TECHNICAL NOTE pubs.acs.org/ac
Rapid Nondestructive Spectrometric Measurement of TemperatureDependent Gas-Liquid Solubility Equilibria Jian Ma and Purnendu K. Dasgupta* Department of Chemistry and Biochemistry, University of Texas, 700 Planetarium Place, Arlington, Texas 76019-0065, United States
Bingcheng Yang School of Pharmacy, East China University of Science and Technology, Shanghai 200237, China
bS Supporting Information ABSTRACT: Gas-liquid solubility equilibria (Henry's Law behavior) are of basic interest to many different areas. Temperature-dependent aqueous solubilities of various organic compounds are of fundamental importance in many branches of environmental science. In a number of situations, the gas/dissolved solute of interest has characteristic spectroscopic absorption that is distinct from that of the solvent. For such cases, we report facile nondestructive rapid measurement of the temperature-dependent Henry's law constant (KH) in a static sealed spectrometric cell. Combined with a special cell design, multiwavelength measurement permits a large range of KH to be spanned. It is possible to derive the KH values from the absorbance measured in the gas phase only, the liquid phase only (preferred), and both phases. Underlying principles are developed, and all three approaches are illustrated for a solute like acetone in water. A thermostatic spectrophotometer cell compartment, widely used and available, facilitates rapid temperature changes and allows rapid temperature-dependent equilibrium measurements. Applicability is shown for both acetone and methyl isobutyl ketone. Very little sample is required for the measurement; the KH for 4-hydroxynonenal, a marker for oxidative stress, is measured to be 56.9 ( 2.6 M/atm (n = 3) at 37.4 °C with 1 mg of the material available.
n his 1803 paper, William Henry credits “DR. PRIESTLEY,... the most ingenious philosopher” as having first observed the effect of pressure of a gas on its aqueous solubility.1 History has justly ascribed to him, however, the credit for quantitatively characterizing this effect that we refer today as Henry's law. Beyond gas-liquid solubility equilibria, applications presently extend to the vapor-liquid equilibrium of binary liquid solutions and the thermodynamics of binary solid solutions. The standard state of the solute in liquid and solid solutions are defined in terms of the Henryan reference state.2 One of the simplest expressions of Henry's law pertaining to dilute aqueous media is
I
½X ¼ K H Px
ð1Þ
where [X] is the liquid-phase molar concentration of solute X, Px is the equilibrium vapor pressure of X over that solution in atmospheres, and KH is the Henry's Law constant (M/atm).3 The dimensionless Henry's law constant H is expressed as H ¼ Xaq =Xg ¼ K H RT
ð2Þ
where Xaq and Xg are both expressed in a common unit, e.g., mol/L. In addition, within a limited temperature range within which the enthalpy ΔH of the process of dissolution of the solute can be assumed to be invariant, a plot of ln KH vs 1/T has the slope -ΔH/R according to the Van't Hoff equation. r 2010 American Chemical Society
Because of the obvious importance of Henry's Law equilibria and the great diversity of chemicals of interest, the literature on the determination of KH and its temperature dependence is vast. Staudinger and Roberts critically reviewed experimental means to determine KH, especially in the environmental context.4 Many computational methods for the estimation of KH based on structureactivity relationships have been developed; a popular one promulgated by the USEPA is HENRYWIN.5 There is, however, no substitute for actual measurements. Experimental methods can be broadly classified as dynamic and static. The former refers to continuous gas-liquid equilibration where at least one fluid stream is continuously flowing and the effluent concentration is (continuously) measured. In static techniques, an equilibrium is established between the two phases and one or both phases are then measured by discrete sampling.3,4 The Staudinger-Roberts reviews are not comprehensive, however; one notable omission of dynamic methods is membrane-based gas-liquid equilibration techniques.6-15 These have also been used to generate gases in standard concentrations. To our knowledge, in situ nondestructive measurements have not been explored to measure KH. Received: November 10, 2010 Accepted: December 14, 2010 Published: December 30, 2010 1157
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An example is shown in Figure S1 in Supporting Information with data for our instrument which has a nominal Z-dimension of 15 mm. If the initial absorbance of the air-filled cuvette is set to zero, it will continue at that level until the water level begins to touch the bottom of the beam (in this case, ∼11 mm). The absorbance will rise, reach a peak when the water level rises to the Z-dimension, and then decrease again. Presently, at 17 mm, when the light path is fully water filled, a stable absorbance is reached (typically at ∼-0.03 absorbance, arising from better light throughput for the water-filled cuvette, as opposed to an air-filled cuvette). In this case, we thus see that the light beam occupies a ∼6 mm height span. When either the pure vapor or the pure liquid phase is to be measured, with some margin of safety, it will be prudent to have a single phase span g8 mm. Thus, if a standard cell is filled with liquid up to an 8 mm depth at the bottom, when put in our cell compartment, the spectrometer will measure purely the gas phase, as the beam will pass entirely above the liquid. If we put a 1 cm tall spacer in the cell compartment before putting the cell thereon, the light beam will pass entirely through the liquid phase. Measurement Approaches. To conform with usual Beer's law notations, eq 2 is rewritten: Figure 1. Temperature-dependent Henry's Law constant for acetone using three different approaches and MIBK. Solid lines are obtained from a linear least-squares analysis. The error bars (n = 3-9) indicate (1 standard deviation. 1a (red): ln KH = (4530 ( 126)/T - (11.93 ( 0.41), r2 = 0.9962; 1b (black): ln KH = (4865 ( 117)/T - (12.91 ( 0.39), r2 = 0.9977; 2 (blue): ln KH = (5119 ( 432)/T - (14.18 ( 1.39), r2 = 0.9723; 3 (hollow green squares): ln KH = (4785 ( 220)/T (12.89 ( 0.71), r2 = 0.9916; purple:17 ln KH = (5975 ( 685)/T (16.67 ( 2.42), r2 = 0.9620; solid green squares:18 ln KH = (3844 ( 153)/T - (9.33 ( 0.51), r2 = 0.9953; orange: MIBK (approach 1b): ln KH = (4274 ( 100)/T - (12.34 ( 0.33), r2 = 0.9967.
