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 · ₁₂)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 ₁₂ is defined by:

B₁₂ = 1/2(B₁₁ + B₂₂) + ₁₂ (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:

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:

where p_sw 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 p_atm.

Substituting x₁´ from equation 21 for x₁ in equation 18 gives:

f₁ = x₁(1-p_sw/p_atm)P_atm exp[(B₁₁ + 2(x₂)² · ₁₂)p_atm/RT] (eq. 22)

Since x₂ is approximately equal to 1 for the analyte gases considered here (equation 20), equation 22 reduces to:

f = x₁(p_atm - p_sw) exp[p_atm(B + 2)/RT] (eq. 23)

where:

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)

p_atm is the total barometric pressure in units of atmospheres

p_sw 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):

B is the virial coefficient for CO₂ and can be calculated using a power series given by Weiss(1974):

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.

= 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.

akozyr 05/31/97