In the Laboratory
Principles of Solution Thermodynamics: Demonstration of Nonideal Behavior of Henry’s Law
W
An Undergraduate Laboratory Experiment Luke Chandler Short* and Thorsten Benter Bergische Universität Wuppertal, Fachbereich C – Naturwissenschaften und Mathematik, Gaußstr. 20 D-42119 Wuppertal, Germany; *
[email protected] While the student of physical chemistry learns the theoretical background of both ideal and nonideal gas solubility, we find that many of the laboratory courses focus on experiments exploring ideal conditions. When nonideal conditions are studied, it is typically the solubility of carbon dioxide (1). We present here an alternative experiment to demonstrate nonideal gas solubility of the environmentally significant molecule formaldehyde, HCHO. While the principles of this laboratory are appropriate for an advanced undergraduate course, we feel that this exercise is excellent in conjunction with other graduate-level courses, for example, atmospheric chemistry, environmental techniques, or biomedical techniques. We have performed this experiment ourselves and with a small group of students. The experimental setup takes one-to-two days of preparation and then roughly four hours of laboratory experimentation. Effective Henry’s Law Coefficient for a Nonideal Solution According to the empirical approximation of Raoult’s law, the partial pressure of one component in the gas phase, Pi, is proportional to the mole fraction, χ i, of that component within the solution and the partial pressure of the pure component, Pi*: (1) Pi = χi Pi * This relationship is used to provide a good estimate of the gas-phase mole fraction, yi, with a total gas pressure, P, above a two-component solution, provided the interactions of the two solvents with each other and themselves are nearly identical, that is, yi P = χi Pi *
(2)
For the specific case of aqueous solutions, a ratio of the liquid-phase mole fraction to that of the gas-phase mole fraction is calculated, termed a Henry’s law coefficient. Henry’s law describes the partitioning of a volatile solute, A, between the gas and liquid phases for an ideal, dilute solution at thermodynamic equilibrium,
A(g) K H, A =
(3)
A(aq) A ( aq )
(4a)
A (g)
or equivalently K H, A =
A ( aq )
(4b)
PA
www.JCE.DivCHED.org
•
where PA is the partial pressure of A in the gas phase (in units of atm) and [A(aq)] is the aqueous-phase concentration of A (in units mol L᎑1 or M) in equilibrium with PA. The customary units of KH,A are M atm᎑1. Equation 4b is an accurate representation of the partition coefficient for gases that behave ideally as they dissolve into a solution. However, in the case with the nonideal HCHO, a further reaction complicates this calculation. Upon mixing with liquid water, HCHO undergoes hydrolysis to yield the gem diol, methylene glycol, according to the two equilibria:
HCHO(g) HCHO(aq) + H2O
HCHO(aq) H2C(OH)2(aq)
(5) (6)
The chemical species HCHO(aq) is thus removed from the left side of the equilibrium eq 6. This results in a much larger uptake of HCHO(g) into the liquid than predicted by the assumption of a simple gas–liquid phase partitioning (eq 5). To provide a more accurate partitioning constant, an effective Henry’s law coefficient, KH,eff, is used to empirically represent the gas- and liquid-phase partitioning of a nonideal gas solute, K H, efff =
C HCHO PHCHO
(7)
where CHCHO is the analytical concentration of the formaldehyde in solution. In this experiment, students measure the gas- and liquid-phase concentrations of a nonideal system, HCHO in water, allowing them to calculate KH,eff for this system. Procedures
Experimental For details on all chemicals and methods used see the Supplemental Material.W The demonstration of Henry’s law is done by first measuring the exact liquid-phase concentration of a stock solution of 20 µM HCHO. This solution is made by taking 0.5 mL of a stock 0.012 M HCHO solution and diluting to 250 mL with HCHO-free water. This liquid-phase solution of HCHO is then poured into a glassfritted bubbler (Figure 1) and nitrogen gas passes through the bubbler, resulting in a flow of HCHO-saturated gas. A water bath is used to maintain room temperature conditions. The gas and liquid are both directly sampled using the HCHO analyzer.
