per unit volume of gas phase
In gas chromatography, from the original equation of James and Martin (6) and also from Equation 2, k =
V i (solution)
vL
(4)
where V i (solution) is the retention volume arising only from solution of solute in the bulk liquid. Similarly, from Equation 2, k,
=
V i (adsorption) 9L
(5)
where V k (adsorption) is the retention volume arising only from adsorption of solute a t the interface. Dimensional comparison of Equations 3, 4,and 5 requires that k , h a r e as dimensions of unit length and measure the following:
k,
=
K i t h Equation 8, adsorption measured by gas chromatography can be compared directly Tvith that measured by the Gibbs equation. Conditions imposed on Equation 8 by the derivation are that the solute be sufficiently dilute, that both solution and "adSorption" are proportional t o qolute concentration, and also that both processes be a t equilibrium. These conditions should be satisfied in the gas-chromatographic column. Equation 8. as well as Equation 2, will be in error when there are significant amounts of solute adsorption a t the liquid-iolid interface. Therefore, in the evaluation of Equation
8, weakly adsorptive solid supports should be used, or the solutes must be much less polar than the liquid phase. CALCULATION A N D DISCUSSION OF ADSORPTION
Equations 1 and 8 ivere used t o calculate adsorption a t the surface of 1-chloronaphthalene for each of 13 hydrocarbon solutes. T o evaluate the Gibbs equation, the decrease in surface tension mas measured with a du Soiiy tensiometer (4) a t a single solute concentration. 0.01 mole fraction. This could be considered equivalent to using the two-dimensional ideal-gas equation ( I ) . Although not highly accurate, this approach was w e d because the decreases in surface tenqion are .mall,
moles of solute per unit area of surface in excess t o that in bulk moles of solute per unit volume of gas phase
(6)
From Equations 3 and 6, k- , _- molee of solute per unit area of surface in excess t o that in bulk E moles of solute per unit volume of bulk liquid
(7)
Table 1.
-
Adsorption on 1 Chloronaphtholene
k5
n-Pentane 3-Methylpentane n-Hexane n-Heptane 2,2,4-Triniethylpentane Cyclopentane Methylcyclopentane Cyclohexane Methylcyclohexane 1-Hexene 2-Methyl-2-pentene Cyclohexene Benzene
69 170 227 725 516 182 333 462 933 “2 296 772 954
k , X lo6,
em.’
61 159 198 634 716 66 171 184 467 192 208 265 342
Moles/sq. cm. x 1011 Gas chromaGibbs tographyb equationc 6.5 6.8 6.4 6.4 10.1 2.6 3.7 2.9 3.7 5.8 5.1
2.5 2.6
4.8 5.7
5.7 6.1 9.3 2.0 2.8 2.4 3.2 4.9 4.4 2.4 2.4
-dr,d dynes/cm. 1.2 1.4 1.4 1.5
2.3
0.5
0.7 0.6
0.8
1.2
1.1
0.6 0.6
Values taken from Table I1 ( 7 ) . Calculated from Equation 8 with k and k , values as given, x = 0.0100, M L = 0.0073. c Calculated from Equation 1, x and dx = 0.0100, R = 8.31 X lo7 ergs . degrees-’ . mole-’. and T = 298’ IC. d Decrease in surface tension of chloronaphthalene N-ith change in solute of 0.0100 mole fraction. a
and accurate evaluation of d y / d x is difficult. Cursory examination indicates that dr/dx is essentially constant in this range of solute concentrations. Higher amounts of solute were avoided, so as not to exceed the applicable range of the equation. Table I gives the surface-tension decreases and the calculated values for solute adsorption in moles per square centimeter. The decreases are average values; t h e individual values varied by about 0.3 unit. Table I also gives values of adsorption calculated by gas chromatography for the same solutes a t the same mole fraction. Values for k and k,, measured previously ( 7 ) ,also are included. The moles of solute adsorbed per square centimeter agree closely as calculated by the two equations. -41though not perfect, the agreement is remarkable, considering the several
assumptions and the error in the evaluation of dr, k , and k,. The adsorption measured by gas chromatography is higher for each solute, but the strong correlation between the two methods is evident by the plot in Figure 1 of adsorption by gas chromatography us. adsorption by the Gibbs equation. The deviation of points from the line is about the same as the uncertainty in the measurements of the decrease in surface tension. The more volatile solutes tend to be below the line and the less volatile ones above the line, which suggests that solute volatility may have slightly lessened the decreases in surface tension. The close agreement between the new equation and the Gibbs equation, in addition to confirming adsorption at the liquid-gas interface in gas chromatography, serves t o verify the Gibbs equation, which has been notoriously
difficult t o confirm experimentally (3, 6,8). Besides chloronaphthalene, values of k and k , have also been calculated for &p’-thiodipropionitrile (7). Adsorption a t the nitrile surface could not be evaluated by the Gibbs equation, because the hydrocarbon solutes are not soluble enough to cause a measurable decrease in surface tension. The calculations are still possible, however, b y gas chromatography; adsorption calculates as about 10 times greater than with chloronaphthalene. Interesting physical-chemical studies of adsorption of volatile solutes on nonvolatile liquids, previously difficult or impossible, should be possible by this new gas-chromatographic approach. ACKNOWLEDGMENT
The author gratefully acknowledges helpful discussions with R. L. Burwell of Sorthm-estern University. LITERATURE CITED
(1) Adamson, A. R., “Physical Chemistry of Surfaces,” p. 91, Interscience, New York, 1960. (2) Gibbs, J . W., ‘Collected Works of J. W. Gibbs,” Longmans, Green, Kern York, 1931. (3) Glasstone, S., “Textbook of Physical Chemistry,” 2nd ed., pp. 1206-9, Van Nostrand, Princeton, S . J., 1946. (4) Harkins, W. D.. Jordan, H. F., J . Am. Chem. Soc. 52, 1751 (1930). ( 5 ) James, A. T., Martin, A . J. P., Biochem. J . 50, 679 (1952). (6) McBain, J. W.,Humphrey, C. W., J . Phys. Chem. 36,300 (1932). (7) Martin, R. L., ASAL. CHEM.33, 347 (1961). (8) Salley, D. J., Weith, A. J., Argyle, 1.9., Dixon, J . K., Proc. Roy. Soc. (London) A203, 42 (19.50). RONALD L. MARTIN American Oil Co. Whiting, Ind.
VOL. 35,
NO. 1 , JANUARY 1963
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