.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/analytical/titration/plot_03_gran_plot.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_03_gran_plot.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_analytical_titration_plot_03_gran_plot.py:


Gran plot: the equivalence point by linear extrapolation
===========================================================

:func:`~chemistrykit.analytical.gran_plot` linearizes the buffer region
of a weak-acid titration: :math:`V_b\,10^{-pH}=K_a(V_e-V_b)`. Plotting
the left side against :math:`V_b` gives a straight line whose
x-intercept is the equivalence volume and whose slope is :math:`-K_a`,
so the endpoint follows from data taken well before it.

.. GENERATED FROM PYTHON SOURCE LINES 13-33

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.analytical import gran_plot
    from chemistrykit.solutions.systems.titration import WeakAcidStrongBaseTitration

    # Acetic acid (Ka = 1.8e-5) titrated by NaOH: exact charge-balance pH.
    titration = WeakAcidStrongBaseTitration(Ca=0.100, Va=0.050, Ka=1.8e-5, Cb=0.100)
    V_eq_true = titration.equivalence_volume()

    # "Measured" pH readings between 20% and 90% of the equivalence volume,
    # with 0.005 pH-unit meter noise:
    rng = np.random.default_rng(12)
    V_data = np.linspace(0.2, 0.9, 10) * V_eq_true
    pH_data = titration.pH_at(V_data) + rng.normal(scale=0.005, size=V_data.size)

    result = gran_plot(V_data, pH_data)
    print(f"Gran equivalence volume: {result.equivalence_volume * 1000:.3f} mL (true {V_eq_true * 1000:.3f} mL)")
    print(f"Gran Ka from slope:      {result.Ka:.3e} (true 1.8e-05)")





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

 .. code-block:: none

    Gran equivalence volume: 50.211 mL (true 50.000 mL)
    Gran Ka from slope:      1.773e-05 (true 1.8e-05)




.. GENERATED FROM PYTHON SOURCE LINES 34-55

.. code-block:: Python

    V_full = np.linspace(1e-6, 0.070, 1000)
    fig, axes = plt.subplots(1, 2, figsize=(11, 4))
    axes[0].plot(V_full * 1000, titration.pH_at(V_full), label="titration curve")
    axes[0].plot(V_data * 1000, pH_data, "o", label="readings used for the Gran plot")
    axes[0].axvline(V_eq_true * 1000, color="gray", linestyle="--", linewidth=0.8)
    axes[0].set_xlabel("NaOH added (mL)")
    axes[0].set_ylabel("pH")
    axes[0].set_title("Weak acid + strong base")
    axes[0].legend()

    V_line = np.linspace(0.0, result.equivalence_volume * 1.05, 50)
    axes[1].plot(result.V * 1000, result.gran_function * 1e6, "o", label=r"$V_b\,10^{-pH}$")
    axes[1].plot(V_line * 1000, (result.slope * V_line + result.intercept) * 1e6, "-", label="least-squares line")
    axes[1].axhline(0.0, color="gray", linewidth=0.8)
    axes[1].plot([result.equivalence_volume * 1000], [0.0], "rx", markersize=10, label=f"$V_e$ = {result.equivalence_volume * 1000:.2f} mL")
    axes[1].set_xlabel(r"$V_b$ (mL)")
    axes[1].set_ylabel(r"$V_b\,10^{-pH}$ ($\mu$L)")
    axes[1].set_title("Gran plot")
    axes[1].legend()
    plt.tight_layout()
    plt.show()



.. image-sg:: /api/gallery/analytical/titration/images/sphx_glr_plot_03_gran_plot_001.png
   :alt: Weak acid + strong base, Gran plot
   :srcset: /api/gallery/analytical/titration/images/sphx_glr_plot_03_gran_plot_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.161 seconds)


.. _sphx_glr_download_api_gallery_analytical_titration_plot_03_gran_plot.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_gran_plot.ipynb <plot_03_gran_plot.ipynb>`

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

      :download:`Download Python source code: plot_03_gran_plot.py <plot_03_gran_plot.py>`

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

      :download:`Download zipped: plot_03_gran_plot.zip <plot_03_gran_plot.zip>`


.. only:: html

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

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