.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/solutions/titration/plot_01_titration_curves.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_titration_plot_01_titration_curves.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_solutions_titration_plot_01_titration_curves.py:


Volumetric titration: locating the equivalence point
======================================================

The volumetric analysis Gay-Lussac and Mohr systematized finds how much
acid a sample contains from the burette volume at which it has been
exactly neutralized -- the equivalence point, seen by eye as an
indicator's sudden colour change and here located numerically as the
steepest point of the pH curve
(:meth:`~chemistrykit.solutions.core.base_system.Titration.find_equivalence_point`).
Comparing a strong-acid/strong-base titration
(:class:`~chemistrykit.solutions.systems.titration.StrongAcidStrongBaseTitration`)
against a weak-acid/strong-base titration
(:class:`~chemistrykit.solutions.systems.titration.WeakAcidStrongBaseTitration`)
of the same concentrations: the weak-acid curve starts at a higher pH,
has a buffer region around its half-equivalence point (where pH = pKa),
and its equivalence point is basic rather than neutral -- all visible
directly from the curve shapes.

.. GENERATED FROM PYTHON SOURCE LINES 22-55

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.solutions.systems.titration import (
        StrongAcidStrongBaseTitration,
        WeakAcidStrongBaseTitration,
    )

    Ca, Va, Cb = 0.100, 0.050, 0.100
    Ka = 1.8e-5  # acetic acid

    strong = StrongAcidStrongBaseTitration(Ca=Ca, Va=Va, Cb=Cb)
    weak = WeakAcidStrongBaseTitration(Ca=Ca, Va=Va, Ka=Ka, Cb=Cb)

    Vb = np.linspace(1e-6, 0.09, 2000)
    result_strong = strong.curve(Vb)
    result_weak = weak.curve(Vb)

    Vb_eq_strong = strong.find_equivalence_point(Vb)
    Vb_eq_weak = weak.find_equivalence_point(Vb)

    fig, ax = plt.subplots(figsize=(8, 6))
    ax.plot(result_strong.Vb * 1000.0, result_strong.pH, label="strong acid + strong base", color="steelblue")
    ax.plot(result_weak.Vb * 1000.0, result_weak.pH, label="weak acid + strong base", color="darkorange")
    ax.axvline(Vb_eq_strong * 1000.0, color="steelblue", linestyle=":", alpha=0.6)
    ax.axvline(Vb_eq_weak * 1000.0, color="darkorange", linestyle=":", alpha=0.6)
    ax.axhline(7.0, color="gray", linestyle="--", linewidth=0.7, label="pH 7")
    ax.set_xlabel("volume of NaOH added (mL)")
    ax.set_ylabel("pH")
    ax.set_title("Titration of 50.0 mL of 0.100 M acid with 0.100 M NaOH")
    ax.legend()
    fig.tight_layout()




.. image-sg:: /api/gallery/solutions/titration/images/sphx_glr_plot_01_titration_curves_001.png
   :alt: Titration of 50.0 mL of 0.100 M acid with 0.100 M NaOH
   :srcset: /api/gallery/solutions/titration/images/sphx_glr_plot_01_titration_curves_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 56-60

The numerically detected equivalence points (steepest-ascent points)
for each curve, compared against the exact stoichiometric volume
(identical for both, since it only depends on moles of acid and base,
not on Ka):

.. GENERATED FROM PYTHON SOURCE LINES 60-66

.. code-block:: Python


    print(f"Stoichiometric equivalence volume: {strong.equivalence_volume() * 1000.0:.3f} mL")
    print(f"Strong-acid titration: numeric equivalence at {Vb_eq_strong * 1000.0:.3f} mL, pH there = 7.00 (neutral)")
    print(f"Weak-acid titration: numeric equivalence at {Vb_eq_weak * 1000.0:.3f} mL, pH there > 7 (basic)")

    plt.show()




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

 .. code-block:: none

    Stoichiometric equivalence volume: 50.000 mL
    Strong-acid titration: numeric equivalence at 50.020 mL, pH there = 7.00 (neutral)
    Weak-acid titration: numeric equivalence at 50.020 mL, pH there > 7 (basic)





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

   **Total running time of the script:** (0 minutes 0.408 seconds)


.. _sphx_glr_download_api_gallery_solutions_titration_plot_01_titration_curves.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_titration_curves.ipynb <plot_01_titration_curves.ipynb>`

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

      :download:`Download Python source code: plot_01_titration_curves.py <plot_01_titration_curves.py>`

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

      :download:`Download zipped: plot_01_titration_curves.zip <plot_01_titration_curves.zip>`


.. only:: html

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

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