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# Heating Water and Air in a Sealed Container

This Demonstration models the behavior of a sealed, 1-L autoclave that initially contains mostly water plus a small volume of air, all at 25 °C. Change the initial volume of water with a slider and the temperature resets to 25 °C. As the temperature increases by moving the slider, liquid water expands and its saturation pressure increases. At the same time, the gas-phase volume decreases, so gas-phase and partial pressures increase (ideal gas law). The amounts of and dissolved in the water increase with pressure, but decrease with temperature. The amounts dissolved are shown in the bar chart (green = gas phase, purple = dissolved). Even at moderate temperatures, the pressure inside the sealed container can be quite high.

### DETAILS

The final liquid volume of water is given by:
,
where is the initial liquid volume (L) at 25 °C, is temperature (°C), and , , and are constants.
The total pressure in the container is equal to the saturation pressure of water plus the partial pressures of oxygen and nitrogen :
.
The saturation pressure of water is calculated using the Antoine equation:
,
where , and are Antoine constants.
The partial pressures of oxygen and nitrogen are calculated using the ideal gas law:
,
where is the fraction of oxygen or nitrogen in air where and , is the moles of in the gas phase, is the ideal gas constant ([L bar]/[mol K]) and is the vapor volume (L).
The total moles of oxygen and nitrogen in the container are calculated at 25 °C and 1 bar pressure, the moles in the gas phase are calculated using the ideal gas law, and the moles dissolved in water are calculated using Henry's law:
,
,
where and are Henry's law constants (mol/[L bar]):
,
.
For all and , the moles in the gas phase and dissolved must equal the total moles at 25 °C and 1 bar:
,
.
The screencast video at [1] shows how to use this Demonstration.
Reference
[1] Heating Water and Air in a Sealed Container [Video]. (Aug 31, 2016) www.colorado.edu/learncheme/thermodynamics/HeatingWaterAirSealedContainer.html.

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