Anal. Chem. 1998, 70, 3481-3487
Simultaneous Measurements of Solute Concentration and Henry’s Constant Using Multiple Headspace Extraction Gas Chromatography X. S. Chai and J. Y. Zhu*
Institute of Paper Science and Technology, 500 10th Street, N.W., Atlanta, Georgia 30318
This study conducted the first experimental work using multiple headspace extraction (MHE) gas chromatographic (GC) techniques to achieve measurement automation in the measurements of solute concentration and vapor-liquid equilibrium partitioning. The study also presented the successful development of a new, accurate MHE GC method to simultaneously measure the concentrations and Henry’s constants of solutes in infinitely diluted solutions. Mathematical precision analysis indicates that the phase ratio β is the key parameter that dictates the accuracy of the MHE GC methods. The precision analysis and experimental verifications indicate that the present method is accurate over a wide range of β. Good agreement of measured methanol concentration in nine environmental samples using the present MHE method and an indirect headspace GC method were obtained. The measured Henry’s constants of 2-propanol and ethanol in water solutions agree with those reported in the literature. Determination of solute concentration and vapor-liquid phase equilibrium (VLE) partitioning in unknown solutions has significant practical importance in chemical and environmental engineering. There are many techniques available for quantitative analysis or VLE studies of trace species in unknown samples. Most existing techniques, such as direct column injection in gas chromatography (GC), directly measure the liquid phase of the sample through calibration and are not suitable for the characterization of many industrial and environmental streams due to the corrosive nature of the samples. Tedious sample pretreatment is required in using these methods.1 Headspace gas chromatography (HSGC) provides direct analysis of the solute vapor in a solution. Many HSGC methods have been developed and described in the literature.2-10 Quantitative analysis of solute (1) Gunshefki, M.; Cloutier, S. NCASI Technical Memo, 1994. (2) Drozd, J.; Novak, J. J. Chromatogr. 1979, 165, 141. (3) Namiesnik, J.; Gorecki, T.; Biziuk, M. Anal. Chim. Acta 1990, 237, 1. (4) Ioffe, B. V.; Vitenbery, A. G. Headspace Analysis and Related Methods in Gas Chromatography; John Wiley & Sons: New York, 1984. (5) Kolb, B.; Ettre, L. S. Static Headspace-Gas Chromatography Theory and Practice; John Wiley & Sons: New York, 1997. (6) Drozd, J.; Novak, J. J. Chromatogr. 1977, 136, 37. (7) Lincoff, A. H.; Gossett, J. M. In Gas Transfer at Water Surfaces; Brutsaert, W.; Jirka, G. H., Eds.; Reidel: Dordrecht, Holland, 1984; p 17. (8) Gossett, J. M. Environ. Sci. Technol. 1987, 21, 202. (9) Ettre, L. S.; Welter, C.; Kolb, B. Chromatographia 1993, 35, 73. S0003-2700(98)00198-X CCC: $15.00 Published on Web 07/03/1998
© 1998 American Chemical Society
concentration can be achieved using HSGC by only measuring the vapor phase without conducting direct analysis of the liquid phase of the solution.6 Indirect HSGC methods have also been developed7-10 to determine the VLE partitioning coefficient, or Henry’s constant, of a solute without analyzing the liquid phase of the solution. Multiple headspace extraction (MHE) gas chromatography has attracted great attention in analytical and VLE studies to achieve measurement automation. The mathematical model of the MHE method was developed by McAuliffe11,12 and Suzuki et al.13 The method was further developed by Kolb and Ettre.14-17 The MHE procedure is very similar to dynamic gas extraction (or the purge and trap) but is carried out in steps. Therefore, the total peak area extrapolated from the sum of the peak areas measured from each extraction is proportional to the total mass of the analyte in the original sample. Based on solute mass conservation between the venting (step 1/2, the vapor volume expanded step after transferring some vapor into the sample loop for GC analysis through venting the headspace) and the new equilibrium step (step 2) and headspace vapor-liquid phase equilibrium, Kolb and Ettre17 conducted a detailed derivation and found that the ratio of the measured GC peak area of any two consecutive MHE measurements is a constant, Q′, and is a function of the VLE partitioning coefficient, K, the phase volume ratio, β, and the ratio of headspace pressure before and after venting, F, as shown below,
Q′ )
K/β + F K/β + 1
(1a)
K)
F - Q′ β Q′ - 1
(1b)
or
Later, they proposed5 to use eq 1b to measure solute VLE partitioning coefficient K. (10) Chai, X. S.; Zhu, J. Y. J. Chromatogr. A 1998, 799, 207. (11) McAuliffe, C. Chem. Technol. 1971, 46. (12) McAuliffe, C. U.S. Pat. 3,759,086, 1973. (13) Suzuki, M.; Tsuge, S.; Takeuchi, T. Anal. Chem. 1970, 42, 1705. (14) Kolb, B. Chromatographia 1982, 15, 587. (15) Ettre, L. S.; Jones, E.; Todd, B. S. Chromatogr. Newsl. 1984, 12, 1. (16) Kolb, B.; Pospisil, P.; Auer, M. Chromatographia 1984, 19, 113. (17) Kolb, B.; Ettre, L. S. Chromatographia 1991, 32, 505.