Vol. 83 No. 8 August 2006
•
Journal of Chemical Education
1233
In the Laboratory
Figure 1. Schematic of HCHO bubbler and analyzer. A stream of 300 mL min-1 N2(g) is introduced into a glass bubbler resulting in the rapid establishment of equilibrium and a gas–liquid partitioning of HCHO. A stream of 700 mL min-1 N2(g) is introduced to dilute and dry the gas sample to minimize surface reactions in the sampling line. The gas passes through the scrubber, the Nash reagent is added, and the derivative compound is detected by fluorescence spectroscopy. To analyze a solution, the liquid is added, the Nash reagent is added, and the derivative compound is detected by fluorescence spectroscopy.
Calculations The formaldehyde solution is directly sampled using the liquid-sampling mode of the HCHO analyzer and CHCHO is given in units of µM. The gas is sampled using the gas-sampling mode of the HCHO analyzer. The measured concentration of a gas is represented by the instrument as a relative concentration per volume, termed a mixing ratio FHCHO, with units of parts-per-billion in a volume of 1 cm3, or ppbV. To convert a mixing ratio F HCHO (ppbV) to a pressure PHCHO (atm), a conversion factor is needed: P HCHO = P y HCHO = P F HCHO 10 −9
C HCHO C HCHO = PHCHO FHCHO 10 −9
(
)
Equipment and Chemicals
Temperature Effect on KH,eff Using the same setup as described in the previous section, the HCHO bubbler is placed in a temperature-controlled water bath. A solution with a HCHO concentration of about 60 µM is poured into the bubbler, and then the gas-phase concentration of the headspace sampled from the bubbler is measured at different temperatures, from 290 K to 300 K. •
(10)
(9)
The liquid-phase and gas-phase concentrations of HCHO are measured for five solutions of 20, 40, 70, 180, and 500 µM. Two plots are made; one with the gasphase mixing ratio, FHCHO, plotted against the liquid-phase concentration, CHCHO, (with a logarithmic regression line), and the second with KH,eff plotted against the liquid-phase concentration (with a linear regression line).
Journal of Chemical Education
∆ S ∆ solnH + soln RT R
(8)
Concentration Effect on KH,eff
1234
ln K H, eff = −
where ∆solnH ⬚ is the solution enthalpy of HCHO, ∆solnS ⬚ is the solution entropy of HCHO, and R is the ideal gas constant, 8.314 J mol᎑1 K᎑1. Assuming that ∆solnH ⬚ and ∆solnS ⬚ are to a good approximation invariant upon temperature, a plot of lnKeff versus 1兾T will have a slope equal to ᎑∆solnH ⬚兾R, and the intercept is ∆solnS ⬚兾R. The student can use this approach to determining the solution enthalpy and entropy of HCHO at standard state, ∆solnH ⬚ and ∆solnS ⬚.
Thus eq 7 can be rewritten as K H, eff =
The resulting gas-to-liquid phase partitioning of HCHO determines the value for KH,eff as a function of temperature, which is calculated using a van’t Hoff plot, expressed thermodynamically as (2, 3):
Experiments are carried out using the AL4001 HCHO analyzer (AERO-LASER, GmbH, Garmisch-Partenkirchen, Germany). Detection of trace quantities of HCHO is accomplished by: (i) scrubbing of gas with a cold sulfuric acid (H2SO4) solution to transfer HCHO to the liquid phase or direct injection into the system if the sample is a liquid; (ii) reaction of this solution containing HCHO with the Nash reagent to form DDL (3,5-diacetly-1,4-dihydrolutidine), and (iii) fluorimetry by absorption of 410-nm light from a filtercoated Hg-lamp and then collection of fluorescent light at 510 nm with a filter and a photomultiplier tube (4). The signal of the analyzer is recorded as a voltage and converted in to concentration units (see the Supplemental MaterialW for details). All chemicals are kept at 277 K in a refrigerator. Stock ∼0.012 M HCHO is prepared from ∼33% formalin (a mixture of HCHO, methanol, and water) by a 1兾1000 dilution with Millipore water (or other HCHO-free water source).
