.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/surface/catalysis/plot_03_sabatier_hydrogenation.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_surface_catalysis_plot_03_sabatier_hydrogenation.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_surface_catalysis_plot_03_sabatier_hydrogenation.py:


Sabatier and Senderens: catalytic hydrogenation over finely divided nickel
============================================================================

Sabatier and Senderens showed from 1897 that finely divided nickel
hydrogenates ethylene (:math:`C_2H_4 + H_2 \to C_2H_6`) at temperatures
where the gas-phase reaction does not run at all. This example uses
illustrative Arrhenius parameters and
:func:`~chemistrykit.surface.systems.catalysis.compare_catalyzed_rate` to
compute the conversion reached in a one-second contact time as the
temperature rises. Over nickel the reaction lights off hundreds of
kelvin earlier. A second panel shows Sabatier's rule of thumb from
screening many metals: a metal that binds the reactant too weakly holds
almost none of it on the surface, and one that binds it too strongly
leaves no free sites. Only a moderate binder has both.

.. GENERATED FROM PYTHON SOURCE LINES 19-37

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.surface.systems.catalysis import compare_catalyzed_rate
    from chemistrykit.surface.systems.langmuir import langmuir_coverage

    tau = 1.0  # contact time, s
    T = np.linspace(250.0, 900.0, 400)
    comparisons = [compare_catalyzed_rate(Ea_uncatalyzed=180e3, Ea_catalyzed=45e3, T=Ti, A_uncatalyzed=1e13, A_catalyzed=1e7) for Ti in T]
    X_uncat = 1.0 - np.exp(-np.array([c.k_uncatalyzed for c in comparisons]) * tau)
    X_ni = 1.0 - np.exp(-np.array([c.k_catalyzed for c in comparisons]) * tau)

    T_half_ni = T[np.searchsorted(X_ni, 0.5)]
    T_half_gas = T[np.searchsorted(X_uncat, 0.5)]
    print(f"50% conversion over Ni at   ~{T_half_ni:.0f} K")
    print(f"50% conversion in gas phase ~{T_half_gas:.0f} K")
    print(f"Nickel lowers the working temperature by ~{T_half_gas - T_half_ni:.0f} K")





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

 .. code-block:: none

    50% conversion over Ni at   ~330 K
    50% conversion in gas phase ~716 K
    Nickel lowers the working temperature by ~386 K




.. GENERATED FROM PYTHON SOURCE LINES 38-40

Sabatier's rule: surface coverage of the reactant (Langmuir) for three
hypothetical metals at the same pressure.

.. GENERATED FROM PYTHON SOURCE LINES 40-46

.. code-block:: Python

    P = 1.0
    metals = {"weak binder": 0.02, "nickel-like": 1.0, "strong binder": 50.0}
    theta = {name: langmuir_coverage(K, P) for name, K in metals.items()}
    for name, th in theta.items():
        print(f"{name:14s} reactant coverage {th:.3f}, free sites {1 - th:.3f}")





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

 .. code-block:: none

    weak binder    reactant coverage 0.020, free sites 0.980
    nickel-like    reactant coverage 0.500, free sites 0.500
    strong binder  reactant coverage 0.980, free sites 0.020




.. GENERATED FROM PYTHON SOURCE LINES 47-65

.. code-block:: Python

    fig, axes = plt.subplots(1, 2, figsize=(11, 4))
    axes[0].plot(T, X_uncat, label="gas phase, no catalyst")
    axes[0].plot(T, X_ni, label="over finely divided Ni")
    axes[0].set_xlabel("temperature (K)")
    axes[0].set_ylabel("conversion of ethylene in 1 s")
    axes[0].set_title("Catalytic hydrogenation lights off far earlier")
    axes[0].legend()

    names = list(metals)
    x = np.arange(len(names))
    axes[1].bar(x - 0.2, [theta[n] for n in names], width=0.4, label="covered by reactant")
    axes[1].bar(x + 0.2, [1 - theta[n] for n in names], width=0.4, label="free sites")
    axes[1].set_xticks(x, names)
    axes[1].set_ylabel("fraction of surface sites")
    axes[1].set_title("Sabatier's rule: bind neither too weakly nor too strongly")
    axes[1].legend()
    plt.tight_layout()
    plt.show()



.. image-sg:: /api/gallery/surface/catalysis/images/sphx_glr_plot_03_sabatier_hydrogenation_001.png
   :alt: Catalytic hydrogenation lights off far earlier, Sabatier's rule: bind neither too weakly nor too strongly
   :srcset: /api/gallery/surface/catalysis/images/sphx_glr_plot_03_sabatier_hydrogenation_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.073 seconds)


.. _sphx_glr_download_api_gallery_surface_catalysis_plot_03_sabatier_hydrogenation.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_sabatier_hydrogenation.ipynb <plot_03_sabatier_hydrogenation.ipynb>`

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

      :download:`Download Python source code: plot_03_sabatier_hydrogenation.py <plot_03_sabatier_hydrogenation.py>`

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

      :download:`Download zipped: plot_03_sabatier_hydrogenation.zip <plot_03_sabatier_hydrogenation.zip>`


.. only:: html

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

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