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Headspace GC Theory Supplement for GC Connections October 2011
Expanded Theoretical Section
This is the supplemental information to the "GC Connections" installment on headspace GC that appears in the October, 2011 issue of LC/GC North America [1].
In equilibrium static headspace sampling, a vial is partially filled with sample then sealed and thermostatted. Compounds in the condensed sample phase, and here we will consider only a liquid sample phase, migrate into the gas phase in the vial—the headspace—and back into the liquid sample. After a period of time the concentrations of each compound in the liquid and gaseous phases reach steady equilibrium levels.
At equilibrium, the chemical system inside a sealed static headspace vial can be characterized with a conventional theoretical treatment. Figure 1 illustrates such a system for a two-phase sample system and names its more important physico–chemical characteristics such as the volumes of the liquid phase, VS, and the gaseous phase, VG, and the concentrations at equilibrium of individual analytes in the liquid phase, CS, and in the gas phase, CG. Figure 1 shows conceptually the migration of solute molecules into and out of the liquid and gas phases. The following derivations assume that the sample volume does not change during the analysis process.
Figure 1. Headspace vial equilibrium
Headspace sampling strives to determine the original concentrations of the compounds of interest in the sample, Co, but a GC analysis measures the gas-phase equilibrium concentration of each analyte instead. Thus, quantitative relationships must be established between the two.
Let Wo be the original amount of a component in the sample phase and VS be the liquid sample volume in the headspace vial. Then
(1)
At equilibrium the concentrations of an analyte in the liquid and gas phases are:
(2)
(3)
and the original analyte weight in the liquid phase is:
(4)
Thus:
(5)
and:
(6)
The ratio of the gaseous to liquid phase volumes in the vial is termed the phase ratio, β:
(7)
which means that:
(8)
Divide this equation by CG:
(9)
In addition to the phase ratio, in order to determine Co we also need to consider the partition or distribution coefficient at equilibrium, K, which is the ratio of a compound's concentration in the liquid phase to that in the gaseous phase:
(10)
Finally, by combining and rearranging the last two equations it can be seen that the original solute concentration in the liquid phase is related to its concentration in the gas phase, the distribution coefficient, and the phase ratio by this relationship, sometimes termed the headspace equation:
(11)
Supplemental Vacuum Outlet Flow Theory for GC Connections January 2011
The supplementary material to the January, 2011, "GC Connections" column in LC/GC North America.[2] has been moved to its own page.
Tables of Chromatography Discussion Groups and Web Sites
The table of Discussion Groups originally was published on-line as "Get Involved!" on the Chromatography Online website as well as in the print version of LC/GC North America in the September 2009 issue[3].
The tables have been moved to their own page.
References
- ↑ John Hinshaw, LC/GC North America, 29 (10), 914–924 (2011).
- ↑ John Hinshaw, LC/GC North America, 29 (1), (2011).
- ↑ John Hinshaw, LC/GC North America, 27 (9), pp. 822–827 (2009).
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