WHAT HAPPENS WHEN GASEOUS SO2 IS DISSOLVED IN WATER, THEN PLACED IN A VESSEL AND SEALED?

Sample Preparation Techniques



167



SO

0

µ 0 2 + RT ln p SO2 = µ aq,SO2 + RT ln aaq 2

HS,SO



We seek to express the ratio of activity to partial pressure so as to be consistent

with a subsequent definition of the partition coefficient. Upon rearranging, we obtain

the following relationship:

 aaq ,SO2 

0

0

RT ln 

 = − µ aq,SO2 − µ HS,SO2

 pHS,SO2 



(



)



Upon further rearranging and proceeding to define the Henry’s law constant, we

obtain

aaq ,SO3

0

SO

= e − ∆µ / RT ≡ K H 2

pHS,SO2



(3.23)



Secondary equilibrium effects are handled by defining the degree of ionization

by α, as done previously [refer to Equations (3.17) and (3.18)], and expressing the

activity of neutral SO2 in terms of α and the total activity, aT, according to

aSO2 = aT (1 − α)

For example, if 0.7643 mol SO2 is dissolved in 1 kg of water in a closed system, a

0.7643 M solution results, and with α = 0.1535, the vapor pressure exerted by SO2

is such that KH is 0.813. When 1.273 g of SO2 is dissolved in the same weight of

water, with α this time being 0.1204, the vapor pressure exerted is such that KH is

again 0.813.40



28. ON WHAT BASIS CAN WE QUANTITATE TCE

IN GROUNDWATER BY HS–GC?

Consider how the priority pollutant VOC trichloroethylene or trichloroethene, abbreviated TCE, is distributed between a sample of groundwater and the headspace in

a sealed HS vial, as shown schematically by



TCE(g)



TCE(aq)



© 2006 by Taylor & Francis Group, LLC



Amt TCE

(HS) in

V(HS)



Amt TCE (S)

in V(S)



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Let us assume that the temperature is fixed such as would be found in a thermostated automated S analyzer. A consideration of mass balance requires that the

original amount of TCE be found in either the headspace or the aqueous sample.

Mathematically stated,

TCE

TCE

TCE

amt o = ams S + amt HS



(3.24)



Using principles encompassed by Equation (3.23), we can proceed to define the

partition coefficient as

K TCE ≡



CS

C HS



(3.25)



It is helpful at this point to define the abbreviations used to develop the equations

that lead to Equation (3.26), derived below. Consider the following definitions:

o = original concentration of TCE in the groundwater sample

S = sample

HS = headspace

amt = amount of TCE

VS = volume of sample placed in the HS vial

VHS = volume of headspace in the HS vial after VS mL have been placed in

the HS vial

C = concentration

β = phase ratio for an HS vial, equals VHS/VS

We can proceed from both the mass balance principle and the definition of KTCE.

Let us divide Equation (3.24) by VS:

amt o amt S amt HS

=

+

VS

VS

VS

C0 = CS +



VHSCHS

VS



TCE

= K H CHS +



VHS

CHS

VS



 TCE V 

= CHS  K H + HS 

VS 



 TCE V 

= CHS  K H + HS 

VS 



© 2006 by Taylor & Francis Group, LLC



(3.26)



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169



Solving Equation (3.26) for CHS gives a useful relationship:





1

TCE

CHS = Co  TCE



 KH + β 



(3.27)



Equation (3.27) suggests that for a given concentration of TCE in the original

sample of groundwater, the concentration of TCE expected to be found in the

TCE

HS, C HS , depends not only on Co, but also on two factors: KTCE, which is due to

the physico-chemical nature of this particular VOC, and β, which is due to the

volumes occupied by HS and sample. β might be thought of in terms of the physical

characteristics of the HS vial. In practice, however, KTCE may exhibit some dependence on temperature and sample ionic strength, whereas the range of values that

β can take on is limited. As we shall see, both factors play off of one another in the

consideration of analyte sensitivity in HS techniques.

