General Discussion of CO₂ Measurements and Fugacity

Field measurements of carbon dioxide gas concentrations are often observed as the mole fraction of CO₂ in an aliquot of dried vapor. The concentration of CO₂ expressed as the mole fraction in dry air is an absolute and observable quantity, but is not necessarily the quantity which geochemists need to evaluate air-sea fluxes or to examine the relationship of dissolved CO₂ with other carbonate parameters. Geochemical assessments generally require the correction of CO₂ concentrations from the measurement units and conditions to units of microatmospheres (µatm) at the in situ sea surface conditions. Partial pressures of CO₂ in units of µatm have been historically reported, but in recent years, fugacities have also been reported. We offer here a brief discussion of the distinction between fugacity and partial pressure, and the motivation for using fugacity in this report.

Fugacity is an expression for the concentration of a real gas in a mixture of real gases, whereas partial pressure is an expression for the concentration of an ideal gas in a mixture of ideal gases. Ideal gases are conceptualized as comprising molecules which occupy no volume and between which no forces exist. The concept of fugacity is introduced in order to use for real gases the thermodynamic relationships established for ideal gases. Fugacity cannot be measured directly, as pressure is, yet the basis for discussion of equilibrium, solubility, etc. is based on the thermodynamic quantity of fugacity, not on the observable quantity of pressure.

The thermodynamic equation of state for ideal gases is PV=nRT, where P is pressure, V is volume, n is number of moles of gas, R is the gas constant, and T is absolute temperature. This equation can be used to convert the number of moles of pure, ideal gas to the pressure of the gas. If we make a plot of pressure vs. PV/nRT for pure nitrogen (N₂), pure carbon dioxide (CO₂), and a pure ideal gas, we can see that an ideal gas is a line with zero slope and y-intercept=1. Nitrogen approximates an ideal gas at low pressures, but becomes less ideal at higher pressures as the volume of the molecules becomes significant relative to the total volume. CO₂ is a highly non-ideal gas, even at low pressures. The negative deviation from ideality at low pressures suggests attractive forces between CO₂ molecules. The significance of this factor becomes less important at higher pressures. The approximation of ideality for CO₂ may be acceptable at ambient pressures when high accuracy is not required.

The difference between pressure and fugacity for a typical ambient CO₂ concentration is 1 to 1.5 µatm (~0.3%) over the temperature range 0 to 30°C. These calculations assume a binary gas mixture of CO₂ and air, where air is treated as a homogeneous gas. For this report, fugacities rather than partial pressures are reported.