.. 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_07_van_slyke_buffer_capacity.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_07_van_slyke_buffer_capacity.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_solutions_acid_base_plot_07_van_slyke_buffer_capacity.py:


Van Slyke's buffer capacity: how strongly a solution resists pH change
========================================================================

Donald Van Slyke defined the buffer value :math:`\beta = dC_b/d\mathrm{pH}`,
the strong base per litre needed to raise the pH by one unit. For a weak
acid/conjugate base pair of total concentration :math:`C`
(:func:`~chemistrykit.solutions.systems.acid_base.buffer_capacity`):

.. math::

   \beta = \ln 10\left([H^+] + \frac{K_w}{[H^+]} + \frac{C K_a [H^+]}{(K_a+[H^+])^2}\right).

The buffer term peaks at :math:`\mathrm{pH} = pK_a` with height
:math:`\ln 10\,C/4`, while water alone buffers only at the extremes of
the pH scale.

.. GENERATED FROM PYTHON SOURCE LINES 20-40

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.solutions.systems.acid_base import buffer_capacity

    pKa = 4.76
    pH = np.linspace(1, 13, 600)

    fig, ax = plt.subplots(figsize=(7, 5))
    for C, color in [(0.01, "seagreen"), (0.05, "darkorange"), (0.10, "steelblue")]:
        ax.plot(pH, buffer_capacity(pH, C=C, Ka=10**-pKa), color=color, label=f"acetate, C = {C} M")
    ax.plot(pH, buffer_capacity(pH, C=0.0, Ka=10**-pKa), color="gray", linestyle="--", label="water only (C = 0)")
    ax.axvline(pKa, color="gray", linestyle=":", linewidth=0.8)
    ax.set_ylim(0, 0.08)
    ax.set_xlabel("pH")
    ax.set_ylabel(r"buffer capacity $\beta$ (mol/L per pH unit)")
    ax.set_title("Van Slyke buffer capacity of acetate buffers")
    ax.legend(fontsize=8)
    fig.tight_layout()




.. image-sg:: /api/gallery/solutions/acid_base/images/sphx_glr_plot_07_van_slyke_buffer_capacity_001.png
   :alt: Van Slyke buffer capacity of acetate buffers
   :srcset: /api/gallery/solutions/acid_base/images/sphx_glr_plot_07_van_slyke_buffer_capacity_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 41-42

Checking the peak against :math:`\ln 10\,C/4`:

.. GENERATED FROM PYTHON SOURCE LINES 42-47

.. code-block:: Python


    for C in (0.01, 0.05, 0.10):
        print(f"C = {C:.2f} M: beta(pKa) = {float(buffer_capacity(pKa, C, 10**-pKa)):.5f}, ln10*C/4 = {np.log(10) * C / 4:.5f}")

    plt.show()




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

 .. code-block:: none

    C = 0.01 M: beta(pKa) = 0.00580, ln10*C/4 = 0.00576
    C = 0.05 M: beta(pKa) = 0.02882, ln10*C/4 = 0.02878
    C = 0.10 M: beta(pKa) = 0.05760, ln10*C/4 = 0.05756





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

   **Total running time of the script:** (0 minutes 0.049 seconds)


.. _sphx_glr_download_api_gallery_solutions_acid_base_plot_07_van_slyke_buffer_capacity.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_07_van_slyke_buffer_capacity.ipynb <plot_07_van_slyke_buffer_capacity.ipynb>`

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

      :download:`Download Python source code: plot_07_van_slyke_buffer_capacity.py <plot_07_van_slyke_buffer_capacity.py>`

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

      :download:`Download zipped: plot_07_van_slyke_buffer_capacity.zip <plot_07_van_slyke_buffer_capacity.zip>`


.. only:: html

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

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