.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/electrochem/electrolysis/plot_01_faradays_laws.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_electrolysis_plot_01_faradays_laws.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_electrochem_electrolysis_plot_01_faradays_laws.py:


Faraday's laws of electrolysis
================================

Faraday's first law: the mass liberated at an electrode is proportional
to the charge passed, :math:`m = QM/(nF)`. His second law: for a fixed
charge, different substances are liberated in proportion to their
equivalent weights :math:`M/n`. This example verifies both with
:func:`~chemistrykit.electrochem.systems.electrolysis.faradays_law_mass`
and :func:`~chemistrykit.electrochem.systems.electrolysis.mass_from_charge`,
recovering the single universal constant -- the Faraday -- that links
charge to chemical change.

.. GENERATED FROM PYTHON SOURCE LINES 16-22

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.constants import FARADAY
    from chemistrykit.electrochem.systems.electrolysis import faradays_law_mass, mass_from_charge








.. GENERATED FROM PYTHON SOURCE LINES 23-26

First law: copper electrorefining, Cu2+ + 2e- -> Cu (M = 63.546 g/mol).
Mass deposited in one hour is a straight line through the origin in
the current.

.. GENERATED FROM PYTHON SOURCE LINES 26-35

.. code-block:: Python

    currents = np.linspace(1.0, 20.0, 8)
    mass_deposited = faradays_law_mass(currents, 3600.0, 63.546, n=2)

    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 4))
    ax1.plot(currents, mass_deposited, "o-")
    ax1.set_xlabel("Current (A)")
    ax1.set_ylabel("Mass Cu deposited in 1 h (g)")
    ax1.set_title("First law: m proportional to Q")




.. image-sg:: /api/gallery/electrochem/electrolysis/images/sphx_glr_plot_01_faradays_laws_001.png
   :alt: First law: m proportional to Q
   :srcset: /api/gallery/electrochem/electrolysis/images/sphx_glr_plot_01_faradays_laws_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    Text(0.5, 1.0, 'First law: m proportional to Q')



.. GENERATED FROM PYTHON SOURCE LINES 36-39

Second law: the same charge (here one faraday) through several
electrolytes connected in series liberates each substance in proportion
to its equivalent weight M/n.

.. GENERATED FROM PYTHON SOURCE LINES 39-53

.. code-block:: Python

    species = {"H2": (2.016, 2), "O2": (31.998, 4), "Cu": (63.546, 2), "Ag": (107.868, 1), "Al": (26.982, 3)}
    masses = {name: mass_from_charge(FARADAY, M, n) for name, (M, n) in species.items()}
    equivalents = {name: M / n for name, (M, n) in species.items()}
    for name in species:
        print(f"{name:3s}: mass per faraday = {masses[name]:7.3f} g, equivalent weight M/n = {equivalents[name]:7.3f} g/mol")

    ax2.scatter(list(equivalents.values()), list(masses.values()))
    for name in species:
        ax2.annotate(name, (equivalents[name], masses[name]), textcoords="offset points", xytext=(5, -10))
    ax2.set_xlabel("Equivalent weight M/n (g/mol)")
    ax2.set_ylabel("Mass liberated by 1 F (g)")
    ax2.set_title("Second law: m proportional to M/n")
    fig.tight_layout()
    plt.show()




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

 .. code-block:: none

    H2 : mass per faraday =   1.008 g, equivalent weight M/n =   1.008 g/mol
    O2 : mass per faraday =   8.000 g, equivalent weight M/n =   8.000 g/mol
    Cu : mass per faraday =  31.773 g, equivalent weight M/n =  31.773 g/mol
    Ag : mass per faraday = 107.868 g, equivalent weight M/n = 107.868 g/mol
    Al : mass per faraday =   8.994 g, equivalent weight M/n =   8.994 g/mol





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

   **Total running time of the script:** (0 minutes 0.042 seconds)


.. _sphx_glr_download_api_gallery_electrochem_electrolysis_plot_01_faradays_laws.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_faradays_laws.ipynb <plot_01_faradays_laws.ipynb>`

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

      :download:`Download Python source code: plot_01_faradays_laws.py <plot_01_faradays_laws.py>`

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

      :download:`Download zipped: plot_01_faradays_laws.zip <plot_01_faradays_laws.zip>`


.. only:: html

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

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