Analytical Chemistry, Vol. 70, No. 16, August 15, 1998 3481
However, Kolb and Ettre5,17 did not conduct actual measurements of VLE partitioning coefficient of solutes using their derivations, nor did they demonstrate the accuracy and measurement limits of their procedure. We found through both mathematical precision analysis and experimental verifications that it is not accurate to determine Henry’s constant (or K) using eq 1b because of the close-to-zero term, Q′ - 1, in the denominator. Furthermore, their procedure requires that one knows the ratio of headspace pressure before and after venting, F, that is not provided by some commercial headspace samplers, such as the one made by Hewlett-Packard (model HP 7694) used in this study, and may vary with the temperature and volume of the headspace. In this study, we developed an improved MHE GC method using the mass balance of the solute between the first step (step 1) and the last step (step n). We conducted the first experimental study on MHE methods (both the present and those of Kolb and Ettre5,17) for simultaneous measurements of the concentration and Henry’s constant using a commercial HSGC system. We found from mathematical error analysis that the precision of the present MHE method for Henry’s constant measurements is as much or more than 1 order of magnitude better than that of Kolb and Ettre.5 Methodology. For a given sample solution of volume VL with a solute mass of m0 introduced into a closed vial of volume VT, vapor-liquid phase equilibrium can be established within the vial with an equilibrium headspace pressure of Po. The equilibrium concentration of the solute in the vapor phase CG is proportional to the concentration in the liquid phase CL. For infinitely diluted solutions, the proportionality coefficient is the dimensionless Henry’s constant Hc of the solute, i.e.,
Hc ) CG/CL
(2)
where CG and CL are volumetric mass concentrations (i.e., mg/ L). Pressurization of the sample vial to a pressure of Ph using inert gas is a common practice in headspace measurements to create a pressure head for sampling. It is assumed that the pressurization time is very short so that the equilibrium remains unchanged. It should be pointed out that the solute volumetric concentration CG within the headspace is a constant before and after pressurization. After pressurization, the headspace vapor is vented out to fill the sample loop. The sample is then injected into the GC column to complete the first headpsace measurement. Further venting is often necessary to reduce the headspace pressure close to its initial equilibrium pressure Po. The headspace measurement disturbed the equilibrium in the vial. According to Kolb and Ettre,17 a new VLE can be reestablished within the vial and the VLE conditions are exactly repeated. A second headspace measurement is then conducted. This procedure can be repeated several times. We label each equilibrium state as 1, 2, ..., i, ..., n, correspondingly, in the following derivation. The initial mass of the solute m1 (or the solute mass at the first equilibrium state) in the sample vial can be expressed as
m1 ) CG1VG + CL1VL
mEX,solute ) φCGVG
(4)
where φ is called the sample volumetric flow fraction. Therefore, the total mass of the solute within the vial after the first headspace extraction can be written as m2,
m2 ) (CG2VG + CL2VL) ) m1 - φ1CG1VG
(5)
We can express the mass of vapor mixture within the headspace after each extraction as follows,
m3 ) (CG3VG + CL3VL) ) m2 - φ2CG2VG ) m1 - VG(φ1CG1 + φ2CG2) (6a) l mn ) (CGnVG + CLnVL) ) m1 - VG(φ1CG1 + φ2CG2 + ... + n-1
