.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/solutions/activity/plot_01_debye_huckel_limiting_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_01_debye_huckel_limiting_law.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_solutions_activity_plot_01_debye_huckel_limiting_law.py:


The Debye-Huckel limiting law: log gamma is linear in the square root of I
============================================================================

Debye and Huckel's screening theory predicts that at low ionic strength

.. math::

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

a straight line in :math:`\sqrt{I}` whose slope scales with the square
of the ion's charge
(:func:`~chemistrykit.solutions.systems.activity.activity_coefficient_debye_huckel_limiting`).
The ionic strength :math:`I = \frac{1}{2}\sum_i c_i z_i^2` that controls
the screening is computed with
:func:`~chemistrykit.solutions.systems.activity.ionic_strength`.

.. GENERATED FROM PYTHON SOURCE LINES 20-41

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.solutions.systems.activity import (
        DEBYE_HUCKEL_A_25C,
        activity_coefficient_debye_huckel_limiting,
        ionic_strength,
    )

    sqrt_I = np.linspace(0.0, 0.1, 50)  # I up to 0.01 M, the limiting-law regime

    fig, ax = plt.subplots(figsize=(7, 5))
    for z, color in [(1, "steelblue"), (2, "darkorange"), (3, "seagreen")]:
        log_gamma = [np.log10(activity_coefficient_debye_huckel_limiting(z, s**2)) for s in sqrt_I]
        ax.plot(sqrt_I, log_gamma, color=color, label=f"z = ±{z}: slope = {-DEBYE_HUCKEL_A_25C * z**2:.3f}")
    ax.set_xlabel(r"$\sqrt{I}$ (mol/L)$^{1/2}$")
    ax.set_ylabel(r"$\log_{10}\gamma$")
    ax.set_title("Debye-Huckel limiting law (water, 25 degC)")
    ax.legend()
    fig.tight_layout()




.. image-sg:: /api/gallery/solutions/activity/images/sphx_glr_plot_01_debye_huckel_limiting_law_001.png
   :alt: Debye-Huckel limiting law (water, 25 degC)
   :srcset: /api/gallery/solutions/activity/images/sphx_glr_plot_01_debye_huckel_limiting_law_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 42-44

Ionic strength of some dilute solutions, and the resulting activity
coefficients of their ions:

.. GENERATED FROM PYTHON SOURCE LINES 44-56

.. code-block:: Python


    solutions = {
        "0.001 M NaCl": ([0.001, 0.001], [1, -1]),
        "0.001 M CaCl2": ([0.001, 0.002], [2, -1]),
        "0.001 M MgSO4": ([0.001, 0.001], [2, -2]),
    }
    for name, (c, z) in solutions.items():
        I = ionic_strength(c, z)
        gammas = ", ".join(f"z={zi:+d}: {activity_coefficient_debye_huckel_limiting(zi, I):.3f}" for zi in z)
        print(f"{name:14s}: I = {I:.4f} M; gamma({gammas})")

    plt.show()




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

 .. code-block:: none

    0.001 M NaCl  : I = 0.0010 M; gamma(z=+1: 0.964, z=-1: 0.964)
    0.001 M CaCl2 : I = 0.0030 M; gamma(z=+2: 0.774, z=-1: 0.938)
    0.001 M MgSO4 : I = 0.0040 M; gamma(z=+2: 0.743, z=-2: 0.743)





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

   **Total running time of the script:** (0 minutes 0.043 seconds)


.. _sphx_glr_download_api_gallery_solutions_activity_plot_01_debye_huckel_limiting_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_01_debye_huckel_limiting_law.ipynb <plot_01_debye_huckel_limiting_law.ipynb>`

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

      :download:`Download Python source code: plot_01_debye_huckel_limiting_law.py <plot_01_debye_huckel_limiting_law.py>`

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

      :download:`Download zipped: plot_01_debye_huckel_limiting_law.zip <plot_01_debye_huckel_limiting_law.zip>`


.. only:: html

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

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