.. _sphx_glr_api_gallery_solutions_acid_base:

Acid-base equilibria
--------------------

The law of mass action, Arrhenius dissociation and Ostwald's dilution
law, Sorensen's pH scale, Bronsted-Lowry conjugate pairs,
Henderson-Hasselbalch buffer design, Van Slyke buffer capacity, and
Bjerrum speciation diagrams for polyprotic acids.


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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="Dissolving less acid in more water increases the fraction of it that dissociates, even though the absolute [H^+] goes down -- the dilution law Wilhelm Ostwald derived in 1888 by applying the mass-action law to Arrhenius&#x27;s dissociation equilibrium,">

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  .. image:: /api/gallery/solutions/acid_base/images/thumb/sphx_glr_plot_01_ostwald_dilution_law_thumb.png
    :alt:

  :doc:`/api/gallery/solutions/acid_base/plot_01_ostwald_dilution_law`

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      <div class="sphx-glr-thumbnail-title">Ostwald's dilution law: weak acids dissociate more when diluted</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="The law of mass action says that at equilibrium the concentrations of products and reactants, each raised to its stoichiometric power, combine into a quotient that is fixed at a given temperature. For HA \rightleftharpoons H^+ + A^-:">

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  .. image:: /api/gallery/solutions/acid_base/images/thumb/sphx_glr_plot_02_law_of_mass_action_thumb.png
    :alt:

  :doc:`/api/gallery/solutions/acid_base/plot_02_law_of_mass_action`

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      <div class="sphx-glr-thumbnail-title">Guldberg and Waage's law of mass action: a constant equilibrium quotient</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Arrhenius proposed that an acid dissolved in water is split, at least in part, into free ions even with no current flowing, and that the degree of dissociation \alpha distinguishes a strong electrolyte (\alpha \approx 1) from a weak one (\alpha \ll 1). The number of dissolved particles per formula unit is then i = 1 + \alpha for a 1:1 electrolyte -- the van &#x27;t Hoff factor that explained anomalous colligative data.">

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  .. image:: /api/gallery/solutions/acid_base/images/thumb/sphx_glr_plot_03_arrhenius_electrolytic_dissociation_thumb.png
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  :doc:`/api/gallery/solutions/acid_base/plot_03_arrhenius_electrolytic_dissociation`

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      <div class="sphx-glr-thumbnail-title">Arrhenius's electrolytic dissociation: how much of an electrolyte is ions?</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Hasselbalch&#x27;s logarithmic form of Henderson&#x27;s buffer relationship,">

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  .. image:: /api/gallery/solutions/acid_base/images/thumb/sphx_glr_plot_04_henderson_hasselbalch_buffer_thumb.png
    :alt:

  :doc:`/api/gallery/solutions/acid_base/plot_04_henderson_hasselbalch_buffer`

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      <div class="sphx-glr-thumbnail-title">The Henderson-Hasselbalch equation and buffer design</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Sorensen&#x27;s 1909 definition \mathrm{pH} = -\log_{10}[H^+] (~chemistrykit.solutions.systems.acid_base.ph_from_h) turns hydrogen-ion concentrations spanning fourteen orders of magnitude into numbers between 0 and 14. Below, the pH of several everyday solutions is computed from their equilibrium [H^+] and placed on the scale, and the companion relation \mathrm{pH} + \mathrm{pOH} = pK_w = 14 is checked with poh_from_oh.">

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  .. image:: /api/gallery/solutions/acid_base/images/thumb/sphx_glr_plot_05_sorensen_ph_scale_thumb.png
    :alt:

  :doc:`/api/gallery/solutions/acid_base/plot_05_sorensen_ph_scale`

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      <div class="sphx-glr-thumbnail-title">Sorensen's pH scale: a logarithm for hydrogen-ion concentration</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Niels Bjerrum&#x27;s 1914 monograph on acid-base titrations introduced diagrams showing what fraction of a polyprotic acid is present in each protonation state as a function of pH -- today called Bjerrum plots or distribution diagrams. The fractions (~chemistrykit.solutions.systems.acid_base.polyprotic_fractions) depend only on pH and the stepwise K_a values, and adjacent species are equally abundant exactly where \mathrm{pH} = pK_j.">

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  .. image:: /api/gallery/solutions/acid_base/images/thumb/sphx_glr_plot_06_bjerrum_speciation_diagram_thumb.png
    :alt:

  :doc:`/api/gallery/solutions/acid_base/plot_06_bjerrum_speciation_diagram`

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      <div class="sphx-glr-thumbnail-title">Bjerrum's speciation diagrams for polyprotic acids</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Donald Van Slyke defined the buffer value \beta = dC_b/d\mathrm{pH}, the strong base per litre needed to raise the pH by one unit. For a weak acid/conjugate base pair of total concentration C (~chemistrykit.solutions.systems.acid_base.buffer_capacity):">

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  .. image:: /api/gallery/solutions/acid_base/images/thumb/sphx_glr_plot_07_van_slyke_buffer_capacity_thumb.png
    :alt:

  :doc:`/api/gallery/solutions/acid_base/plot_07_van_slyke_buffer_capacity`

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      <div class="sphx-glr-thumbnail-title">Van Slyke's buffer capacity: how strongly a solution resists pH change</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="In the Bronsted-Lowry picture an acid is a proton donor and its deprotonated form is a conjugate base -- itself a genuine base that accepts a proton from water. For every pair, K_aK_b = K_w, so the stronger the acid, the weaker its conjugate base. Here the acetate ion is modelled as a base in its own right with WeakBase (K_b = K_w/K_a), alongside acetic acid as WeakAcid, and several conjugate pairs are placed on the line pK_a + pK_b = 14.">

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  .. image:: /api/gallery/solutions/acid_base/images/thumb/sphx_glr_plot_08_bronsted_lowry_conjugate_pairs_thumb.png
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  :doc:`/api/gallery/solutions/acid_base/plot_08_bronsted_lowry_conjugate_pairs`

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      <div class="sphx-glr-thumbnail-title">Bronsted-Lowry conjugate acid-base pairs: pKa + pKb = pKw</div>
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    </div>


.. toctree::
   :hidden:

   /api/gallery/solutions/acid_base/plot_01_ostwald_dilution_law
   /api/gallery/solutions/acid_base/plot_02_law_of_mass_action
   /api/gallery/solutions/acid_base/plot_03_arrhenius_electrolytic_dissociation
   /api/gallery/solutions/acid_base/plot_04_henderson_hasselbalch_buffer
   /api/gallery/solutions/acid_base/plot_05_sorensen_ph_scale
   /api/gallery/solutions/acid_base/plot_06_bjerrum_speciation_diagram
   /api/gallery/solutions/acid_base/plot_07_van_slyke_buffer_capacity
   /api/gallery/solutions/acid_base/plot_08_bronsted_lowry_conjugate_pairs