φn-1CG(n-1)) ) m1 - VG
∑φ C
i Gi
(6b)
1
We neglected the change of solute volume VL due to heating and headspace extraction in the above derivation. Furthermore, we assume that the headspace operating conditions remained unchanged for each headspace extraction, which is valid according to Kolb and Ettre.5,17 Therefore, the sample volumetric flow fractions are a constant; i.e., φ1 ) φ2 ) ... ) φi ) ... ) φn-1 ) φ, though the absolute solute mass extracted out is reduced due to the reduced solute concentrations of the liquid and vapor phases within the vial. For infinitely diluted solutions,
Hc )
CG1 CG2 CG3 CGn ) ) ) ... ) CL1 CL2 CL3 CLn
(7)
Substituting eq 7 into eq 6b, we have
(
CGn VG +
VL
)
Hc
n-1
) m1 - φVG
∑C
Gi
(8)
1
where the solute concentration in the headspace CG is proportional to the measured GC peak area A, i.e., A ) fCG. We can then express eq 8 as a first-order linear equation, n-1
∑A ) a + bA i
n
(9)
1
(3)
where VG and VL are the volumes of vapor and liquid phases in the vial, respectively. 3482 Analytical Chemistry, Vol. 70, No. 16, August 15, 1998
The amount of solute vapor extracted out of the headspace of the sample vial can be expressed as a certain fraction of the solute vapor in the headspace before venting, i.e.,
with
a)
fm1 φVG
(10a)
and
b)-
(
)
(
)
1 1 VL 1 1 1+ )- 1+ φ Hc VG φ βHc
(10b)
where β ) VG/VL is the phase ratio according to Kolb and Ettre.17 We can obtain ∑n-1 Ai and An through MHE GC measurements. 1 We then conduct a linear regression analysis to obtain the intercept a and the slope b of eq 9. The concentration and the Henry’s constant of the solute can be calculated from a and b using eqs 10a and 10b, i.e.,
C0 )
m1 aφ VG aφ ) ) β VL f VL f
(11)
or simply as Kolb and Ettre,5 n
∑A ) f
C0 ) fMHE
i
MHE[a
+ (b + 1)An]
(12)
1
and
Hc ) -
1 1 ) -(1 + φb)β (13) or K ) Hc (1 + φb)β
where f and φ are two unknown constants and can be calibrated. We would like to point out that the present derivation did not assume that each headspace extraction is an identical isothermal expansion and the vapor mixture in the headspace follows ideal gas law that is required to yield eq 1 in the derivation of Kolb and Ettre.5,17 Therefore, the present MHE method to measure Henry’s constant is more universal from both theoretical and practical points of view. Furthermore, with the assumption of isothermal expansion headspace extraction and ideal gas law, the sample volumetric flow fraction φ in eq 13 can be related to the pressure ratio F used by Kolb and Ettre5,17 in eq 1. The amount of solute vapor extracted out of the headspace is simply the product of the total vapor mixture extracted out of the headspace, mEX ) VG(Ph - Po)/(RT) (from ideal gas law) and the solute mass fraction CG/FPh in the headspace before venting (FPh is the headspace mixture gas density before venting), i.e.,
mEX,solute ) mEXCG/F ) CGVG(Ph - P)/Ph ) CGVG(1 - Po/Ph) (14)
Substituting eq 4 into eq 14, we have
φ ) 1 - Po/Ph ) 1 - F or F ) 1 - φ
The MHE method of Kolb and can be expressed as
K)
Ettre5
(15)
as presented in eq 1b
(1 - φ - Q′) 1 F - Q′ β) β ) Hc Q′ - 1 Q′ - 1
(16)
