.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "api/gallery/surface/catalysis/plot_01_doebereiner_berzelius_catalysis.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_api_gallery_surface_catalysis_plot_01_doebereiner_berzelius_catalysis.py: Doebereiner's platinum and Berzelius's catalysis: a catalyst that is not consumed =================================================================================== In 1823 Doebereiner found that spongy platinum ignites a jet of hydrogen in air at room temperature and comes out of the reaction unchanged; in 1835 Berzelius named the phenomenon *catalysis*. This example makes both halves of that observation quantitative with illustrative (not measured) parameters for :math:`2H_2 + O_2 \to 2H_2O`. Lowering the activation energy on platinum (:func:`~chemistrykit.surface.systems.catalysis.compare_catalyzed_rate`) turns a reaction that is frozen at room temperature into a fast one, and the :func:`~chemistrykit.surface.systems.catalysis.turnover_number` keeps growing while the amount of platinum stays exactly the same. The catalyst is used again and again, never used up. .. GENERATED FROM PYTHON SOURCE LINES 19-30 .. code-block:: Python import matplotlib.pyplot as plt import numpy as np from chemistrykit.surface.systems.catalysis import compare_catalyzed_rate, turnover_number T = 293.15 # room temperature, K comparison = compare_catalyzed_rate(Ea_uncatalyzed=170e3, Ea_catalyzed=60e3, T=T, A_uncatalyzed=1e11, A_catalyzed=1e9) print(f"Uncatalyzed k at {T} K: {comparison.k_uncatalyzed:.3e} 1/s") print(f"On platinum: {comparison.k_catalyzed:.3e} 1/s") print(f"Rate enhancement: {comparison.rate_enhancement:.3e}") .. rst-class:: sphx-glr-script-out .. code-block:: none Uncatalyzed k at 293.15 K: 5.120e-20 1/s On platinum: 2.038e-02 1/s Rate enhancement: 3.980e+17 .. GENERATED FROM PYTHON SOURCE LINES 31-35 A batch of hydrogen (first order in H2 for simplicity) over a fixed amount of platinum. The platinum is *not* a reactant: its amount stays constant, while the number of H2 molecules each Pt site has converted (the turnover number) keeps rising. .. GENERATED FROM PYTHON SOURCE LINES 35-44 .. code-block:: Python n_H2_0 = 1.0e-2 # mol n_Pt = 1.0e-6 # mol of surface Pt sites t = np.linspace(0.0, 5.0 / comparison.k_catalyzed, 300) n_H2_cat = n_H2_0 * np.exp(-comparison.k_catalyzed * t) n_H2_uncat = n_H2_0 * np.exp(-comparison.k_uncatalyzed * t) ton = np.array([turnover_number(n_H2_0 - n, n_Pt) for n in n_H2_cat]) print(f"\nTurnover number when the H2 is used up: {ton[-1]:.0f} cycles per Pt site") print(f"Platinum left afterwards: {n_Pt:.1e} mol (unchanged)") .. rst-class:: sphx-glr-script-out .. code-block:: none Turnover number when the H2 is used up: 9933 cycles per Pt site Platinum left afterwards: 1.0e-06 mol (unchanged) .. GENERATED FROM PYTHON SOURCE LINES 45-64 .. code-block:: Python fig, axes = plt.subplots(1, 2, figsize=(11, 4)) axes[0].plot(t, n_H2_uncat / n_H2_0, label="no catalyst") axes[0].plot(t, n_H2_cat / n_H2_0, label="spongy platinum") axes[0].set_xlabel("time (s)") axes[0].set_ylabel("H$_2$ remaining (fraction)") axes[0].set_title("Doebereiner: H$_2$ + O$_2$ at room temperature") axes[0].legend() axes[1].plot(t, ton, color="C1", label="turnover number (cycles per Pt site)") axes[1].set_xlabel("time (s)") axes[1].set_ylabel("turnover number") ax2 = axes[1].twinx() ax2.plot(t, np.full_like(t, n_Pt * 1e6), "k--", label="Pt present (umol)") ax2.set_ylabel("Pt present (umol)") ax2.set_ylim(0, 2) axes[1].set_title("Berzelius: the catalyst is not consumed") axes[1].legend(loc="center right") plt.tight_layout() plt.show() .. image-sg:: /api/gallery/surface/catalysis/images/sphx_glr_plot_01_doebereiner_berzelius_catalysis_001.png :alt: Doebereiner: H$_2$ + O$_2$ at room temperature, Berzelius: the catalyst is not consumed :srcset: /api/gallery/surface/catalysis/images/sphx_glr_plot_01_doebereiner_berzelius_catalysis_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.088 seconds) .. _sphx_glr_download_api_gallery_surface_catalysis_plot_01_doebereiner_berzelius_catalysis.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_doebereiner_berzelius_catalysis.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_01_doebereiner_berzelius_catalysis.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_01_doebereiner_berzelius_catalysis.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_