.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/kinetics/arrhenius/plot_01_arrhenius_fit.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_kinetics_arrhenius_plot_01_arrhenius_fit.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_kinetics_arrhenius_plot_01_arrhenius_fit.py:


Recovering an activation energy from an Arrhenius plot
=========================================================

Synthetic rate-constant-vs-temperature data is generated from a known
activation energy :math:`E_a` and pre-exponential factor :math:`A`, then
:func:`~chemistrykit.kinetics.systems.arrhenius.fit_arrhenius` recovers
both parameters back out via the classic Arrhenius-plot linearization
(:math:`\ln k` vs. :math:`1/T`).

.. GENERATED FROM PYTHON SOURCE LINES 13-31

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.kinetics.systems.arrhenius import arrhenius_rate_constant, fit_arrhenius
    from chemistrykit.kinetics.visualizers.kinetics_plots import plot_arrhenius

    A_true, Ea_true = 4.2e12, 65_000.0  # J/mol
    T = np.linspace(280.0, 360.0, 9)

    rng = np.random.default_rng(0)
    k_exact = arrhenius_rate_constant(A=A_true, Ea=Ea_true, T=T)
    # A small amount of multiplicative noise, as a real kinetics measurement would have.
    k_noisy = k_exact * (1.0 + rng.normal(0.0, 0.02, size=T.shape))

    fit = fit_arrhenius(T, k_noisy)
    print(f"true:   Ea={Ea_true:.0f} J/mol, A={A_true:.3e}")
    print(f"fitted: Ea={fit.Ea:.0f} J/mol, A={fit.A:.3e}, R^2={fit.r_squared:.5f}")





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

 .. code-block:: none

    true:   Ea=65000 J/mol, A=4.200e+12
    fitted: Ea=65046 J/mol, A=4.293e+12, R^2=0.99996




.. GENERATED FROM PYTHON SOURCE LINES 32-33

The Arrhenius plot: a straight line of slope :math:`-E_a/R`.

.. GENERATED FROM PYTHON SOURCE LINES 33-38

.. code-block:: Python


    ax = plot_arrhenius(T, k_noisy, fit=fit)
    ax.set_title(f"Arrhenius plot (fitted Ea = {fit.Ea / 1000:.1f} kJ/mol)")
    plt.tight_layout()
    plt.show()



.. image-sg:: /api/gallery/kinetics/arrhenius/images/sphx_glr_plot_01_arrhenius_fit_001.png
   :alt: Arrhenius plot (fitted Ea = 65.0 kJ/mol)
   :srcset: /api/gallery/kinetics/arrhenius/images/sphx_glr_plot_01_arrhenius_fit_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.038 seconds)


.. _sphx_glr_download_api_gallery_kinetics_arrhenius_plot_01_arrhenius_fit.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_arrhenius_fit.ipynb <plot_01_arrhenius_fit.ipynb>`

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

      :download:`Download Python source code: plot_01_arrhenius_fit.py <plot_01_arrhenius_fit.py>`

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

      :download:`Download zipped: plot_01_arrhenius_fit.zip <plot_01_arrhenius_fit.zip>`


.. only:: html

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

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