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# Adding a Second Component to a Fixed-Volume Container

A constant-volume tank initially contains one component in the vapor phase (either -octane or -hexane), and you can add the other component at constant temperature using a slider. Change the temperature with another slider. Select the component to be added with buttons. The pressure-composition diagram has a blue line for the bubble pressure and an orange curve for the dew-point pressure. The black dot is located at the overall composition and the pressure. When two phases are present, the -hexane mole fractions of the liquid phase (, blue dot) and the vapor phase (, orange dot) are displayed. The bar graph represents the number of moles of each component in the liquid and vapor phase; purple is for -hexane and green is for -octane.

### DETAILS

The saturation pressures are calculated using the Antoine equation:
,
where is the saturation pressure (bar) of component ; , and are Antoine constants; and is temperature (K).
Raoult's law for a binary mixture is used to calculate the bubble and dew pressures:
,
,
where and are the liquid mole fractions of each component and and are the vapor mole fractions .
The overall mole fraction of component 1 is , where and are the total moles of each component.
When only vapor is present,
,
,
where is pressure (bar), is the gas constant ([L bar]/[mol K]), is volume (L) and are moles of vapor.
The following five equations are solved for , , , , and liquid moles when both liquid and vapor are present.
From Raoult's law:
,
.
From overall and species mole balances:
,
.
From a volume balance:
,
where is the molar density of the mixture (mol/L).
The screencast video at [1] explains how to use this Demonstration.
Reference
[1] Adding a Second Component to a Fixed-Volume Container [Video]. (Aug 31, 2016) www.colorado.edu/learncheme/thermodynamics/AddingSecondComponentFixedVolume.xhtml.

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