Therefore, both the present MHE method (eq 13) and that of Kolb and Ettre5 (eq 16) can determine VLE partitioning coefficient K or Hc with or without calibration depending on whether the headspace pressure ratio F is known or not. Neither method is better than the other from an application point of view. However, without the assumptions of ideal gas law and isothermal headspace venting, eq 13 is still valid, but eq 16 is not. EXPERIMENTAL SECTION Chemicals. Methanol, ethanol, and 2-propanol of analytical grade were used as solutes, and deionized water was used as solvent to prepare methanol-, ethanol-, and 2-propanol-water solutions. The methanol-water solution was used as the standard solution for calibration to obtain f and φ with a known methanol concentration of 800 mg/L and Henry’s constant at a temperature range of 25-80 °C according to the literature19-23 and our previous study.10 Apparatus and Operation. All measurements were carried out using an HP-7694 automatic headspace sampler and an HP6890 capillary gas chromatograph (Hewlett-Packard, Palo Alto, CA) equipped with an HP ChemStation for data acquisition and analysis. The basic operating principles and procedures of the headspace sampler for multiple headspace extraction are very similar to that described by Kolb and Ettre,17 except that the venting process was combined with the sample-transfer process in the present headspace sampler. More specifically, the sample loop is open to the atmosphere during sample transfer. The duration of the sample-transfer process (sample loop fill time) controls the pressure inside the sample vial. Headspace operating conditions: compressed air used for vial pressurization; pressurization time of the headspace sampler, 0.2 min; sample loop fill time, 1.0 min; loop equilibration time, 0.05 min. GC conditions: HP-5 capillary column at 30 °C; carrier gas helium flow (He), 3.8 mL/min. A flame ionization detector (FID) was employed with hydrogen and air flow rates of 35 and 400 mL/ min, respectively. The measurement procedure was as follows: 50 µL of sample solution is pipetted into a 20-mL vial, which gives a phase ratio β ) 399. The sample size (or β) can be varied as necessary. The headspace sampler then heats the sample in the vial to a desired temperature with strong shaking for 3 min to achieve vaporliquid equilibrium within the vial. At equilibrium, the vial is pressurized by compressed air, and the headspace is partially withdrawn to fill the sample loop and vent to the atmosphere to reduce the vial pressure to close to its initial vial pressure. The sample is injected into the GC column for analysis. The GC signal as peak area A is recorded. This procedure is repeated 10 times automatically for multiple headspace extraction analysis and can be programmed by the HP ChemStation. Method Calibration. Most commercial headspace systems control the headspace pressure Ph by the pressurization time. Therefore, the pressure ratio F, or the sample volumetric flow (18) Kolb, B.; Welter, C.; Bichler, C. Chromatographia 1992, 34, 235. (19) Hofstee, M. T.; Kwantes, A.; Rijnders, C. W. A. Symp. Dist. Brighton 1960, 105. (20) Pividal, K. A.; Birtigh, A.; Sandler, S. I. J. Chem. Eng. Data 1992, 37, 484. (21) Dallas, A. J. Ph.D. Dissertation, University of Minnesota, Minneapolis, MN, 1993. (22) Kooner, Z. S.; Phutela, R. C.; Fenby, D. V. Aust. J. Chem. 1980, 33, 9. (23) Lebert, A.; Richon, D. J. J. Agric. Food Chem. 1984, 32, 1156.
Analytical Chemistry, Vol. 70, No. 16, August 15, 1998
3483
Table 1. List of Calibration Experimental Results of φ and f at Several Temperatures Using a Methanol-Water Solution of Concentration 800 mg/L temp (°C)
Henry’s constant Hc (lit.)
b (regression obtained)
0.00044 -23.12 ( 0.41 0.00071 -14.92 ( 0.12 0.00112 -9.83 ( 0.13 0.00170 -6.61 ( 0.12 0.00260 -4.55 ( 0.06
40 50 60 70 80
RSTDa n/a a
1.4%
a φ (regression f (calibrated) obtained) (calibrated) 0.271 0.286 0.313 0.354 0.416 n/a
3205 ( 36 2815 ( 14 2496 ( 15 1849 ( 18 1352 ( 10
468 433 420 353 303
0.8%
n/a
Relative standard deviation. b n/a, not applicable.
