.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/thermo/mixtures/plot_03_osmotic_pressure.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_03_osmotic_pressure.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_thermo_mixtures_plot_03_osmotic_pressure.py:


van't Hoff's osmotic pressure law, Pi = iMRT
============================================

van't Hoff found that a dilute solution's osmotic pressure
(:func:`~chemistrykit.thermo.systems.mixtures.osmotic_pressure`) equals
the pressure the solute particles would exert as an ideal gas at the
same concentration and temperature. The factor :math:`i` counts
particles per formula unit: 1 for sucrose, about 2 for NaCl. The same
factor multiplies the other colligative effects, freezing-point
depression and boiling-point elevation
(:func:`~chemistrykit.thermo.systems.mixtures.freezing_point_depression`,
:func:`~chemistrykit.thermo.systems.mixtures.boiling_point_elevation`).

.. GENERATED FROM PYTHON SOURCE LINES 17-52

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.thermo.systems.equations_of_state import IdealGas
    from chemistrykit.thermo.systems.mixtures import (
        CRYOSCOPIC_CONSTANTS,
        boiling_point_elevation,
        freezing_point_depression,
        osmotic_pressure,
    )

    T = 298.15
    c = np.linspace(0.0, 0.5, 100)  # mol/L
    M = c * 1000.0  # mol/m^3

    fig, axes = plt.subplots(1, 2, figsize=(12, 4.8))
    axes[0].plot(c, osmotic_pressure(M, T, i=1.0) / 1e5, label="sucrose (i = 1)")
    axes[0].plot(c, osmotic_pressure(M, T, i=2.0) / 1e5, label="NaCl (i = 2)")
    Vm_gas = 1.0 / np.maximum(M, 1e-12)
    axes[0].plot(c[::10], IdealGas().pressure(Vm_gas[::10], T) / 1e5, "k.", label="ideal gas at same n/V")
    axes[0].set_xlabel("solute concentration (mol/L)")
    axes[0].set_ylabel(r"osmotic pressure $\Pi$ (bar)")
    axes[0].set_title("Solute particles behave like an ideal gas")
    axes[0].legend()

    water = CRYOSCOPIC_CONSTANTS["water"]
    b = c  # dilute aqueous: molality close to molarity
    axes[1].plot(b, freezing_point_depression(water["Kf"], b, i=2.0), label="freezing-point depression")
    axes[1].plot(b, boiling_point_elevation(water["Kb"], b, i=2.0), label="boiling-point elevation")
    axes[1].set_xlabel("NaCl molality (mol/kg)")
    axes[1].set_ylabel(r"$\Delta T$ (K)")
    axes[1].set_title("Other colligative effects share the factor i = 2")
    axes[1].legend()
    fig.tight_layout()




.. image-sg:: /api/gallery/thermo/mixtures/images/sphx_glr_plot_03_osmotic_pressure_001.png
   :alt: Solute particles behave like an ideal gas, Other colligative effects share the factor i = 2
   :srcset: /api/gallery/thermo/mixtures/images/sphx_glr_plot_03_osmotic_pressure_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 53-57

.. code-block:: Python

    print(f"0.1 M sucrose at 25 degC: Pi = {osmotic_pressure(100.0, T) / 1e5:.3f} bar")
    print(f"Isotonic saline (0.154 M NaCl, i = 2) at 37 degC: Pi = {osmotic_pressure(154.0, 310.15, i=2.0) / 1e5:.2f} bar")

    plt.show()




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

 .. code-block:: none

    0.1 M sucrose at 25 degC: Pi = 2.479 bar
    Isotonic saline (0.154 M NaCl, i = 2) at 37 degC: Pi = 7.94 bar





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

   **Total running time of the script:** (0 minutes 0.078 seconds)


.. _sphx_glr_download_api_gallery_thermo_mixtures_plot_03_osmotic_pressure.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_osmotic_pressure.ipynb <plot_03_osmotic_pressure.ipynb>`

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

      :download:`Download Python source code: plot_03_osmotic_pressure.py <plot_03_osmotic_pressure.py>`

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

      :download:`Download zipped: plot_03_osmotic_pressure.zip <plot_03_osmotic_pressure.zip>`


.. only:: html

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

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