benzene-toluene T-x-y
Click on the plot
Click anywhere on the diagram to see phase information, compositions, and relative amounts (for VLE).
Directions
This simulation displays the temperature–composition (T-x-y) phase diagram for a benzene-toluene mixture, which is modeled as an ideal solution.
Use the Pressure slider in the panel on the left to change the system pressure; the bubble-point and dew-point curves are recalculated as the slider moves.
Click anywhere inside the diagram to select an overall state (temperature and overall benzene mole fraction). The panel on the left then reports:
• the phase state (subcooled liquid, vapor-liquid equilibrium, or superheated vapor),
• the temperature,
• the benzene mole fraction of each phase present, and
• for a point in the two-phase region, the relative amounts of liquid and vapor from the lever rule.
For a point in the two-phase region, a dashed tie line is drawn through the selected point; the blue dot on the bubble-point curve is the liquid composition and the red dot on the dew-point curve is the vapor composition.
Details
The benzene (1) / toluene (2) mixture is modeled as an ideal solution using Raoult's law:
\( P = x_1 P_1^{sat} + (1 - x_1)\, P_2^{sat} \)
where \( P \) is the total pressure (mm Hg), \( x_1 \) is the benzene liquid mole fraction, and \( P_i^{sat} \) is the saturation pressure of component \( i \).
The saturation pressures are calculated with the Antoine equation:
\( \log_{10} P_i^{sat} = A_i - \dfrac{B_i}{T + C_i} \)
where \( T \) is the temperature (°C) and \( P_i^{sat} \) is in mm Hg.
| component | \( A \) | \( B \) | \( C \) |
|---|---|---|---|
| benzene | 6.89272 | 1203.531 | 219.888 |
| toluene | 6.95087 | 1342.311 | 219.187 |
At each liquid composition \( x_1 \), the bubble-point temperature is found by solving Raoult's law for \( T \) at the specified pressure. The vapor composition in equilibrium with that liquid, which generates the dew-point curve, is:
\( y_1 = \dfrac{x_1 P_1^{sat}}{P} \)
For an overall composition \( z_1 \) in the two-phase region, the fractions of liquid and vapor are obtained from the lever rule:
\( \dfrac{L}{F} = \dfrac{y_1 - z_1}{y_1 - x_1}, \qquad \dfrac{V}{F} = \dfrac{z_1 - x_1}{y_1 - x_1} \)
where \( F = L + V \) is the total number of moles, \( L \) is the moles of liquid, and \( V \) is the moles of vapor.
About
This simulation was generated by Professor David L. Silverstein and Dr. Loyal Murphy of the University of Mississippi using Google Gemini. It was modified for LearnChemE using Claude AI.