.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/thermo/mixtures/plot_02_henry_law.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_mixtures_plot_02_henry_law.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_thermo_mixtures_plot_02_henry_law.py:


Henry's law: the dilute-solute limit of a real solution
=======================================================

Henry's law, :math:`P_B = x_B K_H`
(:func:`~chemistrykit.thermo.systems.mixtures.henry_law_pressure`),
says the vapor pressure of a dilute solute (equivalently, the amount of
a gas that dissolves at a given pressure) is proportional to its mole
fraction, with an empirical constant :math:`K_H` that differs from the
pure solute's vapor pressure. Below, an illustrative real solute's
partial pressure follows the Henry's-law line at high dilution and
leaves it as the solute becomes concentrated, where Raoult's law
(:func:`~chemistrykit.thermo.systems.mixtures.raoult_vapor_pressure`)
takes over.

.. GENERATED FROM PYTHON SOURCE LINES 18-48

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.thermo.systems.mixtures import henry_law_pressure, raoult_vapor_pressure

    P_B_star = 40.0  # kPa, pure-B vapor pressure
    K_H = 120.0  # kPa, Henry's law constant (slope at infinite dilution)

    x_B = np.linspace(0.0, 1.0, 200)
    # The quadratic that starts with slope K_H at x_B = 0 and reaches P_B* at x_B = 1.
    P_B_real = x_B * (K_H + (P_B_star - K_H) * x_B)

    fig, axes = plt.subplots(1, 2, figsize=(12, 4.8))
    axes[0].plot(x_B, P_B_real, color="black", linewidth=2, label="real (illustrative) partial pressure")
    axes[0].plot(x_B, henry_law_pressure(x_B, K_H), "--", color="darkorange", label=r"Henry's law ($x_B K_H$)")
    axes[0].plot(x_B, raoult_vapor_pressure(x_B, P_B_star), ":", color="steelblue", label=r"Raoult's law ($x_B P_B^*$)")
    axes[0].set_ylim(0, 60)
    axes[0].set_xlabel("mole fraction of solute B")
    axes[0].set_ylabel("partial pressure of B (kPa)")
    axes[0].set_title("Henry's law holds for the dilute solute")
    axes[0].legend()

    x_dilute = np.linspace(1e-4, 0.1, 100)
    error = (henry_law_pressure(x_dilute, K_H) - x_dilute * (K_H + (P_B_star - K_H) * x_dilute)) / (x_dilute * (K_H + (P_B_star - K_H) * x_dilute))
    axes[1].plot(x_dilute, 100 * error, color="darkorange")
    axes[1].set_xlabel("mole fraction of solute B")
    axes[1].set_ylabel("Henry's-law error (%)")
    axes[1].set_title("The error vanishes as the solution becomes dilute")
    fig.tight_layout()




.. image-sg:: /api/gallery/thermo/mixtures/images/sphx_glr_plot_02_henry_law_001.png
   :alt: Henry's law holds for the dilute solute, The error vanishes as the solution becomes dilute
   :srcset: /api/gallery/thermo/mixtures/images/sphx_glr_plot_02_henry_law_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 49-52

Read the other way, Henry's law gives the solubility of a gas: the
dissolved mole fraction is :math:`x_B = P_B/K_H`, doubling when the gas
pressure above the liquid doubles.

.. GENERATED FROM PYTHON SOURCE LINES 52-57

.. code-block:: Python


    for P in (1.0, 2.0, 4.0):
        print(f"P_B = {P:4.1f} kPa -> dissolved x_B = {P / K_H:.4f}")

    plt.show()




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

 .. code-block:: none

    P_B =  1.0 kPa -> dissolved x_B = 0.0083
    P_B =  2.0 kPa -> dissolved x_B = 0.0167
    P_B =  4.0 kPa -> dissolved x_B = 0.0333





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

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


.. _sphx_glr_download_api_gallery_thermo_mixtures_plot_02_henry_law.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_02_henry_law.ipynb <plot_02_henry_law.ipynb>`

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

      :download:`Download Python source code: plot_02_henry_law.py <plot_02_henry_law.py>`

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

      :download:`Download zipped: plot_02_henry_law.zip <plot_02_henry_law.zip>`


.. only:: html

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

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