fraction φ, varies with the headspace temperature and the headspace volume VG (or phase ratio β). We calibrated φ as a function of temperature at β ) 399 (used in the present study) by conducting multiple headspace extraction measurements in a methanol-water solution of concentration 800 mg/L at headspace temperatures of 40, 50, 60, 70, and 80 °C. At a given temperature, we conducted 10 headspace extraction GC measurements of the methanol-water sample. We then carried out a linear regression analysis of the 10 GC peak areas Ai measured at each temperature according to eq 9 to obtain the slope b and the intercept a. Table 1 lists the calibration results. The Henry’s constants of methanol listed in the table are from the literature19-23 and our previous study.10 We calibrated φ at each given temperature using eq 13 with the literature-given Henry’s constant and the regressionobtained slope b as listed in Table 1. We also calibrated constant f at each temperature as listed in Table 1 using the given methanol concentration of 800 mg/L, the regression-obtained intercept a, and the calibrated φ through eq 11 from the same set of measured GC peak areas. We then conducted a linear regression analysis to correlate φ with temperature T (in °C),
φ(β)399) ) 0.3777 - 0.00574T + 7.7614 × 10-5T 2 (17) The above equation of φ is valid for any solute-solution systems as long as the HSGC operating conditions remain the same and the phase ratio β ) 399. If the headspace volume VG or the phase ratio β changes, φ will change. Assuming that headspace operating conditions (temperature and the pressurization pressure; therefore, the total volumetric flow into the headspace) remain the same, we have
φ(βcal)VG(βcal) ) φ(β)VG(β)
(18)
Since VG ) VTβ/(β + 1), we can obtain the following equation to correct the effect of β on the sample volumetric flow fraction φ.
φ(β) )
βcal β + 1 399 β + 1 φ(βcal) ) φ(β ) 399) (19) βcal + 1 β 400 β
RESULTS AND DISCUSSION Precision Analysis. We conducted a mathematical precision analysis of the present MHE GC method for simultaneous 3484 Analytical Chemistry, Vol. 70, No. 16, August 15, 1998
Figure 1. Calculated effect of phase ratio on the measurement uncertainty of solute concentration and Henry’s constants using the present multiple headspace extraction method.
determination of the concentration and the Henry’s constant of a solute by eqs 12 and 13 using the following variance estimation equations, respectively:
σ2(C0) )
( )
( )
( ) ( ) ( ) ( )
∂C0 2 2 ∂C0 2 2 ∂C0 2 2 σ (a) + σ (f) + σ (φ) + ∂a ∂f ∂φ ∂C0 2 2 σ (β) (20) ∂β
σ2(Hc) )
( )
∂Hc 2 2 ∂Hc 2 2 ∂Hc 2 2 σ (b) + σ (φ) + σ (β) (21) ∂b ∂φ ∂β
where the variances σ2(f) ) 2.0%f 2, σ2(φ) ) 2.0%φ2, σ2(a) ) 2.0%a2, and σ2(b) ) 2.0%b2 are determined based on experimentally measured relative standard deviations of f(1.3%), φ(1.8%), a(1.0%), and b(1.7%), respectively, during calibration. The variance of phase ratio σ2(β) ) 2.0 × 10-4β2 is calculated from the variances of the phase volumes σ2(VG) and σ2(VL) similar to eq 20 or 21, with σ2(VG) ) 1.0%VG2 and σ2(VL) ) 1.0%VL2 based on experiments. From mathematical calculations using eqs 20 and 21, we found that the phase ratio β is a key parameter that controls the accuracy of the present MHE method. The results indicate that a β value of greater than 2 is required to obtain good measurements