.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/thermo/mixtures/plot_05_wilson_local_composition.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_thermo_mixtures_plot_05_wilson_local_composition.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_thermo_mixtures_plot_05_wilson_local_composition.py:


Wilson's local-composition model: the ethanol-water azeotrope
==============================================================

Wilson's 1964 model (:class:`~chemistrykit.thermo.WilsonSolution`)
assumes each molecule's immediate neighborhood differs in composition
from the bulk, weighted by Boltzmann factors of the interaction
energies. With just two parameters it describes strongly non-ideal
miscible mixtures. Below, at 70 degC, pure-component vapor pressures come
from Antoine's equation (NIST constants), and Wilson parameters of the
size fitted to ethanol-water data give the familiar maximum-pressure
azeotrope near 90 mol% ethanol. That azeotrope is why ordinary
distillation cannot purify ethanol past about 95 wt%.

.. GENERATED FROM PYTHON SOURCE LINES 17-50

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.thermo import AntoineEquation, BinaryIdealSolution, WilsonSolution

    T = 343.15
    P_ethanol = float(AntoineEquation(5.37229, 1670.409, -40.191).pressure(T)) * 100.0  # kPa
    P_water = float(AntoineEquation(5.08354, 1663.125, -45.622).pressure(T)) * 100.0

    mix = WilsonSolution(Lambda12=0.1782, Lambda21=0.8703, P1_star=P_ethanol, P2_star=P_water)
    ideal = BinaryIdealSolution(P_A_star=P_ethanol, P_B_star=P_water)
    x_az, P_az = mix.azeotrope()

    x = np.linspace(0.0, 1.0, 400)
    fig, axes = plt.subplots(1, 2, figsize=(12, 4.8))
    axes[0].plot(x, mix.total_pressure(x), color="darkorange", label="bubble curve (liquid x)")
    axes[0].plot(mix.vapor_composition(x), mix.total_pressure(x), color="steelblue", label="dew curve (vapor y)")
    axes[0].plot(x, ideal.total_pressure(x), ":", color="gray", label="Raoult's law")
    axes[0].plot([x_az], [P_az], "ko", label=f"azeotrope, x = {x_az:.3f}")
    axes[0].set_xlabel("mole fraction of ethanol")
    axes[0].set_ylabel("pressure (kPa)")
    axes[0].set_title("Ethanol-water P-x-y diagram at 70 degC (Wilson)")
    axes[0].legend()

    g1, g2 = mix.activity_coefficients(x)
    axes[1].plot(x, np.log(g1), color="darkorange", label=r"$\ln\gamma_{ethanol}$")
    axes[1].plot(x, np.log(g2), color="steelblue", label=r"$\ln\gamma_{water}$")
    axes[1].set_xlabel("mole fraction of ethanol")
    axes[1].set_ylabel(r"$\ln\gamma$")
    axes[1].set_title("Wilson activity coefficients")
    axes[1].legend()
    fig.tight_layout()




.. image-sg:: /api/gallery/thermo/mixtures/images/sphx_glr_plot_05_wilson_local_composition_001.png
   :alt: Ethanol-water P-x-y diagram at 70 degC (Wilson), Wilson activity coefficients
   :srcset: /api/gallery/thermo/mixtures/images/sphx_glr_plot_05_wilson_local_composition_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 51-56

.. code-block:: Python

    print(f"azeotrope: x_ethanol = {x_az:.3f} at P = {P_az:.1f} kPa")
    print(f"relative volatility at x = 0.5: {float(mix.relative_volatility(0.5)):.2f}")
    print(f"relative volatility at x = 0.95: {float(mix.relative_volatility(0.95)):.2f}  (< 1: water is now the more volatile)")

    plt.show()




.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    azeotrope: x_ethanol = 0.908 at P = 72.6 kPa
    relative volatility at x = 0.5: 1.96
    relative volatility at x = 0.95: 0.95  (< 1: water is now the more volatile)





.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.087 seconds)


.. _sphx_glr_download_api_gallery_thermo_mixtures_plot_05_wilson_local_composition.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_05_wilson_local_composition.ipynb <plot_05_wilson_local_composition.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_05_wilson_local_composition.py <plot_05_wilson_local_composition.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_05_wilson_local_composition.zip <plot_05_wilson_local_composition.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_