Equation (3.27) is the basis for TEQA, because for a given VOC and fixed

VOC

VOC

sample volume in a headspace vial (i.e., K HS and β), C HS is directly proportional

to the original concentration of VOC in the aqueous sample, Co. The volume of

headspace sampled and injected into a GC is usally held fixed so that the area under

the curve of a chromatographically resolved GC peak, AVOC is directly proportional

VOC

to CHS . As discussed in Chapter 2, Equations (2.1) and (2.2), with respect to the

external mode of instrument calibration, the sensitivity of the HS-GC technique is

HS

related to the magnitude of the response factor, RF , according to

HS

RF =



VOC

AHS

VOC

C HS



TCE

A fixed aliquot of the HS whose concentration of TCE, C HS , is injected into a

GC that incorporates a halogen-specific detector, such as an electrolytic conductivity

detector (ElCD) (refer to EPA Methods 601 and 602, even though these methods

employ P&T techniques). Alternatively, this aliquot can be injected into a gas

chromatograph-mass spectrometer (GC-MS). The mass spectrometer might be operated in the selective ion monitoring (SIM) mode. The most abundant fragment ions

of TCE would then be detected only (refer to EPA Method 624, even though this

method employs P&T techniques). Determinative techniques such as GC-ElCD and

GC-MS are introduced in Chapter 4. Nevertheless, it should be apparent to the reader

at this point that the partition coefficient plays an important role in achieving a high

sensitivity in HS techniques. We digress from here to discuss this a bit more.



29. ON WHAT BASIS DOES KTCE DEPEND?

Let us approach an equivalent to Equation (3.25) from the perspective of applying

the three great laws of phase equilibrium found in most physical chemistry texts:

Dalton’s law of partial pressures, Raoult’s law of ideal solutions, and Henry’s law

© 2006 by Taylor & Francis Group, LLC



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for dissolved gases.41 Applying Dalton’s law enables one to state that the concentration of analyte in the HS is proportional to its partial pressure. The partial pressure

exerted by TCE in the HS is independent of all other gases in the HS mixture and

is related to the total pressure in the HS as follows:

piHS = pT XiHS

This partial pressure exerted by component i is, in turn, related to the vapor

pressure exerted as if i were pure, pio , and the mole fraction of component i dissolved

in the sample, X IS , according to Raoult’s law. An activity coefficient γi is included

to account for nonideality so that

piHS = pio γ i XiS

Also, the partial pressure exerted by component i can be related to the mole

fraction of i dissolved in the sample, S, according to Henry’s law, as follows:

piHS = K H XiS

The partial pressure of component i in the HS can be eliminated so that

pT XiHS = pio γ i XiS

Rearranging the equation to a ratio of mode fractions yields

XiS

p

C iS

= oT ≈ HS = K

HS

Xi

pi γ i C i

This equation yields an alternative relationship for the partition constant in HS,

in which K is found to be inversely proportional to a product of the partial pressure

of component i, if it is pure, and its activity coefficient γi according to

K∝



1

pγ



o

i i



(3.28)



Because Equation (3.25) relates K to a ratio of concentrations, combining Equations (3.25) and (3.28) leads to the following:

CiS

1

∝ o

HS

Ci

pi γ i

© 2006 by Taylor & Francis Group, LLC



(3.29)



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171



o

pTCE refers to the intrinsic volatility exhibited by a chemically pure substance TCE.

TCE is a liquid at room temperature, and if one opens a bottle that contains the pure

liquid, one is immediately struck by virtue of the sense of smell with the concept

o

o

of the vapor pressure of TCE. It is likely that PTCE is greater than PPCE , where PCE

refers to perchlorethylene (tetrachloroethene). PCE is also on the EPA’s priority

HS

pollutant list. One would expect to find that C TCE is greater than CHSPCE, assuming

all other factors equal. This is largely due to the inverse relationship between K and

po, as shown in Equation (3.28). This equation also suggests that if a matrix effect

exists, K is also influenced by differences in the activity coefficient, γ. Changes in

γ might be due to changes in the ionic strength due to the sample matrix and, in

turn, influence K, as shown in Equation (3.28).



30. MUST WE ALWAYS HEAT A SAMPLE IN HS-GC

TO CONDUCT TEQA?

Equations (3.27) to (3.29) lay the foundation for a theoretical understanding of what

factors are involved in obtaining a sufficiently large value for the concentration of

VOC

any VOC in the HS (i.e., C HS ). In this section, we look at the effect of increasing

temperature of a headspace vial that contains priority pollutant VOC dissolved in

water. An example of this might be a sample of groundwater that has been contaminated with priority pollutant VOCs. The static equilibrium HS technique just

described would be used to satisfy the criteria for TEQA.

