.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/thermo/mixtures/plot_04_margules_activity.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_04_margules_activity.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_thermo_mixtures_plot_04_margules_activity.py:


Margules activity coefficients: deviations from Raoult's law
============================================================

Margules wrote the activity coefficients of a binary liquid as power
series in mole fraction. The one-parameter form used by
:class:`~chemistrykit.thermo.systems.mixtures.MargulesSolution`,
:math:`\ln\gamma_1 = A x_2^2` and :math:`\ln\gamma_2 = A x_1^2`, turns
Raoult's straight lines into curves: :math:`A > 0` (unlike molecules
repel) bows the total pressure upward and can produce a maximum-pressure
azeotrope, while :math:`A < 0` bows it downward. The model still obeys
the Gibbs-Duhem relation, and each component tends to Henry's law at
infinite dilution.

.. GENERATED FROM PYTHON SOURCE LINES 17-49

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.thermo.systems.mixtures import MargulesSolution

    P1_star, P2_star = 30.0, 20.0  # kPa
    x1 = np.linspace(0.0, 1.0, 300)

    fig, axes = plt.subplots(1, 3, figsize=(15, 4.5))
    for A, color in [(-1.5, "steelblue"), (0.0, "gray"), (1.5, "crimson")]:
        sol = MargulesSolution(A=A, P1_star=P1_star, P2_star=P2_star)
        g1, g2 = sol.activity_coefficients(x1)
        axes[0].plot(x1, np.log(g1), color=color, label=f"A = {A}: ln gamma_1")
        axes[0].plot(x1, np.log(g2), "--", color=color)
        axes[1].plot(x1, sol.total_pressure(x1), color=color, label=f"A = {A}")
        if A != 0.0:
            axes[2].plot(x1, sol.total_pressure(x1), color=color, label=f"P-x, A = {A}")
            axes[2].plot(sol.vapor_composition(x1), sol.total_pressure(x1), ":", color=color, label=f"P-y, A = {A}")
    axes[0].set_xlabel(r"$x_1$")
    axes[0].set_ylabel(r"ln $\gamma$ (solid: 1, dashed: 2)")
    axes[0].set_title("Activity coefficients")
    axes[0].legend(fontsize=8)
    axes[1].set_xlabel(r"$x_1$")
    axes[1].set_ylabel("total pressure (kPa)")
    axes[1].set_title("Positive and negative deviations from Raoult")
    axes[1].legend()
    axes[2].set_xlabel(r"$x_1$, $y_1$")
    axes[2].set_ylabel("total pressure (kPa)")
    axes[2].set_title("Azeotropes where P-x and P-y touch")
    axes[2].legend(fontsize=8)
    fig.tight_layout()




.. image-sg:: /api/gallery/thermo/mixtures/images/sphx_glr_plot_04_margules_activity_001.png
   :alt: Activity coefficients, Positive and negative deviations from Raoult, Azeotropes where P-x and P-y touch
   :srcset: /api/gallery/thermo/mixtures/images/sphx_glr_plot_04_margules_activity_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 50-52

The azeotrope is where :math:`x_1 = y_1`, and the Henry's-law constant
of component 1 at infinite dilution is :math:`P_1^* e^{A}`:

.. GENERATED FROM PYTHON SOURCE LINES 52-60

.. code-block:: Python


    for A in (-1.5, 1.5):
        sol = MargulesSolution(A=A, P1_star=P1_star, P2_star=P2_star)
        diff = sol.vapor_composition(x1[1:-1]) - x1[1:-1]
        i = int(np.argmin(np.abs(diff)))
        print(f"A = {A:+.1f}: azeotrope near x1 = {x1[1:-1][i]:.3f}, P = {float(sol.total_pressure(x1[1:-1][i])):.2f} kPa; K_H(1) = {sol.henry_constant_1:.1f} kPa")

    plt.show()




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

 .. code-block:: none

    A = -1.5: azeotrope near x1 = 0.365, P = 16.38 kPa; K_H(1) = 6.7 kPa
    A = +1.5: azeotrope near x1 = 0.635, P = 36.63 kPa; K_H(1) = 134.5 kPa





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

   **Total running time of the script:** (0 minutes 0.121 seconds)


.. _sphx_glr_download_api_gallery_thermo_mixtures_plot_04_margules_activity.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_04_margules_activity.ipynb <plot_04_margules_activity.ipynb>`

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

      :download:`Download Python source code: plot_04_margules_activity.py <plot_04_margules_activity.py>`

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

      :download:`Download zipped: plot_04_margules_activity.zip <plot_04_margules_activity.zip>`


.. only:: html

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

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