of solute concentration with uncertainties less than 10% as shown in Figure 1. We used eq 19 to account for the effect of β on the volumetric flow fraction φ in calculating the effect of φ on the measurement uncertainty of the solute Henry’s constant. We found that the measurement uncertainty is also affected by the solute Henry’s constant itself as shown in Figure 1. Figure 1 also indicates that there is an optimum β at which the uncertainty is minimum for a given solute-solvent system or a given solute Henry’s constant. The minimum uncertainty also varies with the Henry’s constant from less than 0.8% at Hc ) 0.001 to 10% at Hc ) 1.0. Furthermore, the optimum phase ratio, βopt, correlates very well with the Henry’s constant to the following relationship as shown in Figure 2,
HcβOpt ) 1.0
(22)
Figure 3. Typical correlation between the gas chromatographic signals (peak areas) and the headspace extraction number in multiple headspace measurements. Figure 2. Comparison of the measurement uncertainties of Henry’s constants at the optimum phase ratios between the present MHE method and that of Kolb and Ettre.5
This relationship agrees with the recommendation of Ioffe and Vitenberg24 in designing MHE experiments. As noticed by Kolb and Ettre,5 this recommendation (eq 22) to chose β is difficult to follow, in particular, in measuring a very small Henry’s constant. Moreover, as shown in Figure 1, the slopes or the derivatives of the uncertainty curve with respect to β are very high in the vicinity of βopt, indicating the difficulties to achieve good precision in experiments because βopt cannot be determined using eq 22 before the Henry’s constant is being measured. Fortunately, Figure 1 shows that the uncertainties will be less than 10% as long as β < 2βopt such as β ≈ 4 can give good measurements of solute Henry’s constant in a wide range (Hc < 1.0, or K > 1.0) using the present MHE method. The present method however is not suitable to measure a solute Henry’s constant of >1.0. The analysis also indicates that increasing the volume of the sample vial VT does not affect the above uncertainty characteristics but shifts the optimum phase ratio β to a greater value. For comparison purposes, we conducted a precision analysis of the MHE method by Kolb and Ettre5 (eq 16) using a similar variance estimation equation,
σ2(K) )
∂K ∂K σ (φ) + ( ) σ (β) (∂Q′ ) σ (Q′) + (∂K ∂φ) ∂β 2 2
2 2
2 2
(23)
We used same variances of φ and β for the analysis of the present MHE method and variance of the ratio of the GC peak areas, σ2(Q′) ) 1.25 × 10-3(Q′)2, by assuming σ2(A1) ) σ2(A2) ) ... ) σ2(Ai) ) ... σ2(An) ) 2.5%A based on the experimentally determined relative standard deviation of A(2.3%). The analysis indicates that the first term in eq 23 is the major contributor to the method uncertainty. Figure 2 plots the optimum phase ratio βopt and the measurement uncertainties at βopt for measuring Henry’s constant in a range of 0.001-100 using the present and the Kolb and Ettre5 MHE GC method. The results show that the βopt for both of these methods correlates with Henry’s constant well to eq 22. Figure 2 clearly indicates that the minimum uncertainties of eq 16 are about 20-30%. The precision of the present MHE method is as much or more than 1 order of (24) Ioffe, B. V.; Vitenberg, A. G. Chromatographia 1978, 11, 282.
