9873

Fugacities in a Can of Soda

The fugacities of water and carbon dioxide are calculated as a function of temperature for a closed container modeled by a can of soda. The concentrations of the two components are calculated in both the liquid and the gas phases. As the 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. Correspondingly, the fugacity is much higher than fugacity. As the temperature increases, the pressure increases. Higher temperatures decrease the concentration in water, but higher pressures increase the concentration in water, so the net effect is that the concentration in the liquid phase does not change much.

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The fugacity of dissolved in water (soda pop) 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 ) in K, is the freezing point depression constant for water (), is the molality of , is Henry's law constant (), is Henry's constant at 298.15 K, 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:
.
Reference
[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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