Fugacities in a Can of Soda

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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.
Contributed by: Rachael L. Baumann (August 2014)
With additional contributions by: John L. Falconer and Nick Bongiardina
(University of Colorado Boulder, Department of Chemical and Biological Engineering)
Open content licensed under CC BY-NC-SA
Snapshots
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. doi:10.1021/ed100255g.
[2] Fugacities in a Can of Soda [Video]. (Dec 16, 2020) www.learncheme.com/simulations/thermodynamics/thermo-2/fugacities-in-a-can-of-soda.
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