.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/solutions/acid_base/plot_03_arrhenius_electrolytic_dissociation.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_acid_base_plot_03_arrhenius_electrolytic_dissociation.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_solutions_acid_base_plot_03_arrhenius_electrolytic_dissociation.py:


Arrhenius's electrolytic dissociation: how much of an electrolyte is ions?
============================================================================

Arrhenius proposed that an acid dissolved in water is split, at least in
part, into free ions even with no current flowing, and that the
*degree of dissociation* :math:`\alpha` distinguishes a strong
electrolyte (:math:`\alpha \approx 1`) from a weak one
(:math:`\alpha \ll 1`). The number of dissolved particles per formula
unit is then :math:`i = 1 + \alpha` for a 1:1 electrolyte -- the van 't
Hoff factor that explained anomalous colligative data.

Here :math:`\alpha` is computed with
:meth:`~chemistrykit.solutions.core.base_system.WeakElectrolyte.percent_dissociation`
for 0.10 M solutions of acids spanning twelve orders of magnitude in
:math:`K_a`.

.. GENERATED FROM PYTHON SOURCE LINES 20-45

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.solutions.systems.acid_base import WeakAcid

    Ca = 0.10
    Ka_values = np.logspace(-10, 2, 200)
    alpha = np.array([WeakAcid(Ca=Ca, Ka=Ka).percent_dissociation() / 100.0 for Ka in Ka_values])

    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(11, 4.5))
    ax1.semilogx(Ka_values, alpha, color="steelblue")
    for name, Ka in [("HCN", 6.2e-10), ("acetic", 1.8e-5), ("HF", 6.8e-4), ("HSO$_4^-$", 1.2e-2)]:
        a = WeakAcid(Ca=Ca, Ka=Ka).percent_dissociation() / 100.0
        ax1.plot(Ka, a, "o", color="darkorange")
        ax1.annotate(name, (Ka, a), textcoords="offset points", xytext=(5, -12), fontsize=8)
    ax1.set_xlabel("acid dissociation constant $K_a$")
    ax1.set_ylabel(r"degree of dissociation $\alpha$")
    ax1.set_title("0.10 M acid: from weak to strong electrolyte")

    ax2.semilogx(Ka_values, 1.0 + alpha, color="seagreen")
    ax2.set_xlabel("acid dissociation constant $K_a$")
    ax2.set_ylabel(r"van 't Hoff factor $i = 1 + \alpha$")
    ax2.set_title("Dissolved particles per formula unit")
    fig.tight_layout()




.. image-sg:: /api/gallery/solutions/acid_base/images/sphx_glr_plot_03_arrhenius_electrolytic_dissociation_001.png
   :alt: 0.10 M acid: from weak to strong electrolyte, Dissolved particles per formula unit
   :srcset: /api/gallery/solutions/acid_base/images/sphx_glr_plot_03_arrhenius_electrolytic_dissociation_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 46-47

Printed values for a few familiar acids at 0.10 M:

.. GENERATED FROM PYTHON SOURCE LINES 47-53

.. code-block:: Python


    for name, Ka in [("hydrocyanic acid", 6.2e-10), ("acetic acid", 1.8e-5), ("hydrofluoric acid", 6.8e-4)]:
        acid = WeakAcid(Ca=Ca, Ka=Ka)
        print(f"{name:18s}: {acid.percent_dissociation():6.3f}% dissociated, i = {1 + acid.percent_dissociation() / 100:.4f}")

    plt.show()




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

 .. code-block:: none

    hydrocyanic acid  :  0.008% dissociated, i = 1.0001
    acetic acid       :  1.333% dissociated, i = 1.0133
    hydrofluoric acid :  7.913% dissociated, i = 1.0791





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

   **Total running time of the script:** (0 minutes 0.087 seconds)


.. _sphx_glr_download_api_gallery_solutions_acid_base_plot_03_arrhenius_electrolytic_dissociation.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_03_arrhenius_electrolytic_dissociation.ipynb <plot_03_arrhenius_electrolytic_dissociation.ipynb>`

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

      :download:`Download Python source code: plot_03_arrhenius_electrolytic_dissociation.py <plot_03_arrhenius_electrolytic_dissociation.py>`

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

      :download:`Download zipped: plot_03_arrhenius_electrolytic_dissociation.zip <plot_03_arrhenius_electrolytic_dissociation.zip>`


.. only:: html

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

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