.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/thermo/equilibrium/plot_03_van_t_hoff_plot.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_thermo_equilibrium_plot_03_van_t_hoff_plot.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_thermo_equilibrium_plot_03_van_t_hoff_plot.py:


The van't Hoff plot: ln K against 1/T
=====================================

van't Hoff's equation :math:`d\ln K/dT = \Delta H^\circ/(RT^2)` makes
:math:`\ln K` a straight line in :math:`1/T` with slope
:math:`-\Delta H^\circ/R` and intercept :math:`\Delta S^\circ/R`. This
example generates noisy equilibrium constants for
:math:`N_2O_4 \rightleftharpoons 2NO_2` from
:func:`~chemistrykit.thermo.systems.equilibrium.van_t_hoff_equilibrium_constant`
and recovers the reaction enthalpy and entropy with
:func:`~chemistrykit.thermo.systems.equilibrium.fit_van_t_hoff`.

.. GENERATED FROM PYTHON SOURCE LINES 16-43

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.constants import R
    from chemistrykit.thermo.systems.equilibrium import fit_van_t_hoff, van_t_hoff_equilibrium_constant

    dH_true, dS_true = 57_200.0, 175.8
    T_ref = 298.15
    K_ref = np.exp(-(dH_true - T_ref * dS_true) / (R * T_ref))

    rng = np.random.default_rng(1)
    T_data = np.linspace(280.0, 360.0, 9)
    K_data = van_t_hoff_equilibrium_constant(T_data, T_ref=T_ref, K_ref=K_ref, delta_h=dH_true)
    K_data = K_data * np.exp(rng.normal(scale=0.05, size=T_data.size))  # 5% multiplicative noise

    fit = fit_van_t_hoff(T_data, K_data)

    fig, ax = plt.subplots(figsize=(7, 5))
    ax.scatter(1000.0 / T_data, np.log(K_data), label="noisy data")
    T_line = np.linspace(T_data.min(), T_data.max(), 100)
    ax.plot(1000.0 / T_line, np.log(fit.predict(T_line)), color="crimson", label=rf"fit: $\Delta H^\circ$ = {fit.delta_h / 1000:.1f} kJ/mol")
    ax.set_xlabel("1000 / T (1/K)")
    ax.set_ylabel("ln K")
    ax.set_title(r"van't Hoff plot for $N_2O_4 \rightleftharpoons 2NO_2$")
    ax.legend()
    fig.tight_layout()




.. image-sg:: /api/gallery/thermo/equilibrium/images/sphx_glr_plot_03_van_t_hoff_plot_001.png
   :alt: van't Hoff plot for $N_2O_4 \rightleftharpoons 2NO_2$
   :srcset: /api/gallery/thermo/equilibrium/images/sphx_glr_plot_03_van_t_hoff_plot_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 44-48

.. code-block:: Python

    print(f"fitted dH = {fit.delta_h / 1000:.2f} kJ/mol (true {dH_true / 1000:.2f})")
    print(f"fitted dS = {fit.delta_s:.1f} J/(mol K) (true {dS_true:.1f}); R^2 = {fit.r_squared:.4f}")

    plt.show()




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

 .. code-block:: none

    fitted dH = 57.14 kJ/mol (true 57.20)
    fitted dS = 175.7 J/(mol K) (true 175.8); R^2 = 0.9996





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

   **Total running time of the script:** (0 minutes 0.039 seconds)


.. _sphx_glr_download_api_gallery_thermo_equilibrium_plot_03_van_t_hoff_plot.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_van_t_hoff_plot.ipynb <plot_03_van_t_hoff_plot.ipynb>`

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

      :download:`Download Python source code: plot_03_van_t_hoff_plot.py <plot_03_van_t_hoff_plot.py>`

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

      :download:`Download zipped: plot_03_van_t_hoff_plot.zip <plot_03_van_t_hoff_plot.zip>`


.. only:: html

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

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