magnitude better than that of the method by Kolb and Ettre5 for Hc < 0.2, a significant progress in the development of MHE GC method for VLE studies. From a mathematical point of view, the poor precision of the Kolb and Ettre5 method is caused by the close-to-zero term, Q′ - 1, in the denominator in eq 1b or 16 that amplifies a small measurement error in the peak areas A or the peak area ratio Q′ to a large error in K or Hc, the fundamental problem of the method. More specifically, the amplification for σ2(Q′) is (∂K/∂Q′)2 ) [(F - 1)β]2/(Q′ - 1)4, which is inversely proportional to the fourth power of (Q′ - 1). For a typical value of Q′ ) 0.85, 1/(Q′ - 1)4 is about 2000. Physically, eq 16 did not take full advantage of multiple headspace extraction techniques; it only uses two headspace extraction measurements. Method Validation. Repeatability Test of Multiple Headspace Extraction. According to the derivation by Kolb and Ettre,17 the logarithmic peak area obtained from the ith headspace extraction Log(Ai) should be linearly proportional to (i - 1) or simply i if the VLE conditions for each headspace extraction can be exactly repeated in MHE measurements. We plotted the GC signal of peak area Ai of methanol measured in a methanol-water solution of concentration 800 mg/L at 60 °C. We obtained a near perfect linear correlation with a correlation coefficient of 0.9987 between the Logarithmic peak area Ai and the extraction number i as shown in Figure 3, indicating the validity of the basic assumption that the VLE conditions were exactly repeated for each headspace measurement in this study. We then carried out a linear regression analysis according to eq 9 to test the validity of our derivation and the accuracy of the experiment. Again, we obtained a near perfect regression as shown in Figure 4 with a correlation coefficient of 0.9997, and the relative fitting errors of the slope and the intercept are 0.9 and 1.5%, respectively. With such a good regression, we are confident that the concentration and the Henry’s constant derived from the intercept a and the slope b of the regression analysis, respectively, will be accurate. It should be pointed out that a minimum of three extractions is required to use the present MHE method through eq 9. Solute Concentration Measurement. The basic principle of the present MHE method (eq 11) is not much different from that of Kolb and Ettre5,17 (eq 12) in measuring solute concentration; therefore, we expect that the measurement accuracy will be the same. We conducted nine replica measurements of a methanolwater solution of 800 mg/L using the present method. The average measured concentration was 797 mg/L. The standard Analytical Chemistry, Vol. 70, No. 16, August 15, 1998
3485
Figure 4. Typical linear correlation between the sum of the gas chromatographic signals (peak areas) of the first (n - 1)th headspace measurements and the signal of the nth measurement. Table 2. Comparisons of Measured Methanol Concentrations in Several Environmental Samples from a Kraft Pulp Mill between the Present MHE Method and an Indirect Headspace Gas Chromatographic Method methanol concentration (mg/L) sample no.
previous method6,25
present MHE method
rel diff (%)
1 2 3 4 5 6 7 8 9
53 94 183 311 402 613 678 775 969
52 91 183 331 390 605 700 808 992
-1.9 -3.2 0.0 6.4 -2.3 -1.0 3.2 4.3 2.4
deviation was 2.7%, within our precision prediction limit as shown in Figure 1. To further validate the present method, we conducted comparison measurements of methanol concentrations in nine environmental samples collected from a kraft pulp mill using both the present MHE method and an indirect HSGC method.6,25 For methanol concentrations ranging from 50 to 1000 mg/L, the relative differences in measured methanol concentrations using these two methods are within (4.5% as listed in Table 2 except one sample for an unknown reason. The 4.5% difference is within the measurement uncertainties of these two methods obtained from several replica measurements. These measurements demonstrate the validity of the present method for solute concentration measurements in any solution. Henry’s Constant Measurement. We measured the Henry’s constants of 2-propanol and ethanol in water solutions at a temperature range of 40-80 °C using the present MHE GC method (eq 13). We compared our measurements to those obtained by Kolb et al.18 using a direct headspace GC method. Linear regression shows that the Logarithm of the Henry’s constants fits very well to the inverse of the temperature in kelvin as shown in Figure 5. Correlation coefficients are 0.9999 and 0.9984 as obtained from the fitting of the 2-propanol and ethanol data both reported by Kolb et al.18 and measured by the present MHE method. The relative errors of the slopes and the intercepts (25) Chai, X. S.; Dhasmana, B.; Zhu, J. Y. J. Pulp Pap. Sci. 1998, 24 (2), 50.
