.. 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_05_sorensen_ph_scale.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_05_sorensen_ph_scale.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_solutions_acid_base_plot_05_sorensen_ph_scale.py:


Sorensen's pH scale: a logarithm for hydrogen-ion concentration
=================================================================

Sorensen's 1909 definition :math:`\mathrm{pH} = -\log_{10}[H^+]`
(:func:`~chemistrykit.solutions.systems.acid_base.ph_from_h`) turns
hydrogen-ion concentrations spanning fourteen orders of magnitude into
numbers between 0 and 14. Below, the pH of several everyday solutions is
computed from their equilibrium :math:`[H^+]` and placed on the scale,
and the companion relation :math:`\mathrm{pH} + \mathrm{pOH} = pK_w = 14`
is checked with :func:`~chemistrykit.solutions.systems.acid_base.poh_from_oh`.

.. GENERATED FROM PYTHON SOURCE LINES 15-43

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.solutions.systems.acid_base import WeakAcid, WeakBase, h_from_ph, ph_from_h, poh_from_oh

    Kw = 1.0e-14
    samples = {
        "0.1 M HCl": 0.1,
        "vinegar (0.8 M acetic)": WeakAcid(Ca=0.8, Ka=1.8e-5).h_concentration(),
        "0.01 M acetic acid": WeakAcid(Ca=0.01, Ka=1.8e-5).h_concentration(),
        "pure water": np.sqrt(Kw),
        "0.1 M ammonia": Kw / WeakBase(Cb=0.1, Kb=1.8e-5).oh_concentration(),
        "0.1 M NaOH": Kw / 0.1,
    }

    pH_axis = np.linspace(0, 14, 200)
    fig, ax = plt.subplots(figsize=(8, 5))
    ax.semilogy(pH_axis, h_from_ph(pH_axis), color="steelblue", label=r"$[H^+] = 10^{-\mathrm{pH}}$")
    for name, h in samples.items():
        pH = float(ph_from_h(h))
        ax.plot(pH, h, "o", color="darkorange")
        ax.annotate(name, (pH, h), textcoords="offset points", xytext=(6, 4), fontsize=8)
    ax.set_xlabel("pH")
    ax.set_ylabel("[H+] (mol/L)")
    ax.set_title("Sorensen's pH scale")
    ax.legend()
    fig.tight_layout()




.. image-sg:: /api/gallery/solutions/acid_base/images/sphx_glr_plot_05_sorensen_ph_scale_001.png
   :alt: Sorensen's pH scale
   :srcset: /api/gallery/solutions/acid_base/images/sphx_glr_plot_05_sorensen_ph_scale_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 44-45

pH and pOH of each sample always sum to :math:`pK_w = 14` at 25 degC:

.. GENERATED FROM PYTHON SOURCE LINES 45-52

.. code-block:: Python


    for name, h in samples.items():
        pH = float(ph_from_h(h))
        pOH = float(poh_from_oh(Kw / h))
        print(f"{name:24s}: [H+] = {h:.2e} M, pH = {pH:5.2f}, pOH = {pOH:5.2f}, sum = {pH + pOH:.2f}")

    plt.show()




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

 .. code-block:: none

    0.1 M HCl               : [H+] = 1.00e-01 M, pH =  1.00, pOH = 13.00, sum = 14.00
    vinegar (0.8 M acetic)  : [H+] = 3.79e-03 M, pH =  2.42, pOH = 11.58, sum = 14.00
    0.01 M acetic acid      : [H+] = 4.15e-04 M, pH =  3.38, pOH = 10.62, sum = 14.00
    pure water              : [H+] = 1.00e-07 M, pH =  7.00, pOH =  7.00, sum = 14.00
    0.1 M ammonia           : [H+] = 7.50e-12 M, pH = 11.12, pOH =  2.88, sum = 14.00
    0.1 M NaOH              : [H+] = 1.00e-13 M, pH = 13.00, pOH =  1.00, sum = 14.00





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

   **Total running time of the script:** (0 minutes 0.059 seconds)


.. _sphx_glr_download_api_gallery_solutions_acid_base_plot_05_sorensen_ph_scale.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_05_sorensen_ph_scale.ipynb <plot_05_sorensen_ph_scale.ipynb>`

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

      :download:`Download Python source code: plot_05_sorensen_ph_scale.py <plot_05_sorensen_ph_scale.py>`

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

      :download:`Download zipped: plot_05_sorensen_ph_scale.zip <plot_05_sorensen_ph_scale.zip>`


.. only:: html

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

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