.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/analytical/titration/plot_02_edta_complexometric_titration.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_analytical_titration_plot_02_edta_complexometric_titration.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_analytical_titration_plot_02_edta_complexometric_titration.py:


EDTA complexometric titration of a metal ion
===============================================

:class:`~chemistrykit.analytical.EDTATitration` follows
:math:`M+Y\rightleftharpoons MY` through its conditional formation
constant :math:`K_f'`. The same EDTA titrant quantifies any metal it
binds strongly enough; the size of the `pM` break at equivalence is set
by :math:`K_f'`, which is why Schwarzenbach's titrations are run in a
buffer at a pH where :math:`K_f'` is large.

.. GENERATED FROM PYTHON SOURCE LINES 14-32

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.analytical import EDTATitration

    V = np.linspace(1e-6, 0.080, 4000)
    curves = {}
    for logK in (6, 8, 10, 12):
        titration = EDTATitration(C_metal=0.0100, V_metal=0.050, K_conditional=10.0**logK, C_edta=0.0100)
        curves[logK] = titration.curve(V)
        V_eq = titration.equivalence_volume()
        pM_before, pM_eq, pM_after = titration.response_at(np.array([0.99 * V_eq, V_eq, 1.01 * V_eq]))
        C_M_eq = 0.0100 * 0.050 / (0.050 + V_eq)
        print(
            f"log K'={logK:2d}: pM at equivalence {pM_eq:.3f} (large-K approximation {0.5 * np.log10(10.0**logK / C_M_eq):.3f}), "
            f"jump over +/-1% of V_eq = {pM_after - pM_before:.2f} pM units, endpoint found at {titration.find_equivalence_point(V) * 1000:.2f} mL"
        )





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

 .. code-block:: none

    log K'= 6: pM at equivalence 4.154 (large-K approximation 4.151), jump over +/-1% of V_eq = 0.30 pM units, endpoint found at 49.97 mL
    log K'= 8: pM at equivalence 5.151 (large-K approximation 5.151), jump over +/-1% of V_eq = 1.72 pM units, endpoint found at 49.99 mL
    log K'=10: pM at equivalence 6.151 (large-K approximation 6.151), jump over +/-1% of V_eq = 3.70 pM units, endpoint found at 49.99 mL
    log K'=12: pM at equivalence 7.151 (large-K approximation 7.151), jump over +/-1% of V_eq = 5.70 pM units, endpoint found at 49.99 mL




.. GENERATED FROM PYTHON SOURCE LINES 33-43

.. code-block:: Python

    fig, ax = plt.subplots(figsize=(7, 4.5))
    for logK, curve in curves.items():
        ax.plot(curve.V * 1000, curve.response, label=f"log $K_f'$ = {logK}")
    ax.axvline(50.0, color="gray", linestyle="--", linewidth=0.8)
    ax.set_xlabel("EDTA added (mL)")
    ax.set_ylabel("pM")
    ax.set_title("Complexometric titration of 0.0100 M M$^{2+}$ with 0.0100 M EDTA")
    ax.legend()
    plt.tight_layout()
    plt.show()



.. image-sg:: /api/gallery/analytical/titration/images/sphx_glr_plot_02_edta_complexometric_titration_001.png
   :alt: Complexometric titration of 0.0100 M M$^{2+}$ with 0.0100 M EDTA
   :srcset: /api/gallery/analytical/titration/images/sphx_glr_plot_02_edta_complexometric_titration_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.070 seconds)


.. _sphx_glr_download_api_gallery_analytical_titration_plot_02_edta_complexometric_titration.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_edta_complexometric_titration.ipynb <plot_02_edta_complexometric_titration.ipynb>`

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

      :download:`Download Python source code: plot_02_edta_complexometric_titration.py <plot_02_edta_complexometric_titration.py>`

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

      :download:`Download zipped: plot_02_edta_complexometric_titration.zip <plot_02_edta_complexometric_titration.zip>`


.. only:: html

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

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