.. 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_06_bjerrum_speciation_diagram.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_06_bjerrum_speciation_diagram.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_solutions_acid_base_plot_06_bjerrum_speciation_diagram.py:


Bjerrum's speciation diagrams for polyprotic acids
====================================================

Niels Bjerrum's 1914 monograph on acid-base titrations introduced
diagrams showing what fraction of a polyprotic acid is present in each
protonation state as a function of pH -- today called Bjerrum plots or
distribution diagrams. The fractions
(:func:`~chemistrykit.solutions.systems.acid_base.polyprotic_fractions`)
depend only on pH and the stepwise :math:`K_a` values, and adjacent
species are equally abundant exactly where :math:`\mathrm{pH} = pK_j`.

.. GENERATED FROM PYTHON SOURCE LINES 15-40

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.solutions.systems.acid_base import polyprotic_fractions

    pH = np.linspace(0, 14, 500)

    systems = {
        "carbonic acid": ([6.35, 10.33], ["H$_2$CO$_3$", "HCO$_3^-$", "CO$_3^{2-}$"]),
        "phosphoric acid": ([2.15, 7.20, 12.35], ["H$_3$PO$_4$", "H$_2$PO$_4^-$", "HPO$_4^{2-}$", "PO$_4^{3-}$"]),
    }

    fig, axes = plt.subplots(1, 2, figsize=(12, 4.5))
    for ax, (name, (pKas, labels)) in zip(axes, systems.items()):
        alpha = polyprotic_fractions(pH, [10.0**-pK for pK in pKas])
        for row, label in zip(alpha, labels):
            ax.plot(pH, row, label=label)
        for pK in pKas:
            ax.axvline(pK, color="gray", linestyle=":", linewidth=0.8)
        ax.set_xlabel("pH")
        ax.set_ylabel(r"fraction $\alpha_j$")
        ax.set_title(f"Bjerrum plot: {name}")
        ax.legend(fontsize=8)
    fig.tight_layout()




.. image-sg:: /api/gallery/solutions/acid_base/images/sphx_glr_plot_06_bjerrum_speciation_diagram_001.png
   :alt: Bjerrum plot: carbonic acid, Bjerrum plot: phosphoric acid
   :srcset: /api/gallery/solutions/acid_base/images/sphx_glr_plot_06_bjerrum_speciation_diagram_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 41-43

At blood pH 7.4, dissolved inorganic carbon is overwhelmingly
bicarbonate -- the basis of the bicarbonate blood buffer:

.. GENERATED FROM PYTHON SOURCE LINES 43-48

.. code-block:: Python


    alpha_blood = polyprotic_fractions(7.4, [10**-6.35, 10**-10.33])[:, 0]
    print("pH 7.4 carbonate speciation: " + ", ".join(f"{a:.4f}" for a in alpha_blood))

    plt.show()




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

 .. code-block:: none

    pH 7.4 carbonate speciation: 0.0817, 0.9172, 0.0011





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

   **Total running time of the script:** (0 minutes 0.078 seconds)


.. _sphx_glr_download_api_gallery_solutions_acid_base_plot_06_bjerrum_speciation_diagram.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_06_bjerrum_speciation_diagram.ipynb <plot_06_bjerrum_speciation_diagram.ipynb>`

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

      :download:`Download Python source code: plot_06_bjerrum_speciation_diagram.py <plot_06_bjerrum_speciation_diagram.py>`

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

      :download:`Download zipped: plot_06_bjerrum_speciation_diagram.zip <plot_06_bjerrum_speciation_diagram.zip>`


.. only:: html

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

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