The Clausius–Clapeyron equation, one of the most famous in physical chemistry,

is most applicable for this discussion. The equation states that the partial differential

with respect to absolute temperature of the logarithm of a pure liquid’s vapor pressure

is inversely related to the liquid’s absolute temperature. We again consider the liquid

TCE and state the Clausius–Clapeyron equation mathematically:42

∆H v

∂

(ln p o ) =

∂T

RT 2

Upon rearranging and expressing this relationship with respect to the VOC that

we are considering, TCE, we obtain



o

ln pTCE =



∆H vTCE

R



∫T



dT

2



The indefinite integral is then evaluated as



−



∆H vTCE

+C

RT



The vapor pressure exerted by pure TCE can then be expressed as

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Trace Environmental Quantitative Analysis, Second Edition



P0



Patm



Tbp

T



FIGURE 3.8 Plot of the vapor pressure of a liquid vs. the liquid’s temperature.



o

TCE



p



=e



  ∆H TCE  

v

 −

 +C 

  RT  

 

 



(3.30)



where ∆H vTCE is the molar heat of vaporization for pure TCE and R is the ideal gas

constant. Equation (3.30) suggests that a pure liquid’s vapor pressure increases

exponentially as the temperature of the liquid is increased, until its vapor pressure

reaches that exerted by the atmosphere. A plot of Equation (3.30) is shown in

Figure 3.8 for three different liquids. For example, if three ClVOCs are plotted, such

as for chloroform, TCE, and PCE, their respective vapor pressure/temperature curves

would resemble the three shown in Figure 3.8. Because the partition coefficient and

the partial pressure of a pure liquid such as TCE are inversely related according to

Equation (3.28), we can relate K and T in the following manner:

TCE

ln K HS =



A

−B

T



(3.31)



where A and B are constants related to TCE. Thus, an increase in T serves to

TCE

decrease K HS and, according to Equation (3.29), partitions a greater percent of more

© 2006 by Taylor & Francis Group, LLC



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173



TCE molecules into the HS vs. the condensed phase. In other words, the

TCE

TCE

ratio CS /CHS is seen to decrease.



31. IS THERE AN EXAMPLE THAT ILLUSTRATES

THE CONCEPT IN EQUATION (3.31)?

One application of these principles is evident in the hypothetical preparation of a

mixture of C5 through C20 alkanes; each alkane is then placed in an HS vial in equal

amounts. Prior to sealing the vial, a 10-µL aliquot of the liquid is taken and injected

into a gas chromatograph with a carbon-selective detector. A chromatogram is

generated that shows a separate peak for each of the 16 alkanes. The HS vial is then

sealed with a crimped-top cap and septum. The vial is placed inside a cylindrical

heater block whose temperature has previously been set to 80°C. A 1.0-cc gas-tight

syringe is used to withdraw an aliquot of the headspace, which is directly injected

into the same GC. A chromatogram is generated that shows a distribution of the 16

peaks that is different from the first. The lower-carbon-number or lower-molecularweight alkanes seem to have been enriched in the HS, compared to the direct liquid

injection. These results are readily explained by considering Equation (3.26) and

the subsequent reexpression of Equation (3.30) in terms of the HS partition coefficient [i.e., Equation (3.31)].

VOC

32. WHAT HAPPENS WHEN KHS VALUES VARY

SIGNIFICANTLY?

VOC

Kolb and Ettre43 recently discussed their work on determining values for K HS and

report some interesting findings. They observed that over a range of some 15 VOCs

that vary in polarity from dioxane to lower-molecular-weight alcohols, through to

ketones, and then to acetate type esters, monoaromatics, and polychlorinated ethenes,

VOC

and finally to C6 alkanes that K HS values vary by over four orders of magnitude.43

VOC

Those VOCs that exhibit low K HS values (i.e., favor a high concentration in the

VOC

HS) (CHS is high at equilibrium) are not influenced by an increase in temperature.

VOC

Those VOCs that exhibit high K HS (i.e., favor a low concentration in the HS)

VOC

(CHS is low at equilibrium) are strongly influenced by an increase in temperature.

Kolb and Ettre chose five solutes as representative of the large number of VOCs that

have a wide range of partition coefficients. These are listed below, along with their

partition coefficients:



VOC



Solute

Ethanol

Methyl ethyl ketone

Toluene

Tetrachloroethylene

n-Hexane



© 2006 by Taylor & Francis Group, LLC



KHS



at 40°C



1355

139.5 at 45°C

2.82

1.48

0.14



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Trace Environmental Quantitative Analysis, Second Edition



As the temperature is increased from 40 to 80°C while β is held fixed at 3.46,

the partition coefficient for ethanol is observed to increase to the greatest degree,

whereas that for methyl ethyl ketone is also increased, but to a lesser degree. Partition

coefficients for toluene, tetrachloroethylene, and n-hexane do not increase to any

extent as the temperature is increased from 40 to 80°C.

This phenomenon is explained by these authors in the following manner. VOCs

whose partition coefficients are already low are enriched in the HS at the lower

temperature, 40°C, and the percent of remaining dissolved VOCs in the condensed

phase that partition into the HS as the temperature is raised to 80°C is not appreciable.

