.. _sphx_glr_api_gallery_thermo_mixtures:

Mixtures and colligative properties
------------------------------------

Raoult's-law P-x-y diagrams, Henry's law for dilute solutes, van't Hoff's
osmotic pressure and the colligative properties, and Margules activity
coefficients for non-ideal solutions.


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Raoult&#x27;s law, P_A = x_A P_A^* (~chemistrykit.thermo.systems.mixtures.raoult_vapor_pressure), makes each partial vapor pressure a straight line in liquid mole fraction. Adding the two lines (Dalton&#x27;s law) gives the total pressure, and BinaryIdealSolution computes the vapor composition, which is always richer in the more volatile component. That enrichment is the basis of fractional distillation.">

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  .. image:: /api/gallery/thermo/mixtures/images/thumb/sphx_glr_plot_01_raoult_law_pxy_thumb.png
    :alt:

  :doc:`/api/gallery/thermo/mixtures/plot_01_raoult_law_pxy`

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      <div class="sphx-glr-thumbnail-title">Raoult's law and the P-x-y diagram of an ideal solution</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Henry&#x27;s law, P_B = x_B K_H (~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 K_H that differs from the pure solute&#x27;s vapor pressure. Below, an illustrative real solute&#x27;s partial pressure follows the Henry&#x27;s-law line at high dilution and leaves it as the solute becomes concentrated, where Raoult&#x27;s law (~chemistrykit.thermo.systems.mixtures.raoult_vapor_pressure) takes over.">

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  .. image:: /api/gallery/thermo/mixtures/images/thumb/sphx_glr_plot_02_henry_law_thumb.png
    :alt:

  :doc:`/api/gallery/thermo/mixtures/plot_02_henry_law`

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      <div class="sphx-glr-thumbnail-title">Henry's law: the dilute-solute limit of a real solution</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="van&#x27;t Hoff found that a dilute solution&#x27;s osmotic pressure (~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 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 (~chemistrykit.thermo.systems.mixtures.freezing_point_depression, boiling_point_elevation).">

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  .. image:: /api/gallery/thermo/mixtures/images/thumb/sphx_glr_plot_03_osmotic_pressure_thumb.png
    :alt:

  :doc:`/api/gallery/thermo/mixtures/plot_03_osmotic_pressure`

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      <div class="sphx-glr-thumbnail-title">van't Hoff's osmotic pressure law, Pi = iMRT</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Margules wrote the activity coefficients of a binary liquid as power series in mole fraction. The one-parameter form used by MargulesSolution, \ln\gamma_1 = A x_2^2 and \ln\gamma_2 = A x_1^2, turns Raoult&#x27;s straight lines into curves: A &gt; 0 (unlike molecules repel) bows the total pressure upward and can produce a maximum-pressure azeotrope, while A &lt; 0 bows it downward. The model still obeys the Gibbs-Duhem relation, and each component tends to Henry&#x27;s law at infinite dilution.">

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  .. image:: /api/gallery/thermo/mixtures/images/thumb/sphx_glr_plot_04_margules_activity_thumb.png
    :alt:

  :doc:`/api/gallery/thermo/mixtures/plot_04_margules_activity`

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      <div class="sphx-glr-thumbnail-title">Margules activity coefficients: deviations from Raoult's law</div>
    </div>


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    </div>


.. toctree::
   :hidden:

   /api/gallery/thermo/mixtures/plot_01_raoult_law_pxy
   /api/gallery/thermo/mixtures/plot_02_henry_law
   /api/gallery/thermo/mixtures/plot_03_osmotic_pressure
   /api/gallery/thermo/mixtures/plot_04_margules_activity