Calculation of f(CO2) for Moist Air Conditions
The first step in evaluating the in situ gas concentration, either in the atmosphere or in vapor equilibrated with surface seawater, is calculation of the gas fugacity in moist air from the measured mole fraction in dry air. Weiss and Price (1980) give the theoretical basis for this calculation based on equations given by Guggenheim (1967, pp. 175-77) for calculating fugacities in binary mixtures:
f1 = x1P exp[(B11 + 2(x2)2 · Δ12)P/RT] (eq. 18)
where x1 is the mole fraction of pure gas 1, x2 is the mole fraction of pure gas 2, P is the total pressure, R is the gas constant, T is the absolute temperature, and Δ12 is defined by:
B12 = 1/2(B11 + B22) + Δ12 (eq. 19)
where B11 is the virial coefficient for interaction between pure gas 1 molecules; B22 is the virial coefficient for interaction between pure gas 2 molecules; and B12 is the virial coefficient for interaction between molecules of gases 1 and 2.
For calculating in situ gas fugacities, gas 1 is here considered as the analyte gas and gas 2 as dry air. The x1 in the above equation is the mole fraction of analyte gas in the analyte gas-dry air mixture. For an analyte like CO2, the atmospheric value of x1 is approximately 350 · 10-6 moles of CO2 per mole of dry gas mixture. The x2 is the mole fraction of dry air in that same mixture, and is approximately equal to 1:
x2 = (1-350 · 10-6)/1.0 = 0.99965 moles of air per mole of dry gas mixture (eq. 20)
To calculate CO2 fugacity for the moist air conditions at the air-sea interface, the measured mole fraction of CO2 in dry air, x1 in equation 18 above, must be corrected to the mole fraction of the CO2 in moist air. If the air-sea interface is regarded as saturated in water vapor at the in situ temperature, the mole fraction of the CO2 in dry air, x1, can be corrected to the mole fraction in moist air x1´ as follows:
x1´ = x1(1-psw/patm) (eq. 21)
where psw is the saturated vapor pressure of seawater at the temperature of the measurement. For atmospheric f(CO2), the temperature of calculation is the in situ air temperature; for f(CO2) in surface seawater, this corresponds to the equilibrator temperature. The total barometric pressure is represented by patm.
Substituting x1´ from equation 21 for x1 in equation 18 gives:
f1 = x1(1-psw/patm)Patm exp[(B11 + 2(x2)2 · Δ12)patm/RT] (eq. 22)
Since x2 is approximately equal to 1 for the analyte gases considered here (equation 20), equation 22 reduces to:
f = x1(patm - psw) exp[patm(B + 2Δ)/RT] (eq. 23)
f is the fugacity of the analyte gas in moist air in units of atmospheres
x1 is the measured mole fraction of the analyte gas in dry air in units of parts per million (ppm)
patm is the total barometric pressure in units of atmospheres
psw is the saturated vapor pressure of seawater (in atmospheres) at the temperature of the measurements and is calculated from equation (3) in the main text from Weiss and Price(1980):
ln psw = 24.4543-67.4509(100/T)-4.8489 ln(T/100)-0.000544S (eq. 24)
B is the virial coefficient for CO2 and can be calculated using a power series given by Weiss(1974):
B=-1636.75 + 12.0408T - 3.27957 · 10-2T2 + 3.16528 · 10-5T3 (eq. 25)
Δ is the cross virial coefficient B12 for interaction between gases 1 and 2 minus the mean of B11 and B22 for two pure gases (see equation 19). Weiss (1974) gives this for CO2 and air as a function of temperature.
Δ = 57.7 - 0.118T cm3/mole (eq. 26)
R is the gas constant
T is the temperature of water in the equilibrator in Kelvin at the time the gas aliquot was removed.
The fugacity obtained is the fugacity of CO2 in the moist equilibrator vapor. Since the temperature in the equilibrator is higher than the sea surface temperature, another calculation is required to correct this value to obtain the fugacity of CO2 at the in situ sea surface conditions.