Vol. 83 No. 8 August 2006
•
www.JCE.DivCHED.org
In the Laboratory
Hazards
6
9 4 6 2 3
0
Results
Effective Henry’s Law Coefficient for a Nonideal Solution The effective Henry’s law coefficient for a dilute solution (20 µM) of HCHO in water is found to be ∼3000 M atm᎑1 (Figure 2). Within experimental error, this compares well to the values reported in literature of 3200 M atm᎑1 (9), 3000 M atm᎑1 (10), and 3100 M atm᎑1 (11). Concentration Effect on KH,eff
100
200
300
400
0 500
[HCHO] / (mol/L) Figure 2. Measured headspace mixing ratios of HCHO over aqueous HCHO solutions of known concentration (triangles and solid regression line). Values for the HCHO mixing ratio correspond to the right axis. In addition, using eq 9, the calculated effective Henry’s law coefficient KH,eff is plotted for each measured gas– liquid HCHO concentration pair (circles and dashed regression line). Corresponding KH,eff values are indicated on the left scale. For comparison, ideal solution behavior is presented as a dotted line.
6
5
4
FHCHO / ( ppbV ) = 1.8 ln [CHCHO / ( µmol/L )] − 4.9 •
(11)
KH,eff
3
2
1 285
290
295
300
305
Temperature, T / K
mol L atm
10
9
8
ln KH,eff
Here we measure five solutions of HCHO(aq), each containing increasing concentrations of HCHO of 20, 40, 70, 180, and 500 µM (Figure 2). The concentration error bars are calculated as 3σ of the measured signal from a HCHOfree solution, which we found to be ±0.4 ppbV HCHO (gas phase) or ±1 µM HCHO (liquid phase). The error bars in Figures 2 and 3 are calculated as the resulting cumulative error (see the Supplemental MaterialW). An ideal solution of a volatile solute with K A ∼3000 M atm᎑1 would result in a linear gas-to-liquid phase concentration dependence, represented as the dotted line in Figure 2. This line starts at the origin, [HCHO(aq)] = 0 µM, and rises with a slope of 0.03 ppbV µM᎑1. At a liquid-phase concentration of 500 µM HCHO, assuming an ideal-solution behavior, the gas-phase concentration above the liquid would be 17 ppbV HCHO. This is not what is observed. As the concentration of the HCHO in the solution increases, the [HCHO]–[HCHO] bond becomes significant. As this bond is stronger than the [H2O]–[HCHO] bond, HCHO within the solution is retained increasingly as the concentration of the HCHO in the solution increases.1 Figure 2 shows the measured concentration of HCHO(g) above the solution follows not the ideal linear, but rather logarithmic response to increasing solution concentrations of HCHO, a result of increasingly significant solute–solute interaction:
www.JCE.DivCHED.org
0
103 mol L atm
There are no significant hazards to the student, so long as basic care is taken during the sampling of the HCHO solutions. High concentration HCHO solutions represent an inhalation hazard, and so the solutions are prepared in a fume hood. A more complete review of hazards associated with HCHO laboratory experiments is found elsewhere (8). The other reagent chemicals pose a minor ventilation and contact hazard, and so the preparations are also made within a fume hood with gloves, lab apron, and eye protectors.
FA / ppbV
103 mol L atm
12
kH,eff /
Calibration of this stock solution is done with iodometric titration with an iodine Titrisol solution (5–7). Additional chemicals required for this step are: acetic acid, sodium carbonate, sodium sulfite, boric acid, and sodium hydroxide. The Nash reagent is composed of ammonium acetate, acetic acid, 2,4-pentanedione, and water, chilled to ∼278 K. The scrubbing solution is made from concentrated sulfuric acid. For details on chemicals and methods used, refer to the Supplemental Material.W
7
6 3.30
3.35
3.40
1 T
(10
3.45
ⴚ3
K
3.50
ⴚ1
)
Figure 3. Data for the temperature dependence of KH,eff, with temperature of the liquid phase: (top) Plot of KH,eff versus temperature. (bottom) Plot of logarithmic of KH,eff versus inverse temperature, showing that the data obtained are accurately described by eq 10.
