The vapor-liquid equilibrium (VLE) behavior of an n-hexane/n-octane mixture is demonstrated in P-x-y and T-x-y diagrams. The blue line represents the liquid-phase boundary (bubble point) and the green line represents the vapor-phase boundary (dew point). Click and drag the black dot on either diagram and the bar chart shows the amounts of liquid (blue) and vapor (green) present; the system contains a total of 1 mole. While dragging the black dot: hold the shift key to maintain constant temperature (on T-x-y diagram) or constant pressure (on P-x-y diagram), or hold the ctrl key to maintain constant mole fraction. The mole fractions of n-hexane in each phase (xH for liquid phase, yH for vapor phase) are shown in the bar graph. Use sliders to vary the temperature for the P-x-y diagram or the pressure for the T-x-y diagram. This system is modeled by Raoult's law because an n-hexane/n-octane liquid phase is assumed ideal.
The saturation pressure of component \( i \) is calculated using the Antoine equation:
$$ [1] \quad P_{i}^{sat} = 10^{ A_{ i } - \frac{ B_{ i } }{ T - C_{ i } } } $$where \( i = 1 \) for n-hexane and \( i = 2 \) for n-octane, \( P_{i}^{sat} \) is saturation pressure (bar), \( A_{i} \), \( B_{i} \), and \( C_{i} \) are Antoine constants, and \( T \) is temperature (°C). Raoult's law is used to calculate the bubble-point and dew-point pressures using the \( K \) factors:
$$ [2] \quad K_{i} = \frac{ y_{i} }{ x_{i} } = \frac{ P_{i}^{sat} }{ P } $$where \( y_{i} \) is the vapor mole fraction and \( y_{1} + y_{2} = 1 \), \( x_{i} \) is the liquid mole fraction and \( x_{1} + x_{2} = 1 \), and \( P \) is the total pressure (bar). The bubble-point pressure is calculated using \( \sum K_{i} x_{i} = 1 \):
$$ [3] \quad P = x_{1} P_{1}^{sat} + x_{2} P_{2}^{sat} $$The dew-point pressure is calculated using \( \sum y_{i} / K_{i} = 1 \):
$$ [4] \quad P = \left( \frac{ y_{1} }{ P_{1}^{sat} } + \frac{ y_{2} }{ P_{2}^{sat} } \right)^{ -1 } $$This simulation was created in the Department of Chemical and Biological Engineering, at University of Colorado Boulder for LearnChemE.com by Neil Hendren under the direction of Professor John L. Falconer. Address any questions or comments to learncheme@gmail.com. All of our simulations are open source, and are available on our LearnChemE Github repository.
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