.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/solutions/solubility/plot_01_le_chatelier_common_ion_effect.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_solutions_solubility_plot_01_le_chatelier_common_ion_effect.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_solutions_solubility_plot_01_le_chatelier_common_ion_effect.py:


Le Chatelier's principle: the common-ion effect on AgCl solubility
===================================================================

Le Chatelier's principle says an equilibrium disturbed by adding one of
its participants shifts to consume it. Adding chloride to saturated AgCl
drives :math:`\text{AgCl}(s) \rightleftharpoons \text{Ag}^+ + \text{Cl}^-`
back toward the solid, so AgCl's molar solubility (:func:`~chemistrykit.solutions.systems.solubility.molar_solubility_from_ksp`)
drops sharply as increasing concentrations of a common ion (here, Cl-
from added NaCl) are introduced -- the direction Le Chatelier predicts,
and the size quantified exactly by :func:`~chemistrykit.solutions.systems.solubility.molar_solubility_with_common_ion`.

.. GENERATED FROM PYTHON SOURCE LINES 15-39

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.solutions.systems.solubility import (
        molar_solubility_from_ksp,
        molar_solubility_with_common_ion,
    )

    Ksp_AgCl = 1.8e-10
    s_pure = molar_solubility_from_ksp(Ksp_AgCl, cation_coeff=1, anion_coeff=1)
    print(f"Molar solubility of AgCl in pure water: {s_pure:.3e} mol/L")

    Cl_added = np.logspace(-4, -1, 60)
    s_common = [molar_solubility_with_common_ion(Ksp_AgCl, 1, 1, C0, common_ion="anion") for C0 in Cl_added]

    fig, ax = plt.subplots(figsize=(7, 5))
    ax.loglog(Cl_added, s_common, color="steelblue", label="with added Cl-")
    ax.axhline(s_pure, color="gray", linestyle=":", label="solubility in pure water")
    ax.set_xlabel("[Cl-] added (mol/L)")
    ax.set_ylabel("AgCl molar solubility (mol/L)")
    ax.set_title("Common-ion suppression of AgCl solubility")
    ax.legend()
    fig.tight_layout()




.. image-sg:: /api/gallery/solutions/solubility/images/sphx_glr_plot_01_le_chatelier_common_ion_effect_001.png
   :alt: Common-ion suppression of AgCl solubility
   :srcset: /api/gallery/solutions/solubility/images/sphx_glr_plot_01_le_chatelier_common_ion_effect_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    Molar solubility of AgCl in pure water: 1.342e-05 mol/L




.. GENERATED FROM PYTHON SOURCE LINES 40-43

At high added Cl-, the salt's own contribution to [Cl-] becomes
negligible, so ``s ~= Ksp/[Cl-]`` -- a straight line on this log-log
plot, which the numerical solver's curve should approach:

.. GENERATED FROM PYTHON SOURCE LINES 43-48

.. code-block:: Python


    s_approx = Ksp_AgCl / Cl_added
    print(f"At [Cl-]=0.10 M: exact s = {s_common[-1]:.3e}, approximation Ksp/[Cl-] = {s_approx[-1]:.3e}")

    plt.show()




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

 .. code-block:: none

    At [Cl-]=0.10 M: exact s = 1.800e-09, approximation Ksp/[Cl-] = 1.800e-09





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

   **Total running time of the script:** (0 minutes 0.082 seconds)


.. _sphx_glr_download_api_gallery_solutions_solubility_plot_01_le_chatelier_common_ion_effect.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_le_chatelier_common_ion_effect.ipynb <plot_01_le_chatelier_common_ion_effect.ipynb>`

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

      :download:`Download Python source code: plot_01_le_chatelier_common_ion_effect.py <plot_01_le_chatelier_common_ion_effect.py>`

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

      :download:`Download zipped: plot_01_le_chatelier_common_ion_effect.zip <plot_01_le_chatelier_common_ion_effect.zip>`


.. only:: html

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

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