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# Fugacities in a Can of Soda

The fugacities of water and carbon dioxide are calculated as a function of temperature for a closed container, which is a model of a can of soda. The concentrations of the two components are calculated in both the liquid and gas phases. As temperature increases, the pressure increases, and therefore the fugacities increase. Note that the concentration is much lower than the concentration in the liquid phase, but the concentration is much higher than the concentration in the gas phase. Because the gas phase is assumed to be ideal, the fugacities of and in both phases are equal to their gas-phase partial pressures, and thus the fugacity is much higher than the fugacity. As the temperature increases, the concentration in liquid water decreases. However, as the temperature increases the pressure increases, and a higher pressure increases the concentration in water, so the net effect is that concentration in the liquid phase does not change much as the temperature increases.

### DETAILS

The fugacity of dissolved in water was calculated using Henry's law and freezing point depression measurements:
,
,
,
,
where is the difference between the freezing point of water and the freezing point of carbon dioxide in water ( and ) (K), is the freezing point depression constant for water ([°C kg]/mol), is the molality of , is Henry's law constant (kg/[mol bar]), is Henry's constant at 273 K, is a constant, is temperature (K), is the partial pressure of (bar), and is the fugacity of (bar).
The fugacity of water was calculated from the saturation pressure of water using the Antoine equation:
,
where is the fugacity of water (bar).
The screencast video at [2] explains how to use this Demonstration.
References
[1] T. S. Kuntzleman and C. Richards, "Another Method for Determining the Pressure inside an Intact Carbonated Beverage Can (or Bottle)," Journal of Chemical Education, 87(9), 2010 p. 993.

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