Polar solutes, on the other hand, are predominantly dissolved in the condensed phase

at 40°C, and the percent that partition into the HS as the temperature is raised to

80°C is much more appreciable.

Let us return to Equation (3.27) and briefly consider the second factor, the phase

ratio β, in the headspace sampling of groundwater to determine trace concentrations

of VOCs in the environment. Kolb and Ettre have studied the influence of β on HS

sensitivity. For a fixed temperature and fixed original concentration of VOC in the

aqueous phase, Co, the influence of changing β from, for example, 4.00 (only 20%

of the total volume of the HS vial contains the sample), to β = 0.250 (80% of the

VOC

total volume of the HS vial contains the sample) depends on the magnitude of K HS .

For nonpolar aliphatic hydrocarbons like n-hexane or for chlorinated C1 or C2

aliphatics such as TCE, a change in β from 4.00 to 0.250 increases the HS sensitivity

by almost a factor of 10. For monoaromatics, the same change in β gives an increase

in HS sensitivity of about 4. For acetate type esters, ketones, lower-molecular-weight

alcohols, and ethers, a change in β from 4.00 to 0.250 gives an insignificant increase

in HS sensitivity.43

The influence of the sample matrix activity coefficient, γ, represents the third

factor that serves to influence HS sensitivity. The theoretical basis for this is encompassed in Equation (3.26) or (3.28). The influence of increasing γ by adding salt to

an aqueous sample, a well-known technique called salting out, has been shown to

have a negligible effect on nonpolar VOCs such as TCE dissolved in water. Polar

solutes, however, are more strongly influenced by changes in the sample matrix

activity coefficient. It has also been observed that a high concentration of salt must

be dissolved in the aqueous sample matrix to have any effect at all. The addition of

a high amount of salt increases the volume of the liquid sample and thus serves to

decrease β. There are a number of drawbacks to adding salt in static HS, including

increases in sample viscosity and the addition of volatile impurities.

Few comprehensive studies have been published on the effect of the sample

matrix on the partitioning of VOCs at trace concentration levels. Friant and Suffet44

chose four model compounds that are polar and representative of the intramolecular

forces of dispersion, dipole orientation, proton-donor capability, and proton-acceptor

capability. These were methyl ethyl ketone, nitroethane, n-butanol, and p-dioxane.

The pH of the aqueous sample matrix had no effect at all except for nitroethane. An

optimum salt concentration was 3.35 M in sodium sulfate, and an optimum HS

sampling temperature of 50˚C. For example, the partition coefficient of methyl ethyl

ketone increased from 3.90 to 260 when the temperature of the aqueous sample that

contained the dissolved ketone was increased from 30 to 50°C, and at the same time,

© 2006 by Taylor & Francis Group, LLC



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175



the concentration of salt increased from zero to 3.35 M. Otson et al.45 compared

static HS, P&T, and LLE techniques for the determination of THMs in drinking

water and found that static HS showed the poorest precision and sensitivity. However,

a manual HS sampling technique was used back in this era and might possibly have

contributed to this loss of precision. LLE was found to be quite comparable to P&T

in this study.45



33. WHY IS STATIC HEADSPACE SAMPLING NOT

MORE ACCEPTABLE TO THE EPA?

This might be close to the $64,000 question. The answer lies somewhere between

“MDLs are not low enough in comparison to those obtained using P&T” and “HS

techniques were not developed in EPA labs, while purge and trap techniques were.”

Static HS, whose principles have already been introduced in this chapter, requires

that analytes be classified as volatile (i.e., having boiling points <125˚C). As also

discussed, the fundamental principles behind the static HS technique are only

recently becoming understood. Most static HS techniques are performed in automated analyzers. These analyzers are directly interfaced to the injection port of a

gas chromatograph via a transfer line. This online instrumental configuration does

not allow for the GC’s IDL to be experimentally measured independently, as is done

for offline LLE in the determination of semivolatile analytes. Thus, the GC detector

that is available is crucial to the notion of HS sensitivity. Because of the low detector

response factor, a given VOC can be highly favored to partition into the headspace,

yet have an MDL that is less than desirable. In the author’s laboratory, the technique

of manual HS sampling is popular among environmental microbiologists who need

analytical results almost immediately after they sample the headspace of their bioreactors. These researchers cannot wait for the long equilibration times of commercial

automated HS analyzers. P&T techniques would likewise be out of the question as

a means to measure trace VOCs, due to the long purging, trapping, and thermal

desorbing times involved.

