David Bastviken
February 2015
Calculation of gas concentrations in water determined by the headspace
extraction method.
The below calculations have been used in several publications on methane (CH4) (e.g. Bastviken et
al., 2004; Bastviken et al., 2008; Bastviken et al., 2010).
The equations are general and apply to headspace extractions of:
• CH4
• N2O
• DIC (dissolved inorganic carbon, ie CO2 if water samples were acidified to pH < 2 before
extraction).
Note that the below calculations may not be suitable for CO2 extractions at pH levels where the
carbonic acid equilibrium system may influence the headspace extraction.
Fundamentals
Be aware of units! (The most common mistake is to mix up units as there are many alternative units
in use for the variables below.)
-
Ptot = total air pressure (atm)
Px =partial pressure for the gas x (atm)
ppm = parts per million, usually comes from GC measurement
V = volume (L)
n = amount of compound (mol)
R = common gas constant = 0.082056 L atm K-1 mol-1
T = temperature (K)
C = concentration (mol/L = M)
KH = Henrys Law constant (M atm-1); varies between gases and with temperature (e.g. Weiss,
1974; Weiss and Price, 1980; Wiesenburg and Guinasso, 1979).
The common gas law: PV = nRT
Henrys law: C = P*KH
Concentration of gas in water based on headspace extraction method
In the headspace extraction the target gas in the water is partially transferred to a headspace which
is analyzed for the gas content. The strategy is to determine both the amount of target gas
transferred to the headspace and the amount remaining in the water. The sum of these two gas
stocks was originally in the water. In this example air is used to create the headspace so the target
gas added with the air has to be discounted as well.
n in headspace (g): ng = (Px * Vg)/(R*T),
where Px = Ptot*(ppmx/106) (atm) and ppmx is the mixing ratio of the gas x (parts per million)
determined in the analysis of the headspace gas sample (by gas chromatography, spectroscopy or
other analysis methods).
David Bastviken
February 2015
Vg = the headspace volume (e.g. 0.020 L if sample comes from a syringe extraction with 40 ml water
and 20 ml headspace, or 0.050 L if sample from a pCO2 bottle extraction with 50 ml headspace).
T = temperature when the equilibration took place (e.g. water temperature when shaking the vessel)
n in the air used to create the headspace: nair =(Px in air * Vg)/(R*T),
where Px in air = Ptot*(ppmairsample/106) (atm)
n in water (aq): naq = Caq * Vaq = Px * KH * Vaq,
where Px = Ptot*(ppmx/106) (atm) and
KH is selected for the appropriate gas and temperature
Total n in vessel = ntot = ng + naq
Original konc. in sample: Caq =(ntot – nair) /Vaq
References
Bastviken, D., Cole, J., Pace, M., and Tranvik, L.: Methane emissions from lakes: Dependence of lake
characteristics, two regional assessments, and a global estimate, Global Biogeochem. Cycles, 18
GB4009, doi:10.1029/2004GB002238, 2004.
Bastviken, D., Cole, J. J., Pace, M. L., and van de Bogert, M.: The fates of methane from different lake
habitats - connecting whole-lake budgets and CH4 emissions, J. Geophys. Res., 113, G02024,
doi:10.1029/2007JG000608, 2008.
Bastviken, D., Santoro, A. L., Marotta, H., Pinho, L. Q., Calheiros, D. F., Crill, P., and Enrich-Prast, A.:
Methane Emissions from Pantanal, South America, during the Low Water Season: Toward More
Comprehensive Sampling, Environ. Sci. Technol., 44, 5450-5455, 2010.
Weiss, R. F.: Carbon dioxide in water and seawater: the solubility of a non-ideal gas, Mar. Chem., 2,
203-215, 1974.
Weiss, R. F. and Price, B. A.: Nitrous oxide solubility in water and seawater, Mar. Chem., 8, 347-359,
1980.
Wiesenburg, D. A. and Guinasso, N. L.: Equilibrium solubilities of methane, carbon monoxide, and
hydrogen in water and sea water, Journal of Chemical and Engineering Data, 24, 356-360, 1979.