Vol. 83 No. 8 August 2006
•
Journal of Chemical Education
1235
In the Laboratory
When the ratio of liquid-phase HCHO-to-gas-phase HCHO is calculated, that is, KH,eff, then the slope is linearly dependent upon concentration within the range studied, as predicted by eq 11. For the given data, the linear fit is: K H, eff /
mool L ⋅ atm
= 11 CHCHO / ( µmol/L ) − 2552
(12)
The intercept of this straight line with the [HCHO] = 0 µM gives an Keff value of ∼3000 M atm᎑1, in agreement with values reported in literature. If a solution of HCHO were to have an ideal gas-to-liquid phase partition, then the Keff value would not be concentration dependant.
equilibrium. Two scenarios are studied to demonstrate factors affecting this thermodynamic ratio; namely, concentration effects and temperature effects. Acknowledgment Financial support of this work was made by the Fulbright Commission. W
Supplemental Material
Instructions for the students and notes for the instructor are available in this issue of JCE Online.
Temperature Effect on KH,eff
Note
The concentration of the HCHO solution used here is 57.6 µM. The natural logarithm of the concentration of the HCHO in the gas phase is measured as a function of the temperature of the bubbler (Figure 3). Using the data from Figure 3 and eq 10, the standardstate enthalpy of solution for HCHO is calculated to be ᎑54 kJ mol᎑1 and the standard-state entropy of solution is calculated to be ᎑120 J mol᎑1 K᎑1. The value for the standardstate enthalpy compares to that reported in the literature ᎑57 kJ mol᎑1 (9), ᎑60 kJ mol᎑1(10), and ᎑54 kJ mol᎑1 (11). The value for the standard-state entropy compares to that reported in the literature ᎑90 J mol᎑1 K᎑1 (9) and ᎑120 J mol᎑1 K᎑1 (11). This chemical derivatization technique can therefore be used to determine the standard-state enthalpy and entropy of dilute aqueous solutions of HCHO.
1. In dilute solutions of formaldehyde in water the only significant reactions are water–formaldehyde as shown in eq 6; however, as the concentration of formaldehyde goes up, the "stickiness" of the solution also goes up and the formaldehyde–formaldehyde interactions dominate.
Conclusion Using a commercially-available HCHO-analyzer, the gas–liquid phase partitioning of a nonideal, solute–solvent mixture is measured. This instrument, coupled with the experiment described herein, is designed for the instructor of physical chemistry in an advanced undergraduate laboratory course. The experiment first provides hands-on experience of a commonly-used type of HCHO analyzer used for environmental and medical analysis, and then applies this knowledge to demonstrate nonideal, biphase thermodynamic
1236
Journal of Chemical Education
•
Literature Cited 1. Koster, D.; Trimble, R. J. Chem. Educ. 1994, 71, 528. 2. Tenhulscher, T. E. M.; Vandervelde, L. E.; Bruggeman, W. A. Environ. Tox. Chem. 1992, 11, 1595–1603. 3. Raldow, W.; Wentworth, W. J. Chem. Educ. 1980, 57, 879. 4. Dong, S.; Dasgupta, P. K. Environ. Sci. Technol. 1987, 21, 581–588. 5. Silva, C.; Simoni, J.; Collins, C.; Volpe, P. J. Chem. Educ. 1999, 76, 1421. 6. Petersen, H.; Norbert, P. Melliand Textilberichte 1985, 3, 217. 7. de Jong, J.; de Jonge, J. Recueil Trav chim Pays-Bas 1952, 643, 890. 8. Clausz, J.; Mac Intyre, B.; Malone, E. J. Chem. Educ. 1984, 61, A121–A126. 9. Staudinger, J.; Roberts, P. Critical Rev. Environ. Sci. Tech. 1996, 26, 205–297. 10. Moller, D.; Mauersberger, G. J. Atmos. Chem. 1992, 14, 153– 165. 11. Zhou, X. L.; Mopper, K. Environ. Sci. Technol. 1990, 24, 1864–1869.
Vol. 83 No. 8 August 2006
•
www.JCE.DivCHED.org
