.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/solutions/activity/plot_02_guntelberg_extended_law.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_solutions_activity_plot_02_guntelberg_extended_law.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_solutions_activity_plot_02_guntelberg_extended_law.py:


Guntelberg's extended law: correcting Debye-Huckel for finite ion size
========================================================================

The limiting law treats ions as point charges and over-corrects above
:math:`I \approx 0.01` mol/L. Guntelberg's extended form adds a
finite-size denominator with a single universal size parameter,
:math:`Ba \approx 1`,

.. math::

   \log_{10}\gamma = \frac{-A z^2 \sqrt{I}}{1 + \sqrt{I}},

implemented by
:func:`~chemistrykit.solutions.systems.activity.activity_coefficient_debye_huckel_extended`.
It coincides with the limiting law
(:func:`~chemistrykit.solutions.systems.activity.activity_coefficient_debye_huckel_limiting`)
at high dilution and stays much closer to reality an order of magnitude
further in ionic strength.

.. GENERATED FROM PYTHON SOURCE LINES 23-51

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.solutions.systems.activity import (
        activity_coefficient_debye_huckel_extended,
        activity_coefficient_debye_huckel_limiting,
    )

    I_range = np.logspace(-4, -0.3, 100)

    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 4.5))
    for z, color in [(1, "steelblue"), (2, "darkorange"), (3, "seagreen")]:
        g_lim = np.array([activity_coefficient_debye_huckel_limiting(z, I) for I in I_range])
        g_gun = np.array([activity_coefficient_debye_huckel_extended(z, I, Ba=1.0) for I in I_range])
        ax1.semilogx(I_range, g_lim, linestyle="--", color=color, alpha=0.6, label=f"z={z}, limiting")
        ax1.semilogx(I_range, g_gun, color=color, label=f"z={z}, Guntelberg")
        ax2.semilogx(I_range, g_gun / g_lim, color=color, label=f"z={z}")
    ax1.set_xlabel("ionic strength I (mol/L)")
    ax1.set_ylabel(r"activity coefficient $\gamma$")
    ax1.set_title("Limiting law vs. Guntelberg's extended law")
    ax1.legend(fontsize=8)
    ax2.axvline(0.01, color="gray", linestyle=":", label="I = 0.01 M")
    ax2.set_xlabel("ionic strength I (mol/L)")
    ax2.set_ylabel(r"$\gamma_{\mathrm{Guntelberg}}/\gamma_{\mathrm{limiting}}$")
    ax2.set_title("Size of the finite-ion-size correction")
    ax2.legend(fontsize=8)
    fig.tight_layout()




.. image-sg:: /api/gallery/solutions/activity/images/sphx_glr_plot_02_guntelberg_extended_law_001.png
   :alt: Limiting law vs. Guntelberg's extended law, Size of the finite-ion-size correction
   :srcset: /api/gallery/solutions/activity/images/sphx_glr_plot_02_guntelberg_extended_law_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 52-54

Effect of the ion-size parameter Ba for a singly charged ion at I = 0.1 M
(Guntelberg's choice is Ba = 1):

.. GENERATED FROM PYTHON SOURCE LINES 54-59

.. code-block:: Python


    for Ba in (0.0, 0.5, 1.0, 1.5, 2.0):
        print(f"Ba = {Ba:.1f}: gamma = {activity_coefficient_debye_huckel_extended(1, 0.1, Ba=Ba):.4f}")

    plt.show()




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

 .. code-block:: none

    Ba = 0.0: gamma = 0.6903
    Ba = 0.5: gamma = 0.7261
    Ba = 1.0: gamma = 0.7546
    Ba = 1.5: gamma = 0.7777
    Ba = 2.0: gamma = 0.7969





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

   **Total running time of the script:** (0 minutes 0.118 seconds)


.. _sphx_glr_download_api_gallery_solutions_activity_plot_02_guntelberg_extended_law.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_02_guntelberg_extended_law.ipynb <plot_02_guntelberg_extended_law.ipynb>`

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

      :download:`Download Python source code: plot_02_guntelberg_extended_law.py <plot_02_guntelberg_extended_law.py>`

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

      :download:`Download zipped: plot_02_guntelberg_extended_law.zip <plot_02_guntelberg_extended_law.zip>`


.. only:: html

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

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