.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/electrochem/nernst/plot_01_nernst_equation.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_electrochem_nernst_plot_01_nernst_equation.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_electrochem_nernst_plot_01_nernst_equation.py:


The Nernst equation: cell potential versus concentration
==========================================================

:func:`~chemistrykit.electrochem.systems.nernst.nernst_potential`
implements :math:`E = E^\circ - \frac{RT}{nF}\ln Q`. This example checks
that it reduces to :math:`E^\circ` at :math:`Q=1`, plots the logarithmic
dependence on the reaction quotient, and then builds a concentration cell
(:func:`~chemistrykit.electrochem.systems.nernst.concentration_cell_potential`)
whose voltage comes entirely from a concentration difference -- about
59 mV per decade for a one-electron couple at 25 degC, as Nernst predicted.

.. GENERATED FROM PYTHON SOURCE LINES 15-29

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.electrochem.systems.nernst import concentration_cell_potential, nernst_potential
    from chemistrykit.electrochem.visualizers.electrochem_plots import plot_nernst_concentration_dependence

    E_standard, n = 0.34, 2  # Cu2+/Cu half-reaction vs. SHE
    for Q in np.logspace(-3, 3, 7):
        print(f"Q={Q:9.3g}  E = {nernst_potential(E_standard, n, Q):+.4f} V")
    print(f"\nNernst at Q=1: {nernst_potential(E_standard, n, Q=1.0)} V (= E_standard)")

    ax = plot_nernst_concentration_dependence(E_standard=E_standard, n=n)
    plt.tight_layout()




.. image-sg:: /api/gallery/electrochem/nernst/images/sphx_glr_plot_01_nernst_equation_001.png
   :alt: Nernst equation: cell potential vs. reaction quotient
   :srcset: /api/gallery/electrochem/nernst/images/sphx_glr_plot_01_nernst_equation_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    Q=    0.001  E = +0.4287 V
    Q=     0.01  E = +0.3992 V
    Q=      0.1  E = +0.3696 V
    Q=        1  E = +0.3400 V
    Q=       10  E = +0.3104 V
    Q=      100  E = +0.2808 V
    Q=    1e+03  E = +0.2513 V

    Nernst at Q=1: 0.34 V (= E_standard)




.. GENERATED FROM PYTHON SOURCE LINES 30-32

A concentration cell: identical half-cells, E_standard = 0, so the
voltage is pure Nernst term.

.. GENERATED FROM PYTHON SOURCE LINES 32-42

.. code-block:: Python

    ratios = np.array([2.0, 5.0, 10.0, 50.0, 100.0])
    E_conc = concentration_cell_potential(n=1, C_cathode=ratios * 0.01, C_anode=0.01)
    fig, ax2 = plt.subplots()
    ax2.plot(ratios, E_conc * 1e3, "o-")
    ax2.set_xscale("log")
    ax2.set_xlabel(r"$C_{cathode}/C_{anode}$")
    ax2.set_ylabel("E (mV)")
    ax2.set_title("Concentration cell: about 59 mV per decade (n = 1)")
    fig.tight_layout()
    plt.show()



.. image-sg:: /api/gallery/electrochem/nernst/images/sphx_glr_plot_01_nernst_equation_002.png
   :alt: Concentration cell: about 59 mV per decade (n = 1)
   :srcset: /api/gallery/electrochem/nernst/images/sphx_glr_plot_01_nernst_equation_002.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.102 seconds)


.. _sphx_glr_download_api_gallery_electrochem_nernst_plot_01_nernst_equation.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_nernst_equation.ipynb <plot_01_nernst_equation.ipynb>`

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

      :download:`Download Python source code: plot_01_nernst_equation.py <plot_01_nernst_equation.py>`

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

      :download:`Download zipped: plot_01_nernst_equation.zip <plot_01_nernst_equation.zip>`


.. only:: html

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

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