3486 Analytical Chemistry, Vol. 70, No. 16, August 15, 1998
Figure 5. Comparisons of measured Henry’s constants of 2-propanol and ethanol in water solutions with literature data, respectively, at various temperatures. Table 3. Sample Calculations of Henry’s Constants of 2-Propanol and Ethanol in Water Solutions at 60 °C Using the MHE Method of Kolb and Ettre5 with the Raw Data Measured in This Study 2-propanol headspace ext no. 1 2 3 4 5 6 7 8 9 10 mean RSTD a
peak area Ai
Q′ ) Ai/Ai-1
593.2 546.7 464.2 398.7 319.8 263.7 218.8 178.6 146.8 118.9 n/a n/a
ethanol
Hca
peak area Ai
Q′ ) Ai/Ai-1
Hca
0.9216 0.8491 0.8589 0.8021 0.8246 0.8297 0.8163 0.8219 0.8099
0.000 84 0.002 33 0.002 06 0.004 31 0.003 20 0.002 99 0.003 56 0.003 31 0.003 87
396.5 352.3 328.6 288.4 253.8 222.0 193.3 169.4 147.6 127.9
0.8885 0.9327 0.8777 0.8800 0.8747 0.8707 0.8764 0.8713 0.8665
0.001 39 0.000 69 0.001 61 0.001 56 0.001 67 0.001 76 0.001 64 0.001 75 0.001 86
0.8371 0.043
0.002 94 0.359
n/a n/a
0.8820 0.023
0.001 55 0.227
Calculated from eq 16. b n/a, not applicable.
are 1.2 and 1.9% and 6.2 and 4.0% for the 2-propanol and ethanol linear lines, respectively. The linear relationship obtained agrees with the van’t Hoff equation26 in basic thermodynamic theory for solute; i.e., the Henry’s constant is proportional to the partial molar excess enthalpy, a function of temperature. Because Kolb et al.18 did not provide the standard deviations of their measurements, we compared our data with the fitted equations to both sets of data as shown in Figure 5. We found that the residual sums of squares of the fits are 1.1 × 10-4 and 1.37 × 10-3 for 2-propanol and ethanol, respectively. We also plotted (10% relative error bars of our data based on our replica measurements and uncertainty predictions for Hc ) 0.001-0.01 as shown in Figure 1, most of the data points fall onto the two fitted lines within the (10% error bars. We calculated the Henry’s constants of 2-propanol and ethanol at the temperature range stated above with present experimental data using eq 16 to experimentally verify the measurement uncertainty of the MHE method by Kolb and Ettre.5 The pressure (26) Snoeynik, V. L.; Jenkins, D. Water Chemistry; Wiley: New York, 1980; p 463.
ratio is calculated using eq 15; i.e., F ) (1 - φ) with φ ) 0.313 calculated from eq 17. The peak area ratios Q′ are calculated from the measured peak areas. Table 3 lists two sample calculations of Henry’s constants of 2-propanol and ethanol in water solutions at 60 °C. It was found that the relative standard deviations of Q′ in the two experiments are only about 4.3 and 2.3% (close to those used in precision analysis), respectively. However, the relative standard deviations in measured Henry’s constants are 36 and 23% for 2-propanol and ethanol, respectively, which agree with our mathematical predictions as shown in Figure 1. This is an indication of the poor precision of the MHE method by Kolb and Ettre5 due to the error amplification effect of the (Q′ - 1) term in eq 16 as discussed previously.
method is very accurate for measurements of solute concentrations and Henry’s constants in a wide range of β. The precision of the present MHE method for measuring Henry’s constant is as much or more than 1 order of magnitude better than the MHE method developed by Kolb and Ettre.5 The methanol concentrations measured by the present method in several samples from a kraft pulp mill are in good agreement with those measured by an indirect HSGC method. The measured Henry’s constants of 2-propanol and ethanol in water solutions are in excellent agreement with those in the literature. The present method is very simple, efficient, and fully automated. It can be easily applied to any environmental and industrial samples with complicated matrixes.
CONCLUSION We developed a multiple headspace extraction technique for simultaneous measurements of concentrations and Henry’s constants of solutes in infinitely diluted solutions. We successfully conducted the first experimental work on determining Henry’s constants using MHE GC techniques. Mathematical precision analysis of the method indicates that the phase ratio β is a key factor that dictates the accuracy of the method and the present
ACKNOWLEDGMENT This research was supported by the U.S. Department of Energy (Grant DE-FC07-96ID13438).
Received for review February 23, 1998. Accepted May 29, 1998. AC980198U
Analytical Chemistry, Vol. 70, No. 16, August 15, 1998
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