.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/thermo/equilibrium/plot_04_le_chatelier.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_equilibrium_plot_04_le_chatelier.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_thermo_equilibrium_plot_04_le_chatelier.py:


Le Chatelier's principle: equilibrium shifts that oppose a disturbance
======================================================================

Two disturbances of :math:`N_2O_4 \rightleftharpoons 2NO_2`, an
endothermic reaction that increases the number of gas molecules:

* **Heating** raises :math:`K`
  (:func:`~chemistrykit.thermo.systems.equilibrium.van_t_hoff_equilibrium_constant`),
  shifting toward :math:`NO_2` to absorb the added heat; an exothermic
  reaction shifts the other way.
* **Compressing** leaves :math:`K` unchanged but moves the equilibrium
  found by
  :func:`~chemistrykit.thermo.systems.equilibrium.solve_equilibrium_composition`
  toward :math:`N_2O_4`, the side with fewer molecules, partly relieving
  the pressure rise.

.. GENERATED FROM PYTHON SOURCE LINES 20-35

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.constants import R
    from chemistrykit.thermo.systems.equilibrium import solve_equilibrium_composition, van_t_hoff_equilibrium_constant

    T = np.linspace(260.0, 380.0, 200)
    fig, axes = plt.subplots(1, 2, figsize=(12, 4.8))
    axes[0].semilogy(T, van_t_hoff_equilibrium_constant(T, 298.15, 1.0, 57_200.0), label=r"endothermic, $\Delta H^\circ$ = +57.2 kJ/mol")
    axes[0].semilogy(T, van_t_hoff_equilibrium_constant(T, 298.15, 1.0, -57_200.0), label=r"exothermic, $\Delta H^\circ$ = -57.2 kJ/mol")
    axes[0].set_xlabel("T (K)")
    axes[0].set_ylabel(r"$K / K(298\,K)$")
    axes[0].set_title("Heating favors the endothermic direction")
    axes[0].legend()




.. image-sg:: /api/gallery/thermo/equilibrium/images/sphx_glr_plot_04_le_chatelier_001.png
   :alt: Heating favors the endothermic direction
   :srcset: /api/gallery/thermo/equilibrium/images/sphx_glr_plot_04_le_chatelier_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <matplotlib.legend.Legend object at 0x11b152270>



.. GENERATED FROM PYTHON SOURCE LINES 36-37

Fraction of N2O4 dissociated at 298.15 K as the total pressure rises.

.. GENERATED FROM PYTHON SOURCE LINES 37-55

.. code-block:: Python


    T0 = 298.15
    gf = [0.0, (57_200.0 - T0 * 175.8) / 2.0]
    P_bar = np.logspace(-2, 2, 40)
    alpha = []
    for P in P_bar:
        res = solve_equilibrium_composition(("N2O4", "NO2"), [[-1.0], [2.0]], [1.0, 0.0], gf, T0, P=P * 1e5)
        alpha.append(res.extents[0])
    K = np.exp(-(2 * gf[1]) / (R * T0))
    axes[1].semilogx(P_bar, alpha, "o", label="Gibbs-minimization solver")
    axes[1].semilogx(P_bar, np.sqrt(K / (K + 4 * P_bar)), color="crimson", label=r"closed form $\sqrt{K/(K+4P/P^\circ)}$")
    axes[1].set_xlabel("total pressure (bar)")
    axes[1].set_ylabel(r"fraction of $N_2O_4$ dissociated")
    axes[1].set_title("Compression favors the side with fewer gas molecules")
    axes[1].legend()
    fig.tight_layout()

    plt.show()








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

   **Total running time of the script:** (0 minutes 0.129 seconds)


.. _sphx_glr_download_api_gallery_thermo_equilibrium_plot_04_le_chatelier.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_le_chatelier.ipynb <plot_04_le_chatelier.ipynb>`

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

      :download:`Download Python source code: plot_04_le_chatelier.py <plot_04_le_chatelier.py>`

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

      :download:`Download zipped: plot_04_le_chatelier.zip <plot_04_le_chatelier.zip>`


.. only:: html

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

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