.. _sphx_glr_api_gallery_solutions_complexation:

Complexation equilibria
-----------------------

Stepwise metal-ligand complex formation: species-distribution diagrams,
Bjerrum's formation function, and speciation from total concentrations.


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


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    <div class="sphx-glr-thumbnails">

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    <div class="sphx-glr-thumbcontainer" tooltip="Copper(II) binds ammonia one ligand at a time, Cu(NH_3)_{n-1}^{2+} + NH_3 \rightleftharpoons Cu(NH_3)_n^{2+}, with stepwise constants K_1 &gt; K_2 &gt; K_3 &gt; K_4. Bjerrum showed that the whole ladder follows from the free-ligand concentration alone. The fractions \alpha_n (~chemistrykit.solutions.complex_fractions) and the mean number of bound ligands \bar n (~chemistrykit.solutions.average_ligand_number, Bjerrum&#x27;s formation function) are functions of p[NH_3] only. His &quot;half-\bar n&quot; rule runs the logic backwards: where \bar n = n - \tfrac12, p[NH_3] \approx \log K_n, so the constants can be read off a measured formation curve. The stepwise constants below are of the size Bjerrum measured for Cu(II)-ammonia.">

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  .. image:: /api/gallery/solutions/complexation/images/thumb/sphx_glr_plot_01_bjerrum_metal_ammine_formation_thumb.png
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  :doc:`/api/gallery/solutions/complexation/plot_01_bjerrum_metal_ammine_formation`

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      <div class="sphx-glr-thumbnail-title">Jannik Bjerrum's stepwise metal-ammine formation</div>
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    </div>


.. toctree::
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   /api/gallery/solutions/complexation/plot_01_bjerrum_metal_ammine_formation