.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/thermo/mixtures/plot_01_raoult_law_pxy.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_01_raoult_law_pxy.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_thermo_mixtures_plot_01_raoult_law_pxy.py:


Raoult's law and the P-x-y diagram of an ideal solution
=======================================================

Raoult's law, :math:`P_A = x_A P_A^*`
(:func:`~chemistrykit.thermo.systems.mixtures.raoult_vapor_pressure`),
makes each partial vapor pressure a straight line in liquid mole
fraction. Adding the two lines (Dalton's law) gives the total pressure,
and
:class:`~chemistrykit.thermo.systems.mixtures.BinaryIdealSolution`
computes the vapor composition, which is always richer in the more
volatile component. That enrichment is the basis of fractional
distillation.

.. GENERATED FROM PYTHON SOURCE LINES 17-43

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.thermo.systems.mixtures import BinaryIdealSolution, raoult_vapor_pressure

    P_benzene, P_toluene = 12.7, 3.8  # kPa, pure vapor pressures near 25 degC
    solution = BinaryIdealSolution(P_A_star=P_benzene, P_B_star=P_toluene)
    x = np.linspace(0.0, 1.0, 200)

    fig, axes = plt.subplots(1, 2, figsize=(12, 4.8))
    axes[0].plot(x, raoult_vapor_pressure(x, P_benzene), "--", label=r"benzene, $x_B P_B^*$")
    axes[0].plot(x, raoult_vapor_pressure(1 - x, P_toluene), "--", label=r"toluene, $x_T P_T^*$")
    axes[0].plot(x, solution.total_pressure(x), color="black", label="total")
    axes[0].set_xlabel("liquid mole fraction benzene")
    axes[0].set_ylabel("P (kPa)")
    axes[0].set_title("Raoult's law: straight partial-pressure lines")
    axes[0].legend()

    axes[1].plot(x, solution.total_pressure(x), label="liquid (P-x, bubble line)")
    axes[1].plot(solution.vapor_composition(x), solution.total_pressure(x), label="vapor (P-y, dew line)")
    axes[1].set_xlabel("mole fraction benzene")
    axes[1].set_ylabel("P (kPa)")
    axes[1].set_title("P-x-y diagram for benzene/toluene")
    axes[1].legend()
    fig.tight_layout()




.. image-sg:: /api/gallery/thermo/mixtures/images/sphx_glr_plot_01_raoult_law_pxy_001.png
   :alt: Raoult's law: straight partial-pressure lines, P-x-y diagram for benzene/toluene
   :srcset: /api/gallery/thermo/mixtures/images/sphx_glr_plot_01_raoult_law_pxy_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 44-47

A 50:50 liquid gives a vapor much richer in benzene; condensing and
re-evaporating repeats the enrichment (each step is one theoretical
plate of a distillation column):

.. GENERATED FROM PYTHON SOURCE LINES 47-54

.. code-block:: Python


    x_step = 0.5
    for plate in range(1, 5):
        x_step = float(solution.vapor_composition(x_step))
        print(f"after plate {plate}: benzene mole fraction = {x_step:.3f}")

    plt.show()




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

 .. code-block:: none

    after plate 1: benzene mole fraction = 0.770
    after plate 2: benzene mole fraction = 0.918
    after plate 3: benzene mole fraction = 0.974
    after plate 4: benzene mole fraction = 0.992





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

   **Total running time of the script:** (0 minutes 0.072 seconds)


.. _sphx_glr_download_api_gallery_thermo_mixtures_plot_01_raoult_law_pxy.py:

.. only:: html

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

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

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

      :download:`Download Python source code: plot_01_raoult_law_pxy.py <plot_01_raoult_law_pxy.py>`

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      :download:`Download zipped: plot_01_raoult_law_pxy.zip <plot_01_raoult_law_pxy.zip>`


.. only:: html

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

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