.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/thermo/equilibrium/plot_01_law_of_mass_action.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_01_law_of_mass_action.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_thermo_equilibrium_plot_01_law_of_mass_action.py:


Guldberg and Waage's law of mass action: Q = K at equilibrium
=============================================================

For :math:`N_2O_4 \rightleftharpoons 2NO_2` the reaction quotient
:math:`Q = x_{NO_2}^2/x_{N_2O_4}` (at :math:`P = P^\circ`), computed by
:func:`~chemistrykit.thermo.systems.equilibrium.reaction_quotient`,
rises monotonically with the extent of reaction. The law of mass action
says the mixture stops changing where :math:`Q` reaches the
equilibrium constant :math:`K`. Starting from different mixtures of
reactant and product, the equilibrium compositions found by
:func:`~chemistrykit.thermo.systems.equilibrium.solve_equilibrium_composition`
all give the same :math:`Q = K`.

.. GENERATED FROM PYTHON SOURCE LINES 17-40

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

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

    T = 298.15
    K = 4.0
    gibbs_formation = [0.0, -R * T * np.log(K) / 2.0]  # [N2O4, NO2]
    nu = np.array([-1.0, 2.0])

    xi = np.linspace(0.01, 0.99, 300)
    Q = [reaction_quotient([(1 - x) / (1 + x), 2 * x / (1 + x)], nu) for x in xi]

    fig, ax = plt.subplots(figsize=(7, 5))
    ax.semilogy(xi, Q, color="steelblue", label=r"$Q(\xi)$ starting from pure $N_2O_4$")
    ax.axhline(K, color="crimson", linestyle="--", label=f"K = {K}")
    ax.set_xlabel(r"extent of reaction $\xi$ (mol)")
    ax.set_ylabel("reaction quotient Q")
    ax.set_title(r"$N_2O_4 \rightleftharpoons 2NO_2$: the reaction stops where Q = K")
    ax.legend()
    fig.tight_layout()




.. image-sg:: /api/gallery/thermo/equilibrium/images/sphx_glr_plot_01_law_of_mass_action_001.png
   :alt: $N_2O_4 \rightleftharpoons 2NO_2$: the reaction stops where Q = K
   :srcset: /api/gallery/thermo/equilibrium/images/sphx_glr_plot_01_law_of_mass_action_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 41-44

Different starting mixtures end with different amounts of each gas, but
always with the same value of the mass-action ratio (at fixed total
pressure, that also pins the mole fractions):

.. GENERATED FROM PYTHON SOURCE LINES 44-51

.. code-block:: Python


    for n0 in ([1.0, 0.0], [0.05, 1.9], [1.0, 1.0], [0.2, 3.0]):
        res = solve_equilibrium_composition(("N2O4", "NO2"), [[-1.0], [2.0]], n0, gibbs_formation, T)
        Q_eq = reaction_quotient(res.x, nu)
        print(f"start n = {n0}: equilibrium n = {np.round(res.n, 4)} mol, Q = {Q_eq:.4f}")

    plt.show()




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

 .. code-block:: none

    start n = [1.0, 0.0]: equilibrium n = [0.2929 1.4142] mol, Q = 3.9999
    start n = [0.05, 1.9]: equilibrium n = [0.2929 1.4142] mol, Q = 4.0000
    start n = [1.0, 1.0]: equilibrium n = [0.4393 2.1213] mol, Q = 4.0000
    start n = [0.2, 3.0]: equilibrium n = [0.4979 2.4042] mol, Q = 4.0000





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

   **Total running time of the script:** (0 minutes 0.076 seconds)


.. _sphx_glr_download_api_gallery_thermo_equilibrium_plot_01_law_of_mass_action.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_01_law_of_mass_action.ipynb <plot_01_law_of_mass_action.ipynb>`

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

      :download:`Download Python source code: plot_01_law_of_mass_action.py <plot_01_law_of_mass_action.py>`

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

      :download:`Download zipped: plot_01_law_of_mass_action.zip <plot_01_law_of_mass_action.zip>`


.. only:: html

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

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