.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/analytical/stoichiometry/plot_02_liebig_combustion_analysis.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_analytical_stoichiometry_plot_02_liebig_combustion_analysis.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_analytical_stoichiometry_plot_02_liebig_combustion_analysis.py:


Liebig's combustion analysis: an empirical formula from CO2 and H2O masses
==========================================================================

Justus von Liebig's *Kaliapparat* made organic elemental analysis
routine. The sample is burned in oxygen over hot copper oxide, the water
is caught in calcium chloride, the CO2 in potash bulbs, and both are
weighed. Carbon and hydrogen follow from those two masses, oxygen by
difference. Below, a 10.00 mg sample of ascorbic acid (vitamin C) is
"burned". Its mass percentages go to
:func:`~chemistrykit.stoichiometry.empirical_formula`, which converts to
moles, divides by the smallest, and searches for the smallest multiplier
that gives whole numbers. Here that gives C3H4O3, and a molar mass of
about 176 g/mol then fixes the molecular formula as C6H8O6. The right
panel shows why the multiplier search is needed: the raw mole ratios are
1 : 1.33 : 1, which become whole only after multiplying by 3.

.. GENERATED FROM PYTHON SOURCE LINES 20-63



.. image-sg:: /api/gallery/analytical/stoichiometry/images/sphx_glr_plot_02_liebig_combustion_analysis_001.png
   :alt: Composition of ascorbic acid from combustion, Smallest multiplier giving whole numbers: 3
   :srcset: /api/gallery/analytical/stoichiometry/images/sphx_glr_plot_02_liebig_combustion_analysis_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    weighed: 14.99 mg CO2, 4.09 mg H2O
    %C = 40.91, %H = 4.58, %O (by difference) = 54.51
    empirical formula C3H4O3; molar mass 176 g/mol -> 2 x C3H4O3






|

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.periodic_table import get_element, molar_mass
    from chemistrykit.stoichiometry import empirical_formula, mass_percent

    sample_mg = 10.00
    true = mass_percent("C6H8O6")
    m_CO2 = sample_mg * true["C"] / 100 * molar_mass("CO2") / get_element("C").atomic_mass
    m_H2O = sample_mg * true["H"] / 100 * molar_mass("H2O") / (2 * get_element("H").atomic_mass)
    m_CO2, m_H2O = round(m_CO2, 2), round(m_H2O, 2)  # a microbalance reads to 0.01 mg
    print(f"weighed: {m_CO2:.2f} mg CO2, {m_H2O:.2f} mg H2O")

    pct_C = 100 * m_CO2 * get_element("C").atomic_mass / molar_mass("CO2") / sample_mg
    pct_H = 100 * m_H2O * 2 * get_element("H").atomic_mass / molar_mass("H2O") / sample_mg
    pct_O = 100.0 - pct_C - pct_H
    measured = {"C": pct_C, "H": pct_H, "O": pct_O}
    formula = empirical_formula(measured)
    unit = "".join(f"{e}{n}" for e, n in formula.items())
    n_units = round(176.0 / molar_mass(formula))
    print(f"%C = {pct_C:.2f}, %H = {pct_H:.2f}, %O (by difference) = {pct_O:.2f}")
    print(f"empirical formula {unit}; molar mass 176 g/mol -> {n_units} x {unit}")

    moles = np.array([measured[e] / get_element(e).atomic_mass for e in "CHO"])
    ratios = moles / moles.min()

    fig, axes = plt.subplots(1, 2, figsize=(12, 4.8))
    axes[0].bar(["C", "H", "O"], [pct_C, pct_H, pct_O], color=["black", "lightgray", "firebrick"], edgecolor="black")
    axes[0].set_ylabel("mass percent")
    axes[0].set_title("Composition of ascorbic acid from combustion")

    m = np.arange(1, 7)
    for ratio, e, color in zip(ratios, "CHO", ["black", "gray", "firebrick"], strict=True):
        scaled = ratio * m
        axes[1].plot(m, np.abs(scaled - np.round(scaled)), "o-", color=color, label=e)
    axes[1].axhline(0.05, color="gray", linestyle="--", label="whole-number tolerance")
    axes[1].set_xlabel("multiplier")
    axes[1].set_ylabel("distance from a whole number")
    axes[1].set_title("Smallest multiplier giving whole numbers: 3")
    axes[1].legend()
    fig.tight_layout()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.062 seconds)


.. _sphx_glr_download_api_gallery_analytical_stoichiometry_plot_02_liebig_combustion_analysis.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_02_liebig_combustion_analysis.ipynb <plot_02_liebig_combustion_analysis.ipynb>`

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

      :download:`Download Python source code: plot_02_liebig_combustion_analysis.py <plot_02_liebig_combustion_analysis.py>`

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

      :download:`Download zipped: plot_02_liebig_combustion_analysis.zip <plot_02_liebig_combustion_analysis.zip>`


.. only:: html

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

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