We report a simple method to measure KH by direct UV-vis spectrometry. There is the limitation that the solute must be available in pure form. It must also have measurable optical absorption in the solution or the gas phase. While applicability is, therefore, not universal, a great variety of organic compounds of interest do meet these criteria. The useful range is extended by a specially designed cell and the use of multiwavelength spectrometry. In situ nondestructive measurement requires very little sample. At the minimum, this simple technique is an ideal pedagogical experiment pertaining to KH measurements. For spectrometers equipped with thermostatting arrangements, it allows the ready examination of the Van't Hoff relationship, e.g., at five temperatures, easily in less than an hour.
’ PRINCIPLES Dimensional Considerations of Measurement Cell. Consider a standard 1 cm path length spectrometric cuvette that can be sealed at the top. Alternatively, a custom cuvette may have much smaller path length at the bottom as shown in the inset of Figure 1 (see also Figure S1 in the Supporting Information). Note that some micro and disposable spectrophotometer cells may resemble the above geometry but are designed to only minimize needed liquid volume; path lengths are the same at the top and the bottom. Presently, we are also concerned with the height span of the cell where the light beam passes through. The Z-dimension,16 the distance from the bottom of the cell compartment to the center of the light beam, is listed by the instrument manufacturer, but this index is only a single value. The information we desire is readily obtained by filling a standard 1 cm2 cross section cell 100 μL at a time (i.e., 1 mm height increments) and measuring the absorbance.
H ¼ C l =C g
ð3Þ
the subscripts denoting liquid and gas phase. For either phase, Beer's law holds: C i ¼ A i =εi b i
ð4Þ
There are three distinct modes in which the measurements can be made. Measure Both Gas and Liquid Phase Absorbance. Substituting eq 4 in eq 3, H ¼ ðA l =εl b l Þ=ðA g =εg b g Þ
ð5Þ
The ratio b l =b g (the ratio of liquid/gas path lengths) is either unity (conventional cell) or is known for a custom cell (or measured by filling with a suitable dye solution and measuring absorbances at two respective heights). Presently let b l =b g ¼ χ; eq 5 reduces to H ¼ χðA l =A g Þ=ðεl =εg Þ
ð6Þ
When A l and A g are measured, H is readily computed if (a) the absorbing form of the molecule does not change upon dissolution (e.g., HCHO becoming (CH2(OH)2) and we make the approximation that the absorbance for the same number of molecules in the light path will be the same whether they are in the liquid phase or gas phase, i.e., εl = εg. This approximation is not always defensible. (b) We measure εl and εg. The first is measured by making a solution of known concentration and measuring the absorbance with little or minimum headspace in the cuvette to prevent solute transfer to the gas phase. The second is measured by introducing a known amount of the pure compound to a septum-equipped cuvette (or as a solution aliquot in a volatile solvent that does not absorb in the region of interest) using a microliter syringe. Evaporation can be promoted by heating the cuvette/thermostated compartment, it is generally defensible that the gas phase absorptivity will be reasonably temperature independent. Nevertheless, there will be cases where getting a pure known amount of solute entirely into the gas phase may prove difficult. With the majority of solutes of interest, H will be .1. This means that if liquid and gas phase volumes (V l and V g ) were comparable, a relatively small solute fraction will transfer to V g ; A g may be not sufficient to measure accurately. The specially 1158
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designed cell addresses this problem, using a shorter path length for the liquid phase. A smaller V l maximizes the V g =V l ratio; the shorter b l permits a higher C l . These advantages can be further enhanced by choosing different wavelengths for liquid vs gas phase measurements such that εg . εl. Measure Only Liquid Phase Absorbance. Measurement of liquid phase absorbance of solute solutions is convenient as measurement of εl is least error prone and it will generally not be necessary to measure at two different heights/pathlengths in the cell. The absorbance A l , in of a solution of the solute in known concentration (C l , in mol/cm3) is first measured by completely filling a cuvette. For a high-value solute, the solution can be recovered. Following washing and drying, the minimum volume (V l , in cm3) of the solution needed to fill a span sufficient to make a liquid phase measurement is pipetted into the cell, and the cell is quickly capped. Some liquid may evaporate; let the equilibrium liquid volume be V l , eq : V l , eq ¼ V l , in - nsolv =V m
ð7Þ
V m and nsolv are respectively the molar volume and the gas phase and the number of moles of the solvent: nsolv ¼ pðV T - V l , eq Þ=RT Incorporating eq 8 in 7: V l , eq ¼ ðV l , in RTV m - pV T Þ=ðRTV m - pÞ
ð8Þ ð9Þ
where p is the saturation vapor pressure of the solvent. We assume dilute solutions, so this is the vapor pressure of the pure solvent. For water, this is readily available as a function of temperature. For solutions that are not dilute, p can be computed from Raoult's law. Overall, the correction due to solvent evaporation, represented by eqs 7-9, is rather small for water as solvent. Up to temperatures of 50 °C for the special construction cell with a total volume of 3.1 cm3 that is filled initially with 80 μL water,