The difficulty that the EPA has had with the static headspace technique might

be seen in the comment from Method 3810 (SW-846, third edition). This method

was eliminated in the recently published final update (III) and replaced by Method

5021. The authors who wrote Method 3810 state:46

Detection limits for this method may vary widely among samples because of the large

variability and complicated matrices of waste samples.… The sensitivity of this method

will depend on the equilibria of the various compounds between the vapor and dissolved

phases.… Due to the variability of this method, this procedure is recommended for

use only as a screening procedure for other, more accurate determinative methods.



Method 3810 recommends that a sample be heated to 90˚C and 2 mL of headspace gas taken with a gas-tight syringe. The written procedure for this method was

published in SW-846 and provided no data on method performance at that time. The

publication of a method from a regulatory agency without even a minimum of quality

assurance and quality control is inexcusable. This method serves as one example of

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Trace Environmental Quantitative Analysis, Second Edition



neglected GLP. The importance of GLP was introduced in Chapter 1, and this neglect

attests to the fact that little to no interest in static HS technique existed in 1986.



34. IS THERE A RECENTLY UPDATED EPA METHOD

FOR VOC USING STATIC HS TECHNIQUES?

Yes, there is, and it is Method 5021 from the recently updated SW-846 series of

methods published by the Office of Solid Waste at EPA. The method uses the static

HS technique to determine VOCs from soil or another solids matrix. This section

will focus on some of the details of this method because it includes many of the

quality control (QC) features that were absent in the method just discussed. This

method also introduced some experimental considerations with respect to trace VOC

analyses of soil samples.47 The method is applicable to a wide range of organic

compounds that have sufficiently high volatility to be effectively removed from soil

samples using the static HS technique. The method is used in combination with a

determinative technique that is described in the 8000 series. The method cautions

the user to the fact that solid samples whose organic matter content exceeds 1%, or

compounds with high octanol–water partition coefficients, may yield a lower result

for the determination of VOCs by static HS than dynamic headspace (P&T). It is

recommended to add surrogates to each and every sample to evaluate the so-called

matrix effect.



35. HOW SHOULD I PROCEED TO QUANTITATE VOCs?

The EPA’s approach to sample preparation to determine trace concentration levels

of various VOCs is discussed in this section. We have already introduced the static

HS technique from a theoretical point of view. Purge-and-trap (P&T) techniques, in

contrast to static HS, involve passing an inert gas through an aqueous sample such

as drinking water or groundwater. The purge gas is directed to a trap, a term

commonly used to describe a packed column that contains an adsorbent that exhibits

a high efficiency for VOCs. After sufficient time for purging and trapping has been

allowed, the trap is rapidly heated to thermally desorb the VOCs off of the adsorbent

and directly into the GC. In his manner, VOCs are removed from the environmental

sample without a matrix effect, and the objectives of TEQA can be met.

Purge and trap is dynamic; the analyte is merely transferred from the sample to

an organic polymeric matrix that exhibits a large surface area. One point of view

assumes that static HS is merely a screen for dynamic HS (P&T) because MDLs

for P&T are significantly lower than those for static HS. A second approach to

screening for particular priority pollutant VOCs is called hexadecane screening. The

logic as to what technique to use is depicted in the flowchart in Scheme 3.3. The

sample matrix plays a significant role as to whether one chooses the static or dynamic

HS technique for the isolation and recovery of VOCs from environmental samples.

When analyzing environmental samples that are considered grossly contaminated, screening techniques are essential. Screening techniques serve to inform the

analyst as to whether a dilution of the original is warranted. Laboratories that have

both automatic static HS and automated P&T systems are more likely to use static

© 2006 by Taylor & Francis Group, LLC



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177



Does sample

appear grossly

contaminated?



No



Proceed to conduct static

HS, SPME-HS, P&T,

LLE, manual HS

sampling, or other trace

VOCs sample prep



Yes



Is HxdLLE to be

used to

screen?



No



Is staticHS to be

used to

screen?



No



Yes

Yes

Conduct Hxd_LLE



Estimate concentration of contaminants

from either the Hxd screen or HS screen.

Calculate a dilution factor for the sample.



Is staticHS to be

used to

quantitate



No



Proceed to conduct

TEQA using P&T



Yes



Proceed to conduct

TEQA using staticHS



SCHEME 3.3 Flowchart for decisions involving screening of environmental samples for

VOCs.



HS for the initial screen, followed by P&T for the quantitative analysis. This is

particularly true for labs that engage in EPA contract work. Labs that have either

static HS or P&T, but not both, often elect to use hexadecane screening prior to the

quantitative determination by either static HS or P&T. Labs that analyze predominantly drinking water samples most likely do not have a need to screen samples and

usually proceed directly to the available determinative technique.

© 2006 by Taylor & Francis Group, LLC