would equal b-b, but due to the loss of carbon dioxide, this was never the case.
Although the experiment was well planned, his results are inaccurate, and there may
be several reasons for that. First, the water content of the acids was not known, and
this is a particular problem with hydrochloric acid and carbonic acids which are
aqueous solutions.
Bergman reported that 100 parts of sodium hydroxide required 177 parts of
sulphuric acid, 135½ parts of nitric acid or 125 parts of hydrochloric for neutralisation. The expected values are 123 parts of sulphuric acid, 158 parts of nitric acid
or 260 parts of hydrochloric acid (assumed to 35%). He reported that 100 parts of
potassium hydroxide required 78½ parts of sulphuric acid, 64 parts of nitric acid or
51½ parts of hydrochloric acid for neutralisation. The expected values are 87 parts
of sulphuric acid, 112 parts of nitric acid or 186 parts of hydrochloric acid (assumed
to be 35%). It is not easy to trace the origins of the low accuracy of Bergman’s
results. Partington suggested that Bergman’s experiments may have been performed
by his assistant, which could explain the lack of accuracy [22]. It should be noted
that this was over two decades before the famous tabulation of equivalent weights
by Ernst Gottfried Fischer (1754–1831) in his 1802 translation of Berthollet’s
Statique Chemique [23]. Fischer, who based his table on the work of Richter,
tabulated the mass of different bases and acids that were equivalent to 1,000 parts
sulphuric acid. He gave the values 859, 1605, 712, 1405 and 577, respectively, for
sodium hydroxide (natron), potassium hydroxide (kali), hydrochloric acid, nitric
acid and carbonic acid, respectively. Assuming that the alkalis are the pure
hydroxides and the acids are water-free (carbonic acid thus being carbon dioxide),
the expected values are 816, 1144, 744, 1285 and 449, respectively. Richard
Kirwan also started to study equivalent weights in the 1780s, but initially believed
that a certain amount of alkali needed the same weight of different acids for
neutralisation.
Bergman’s table of equivalent weights is also included in his paper on carbonic
acid (Sect. 18.3) published the same year, 1775. In The Chemical Lectures of
H.T. Scheffer, Bergman also gave the quantitative compositions of many salts given
as parts alkali and parts acid per 100 parts of salt. It is unfortunately not easy to
estimate the accuracy of these results, as the water content of the salts, acids and
alkalis Bergman used are unknown.
Several other examples of Bergman’s use of the concept of constant proportions
and stoichiometry in quantitative chemical analysis will follow in this chapter; his
accidental determination of equivalent weights while trying to determine the relative phlogiston content of metals was discussed in Sect. 22.5.
In his paper on the isolation of oxalic acid (Sect. 24.1), Scheele also used
stoichiometry in an ingenious method to determine the proper amount of sulphuric
acid required to decompose lead(II) oxalate to lead sulphate and oxalic acid without
adding an excess of sulphuric acid: [24]: he precipitated lead oxalate from potassium oxalate solution using lead acetate, noting the amount of lead acetate required.
He then measured the amount of sulphuric acid required to quantitatively precipitate
lead sulphate from this amount of lead acetate. Finally, he added the same amount
of sulphuric acid to his lead oxalate to liberate the oxalic acid quantitatively.
314
23 Bergman as an Analytical Chemist
Although the experiment was well planned, his results are inaccurate, and there may
be several reasons for that. First, the water content of the acids was not known, and
this is a particular problem with hydrochloric acid and carbonic acids which are
aqueous solutions.
Bergman reported that 100 parts of sodium hydroxide required 177 parts of
sulphuric acid, 135½ parts of nitric acid or 125 parts of hydrochloric for neutralisation. The expected values are 123 parts of sulphuric acid, 158 parts of nitric acid
or 260 parts of hydrochloric acid (assumed to 35%). He reported that 100 parts of
potassium hydroxide required 78½ parts of sulphuric acid, 64 parts of nitric acid or
51½ parts of hydrochloric acid for neutralisation. The expected values are 87 parts
of sulphuric acid, 112 parts of nitric acid or 186 parts of hydrochloric acid (assumed
to be 35%). It is not easy to trace the origins of the low accuracy of Bergman’s
results. Partington suggested that Bergman’s experiments may have been performed
by his assistant, which could explain the lack of accuracy [22]. It should be noted
that this was over two decades before the famous tabulation of equivalent weights
by Ernst Gottfried Fischer (1754–1831) in his 1802 translation of Berthollet’s
Statique Chemique [23]. Fischer, who based his table on the work of Richter,
tabulated the mass of different bases and acids that were equivalent to 1,000 parts
sulphuric acid. He gave the values 859, 1605, 712, 1405 and 577, respectively, for
sodium hydroxide (natron), potassium hydroxide (kali), hydrochloric acid, nitric
acid and carbonic acid, respectively. Assuming that the alkalis are the pure
hydroxides and the acids are water-free (carbonic acid thus being carbon dioxide),
the expected values are 816, 1144, 744, 1285 and 449, respectively. Richard
Kirwan also started to study equivalent weights in the 1780s, but initially believed
that a certain amount of alkali needed the same weight of different acids for
neutralisation.
Bergman’s table of equivalent weights is also included in his paper on carbonic
acid (Sect. 18.3) published the same year, 1775. In The Chemical Lectures of
H.T. Scheffer, Bergman also gave the quantitative compositions of many salts given
as parts alkali and parts acid per 100 parts of salt. It is unfortunately not easy to
estimate the accuracy of these results, as the water content of the salts, acids and
alkalis Bergman used are unknown.
Several other examples of Bergman’s use of the concept of constant proportions
and stoichiometry in quantitative chemical analysis will follow in this chapter; his
accidental determination of equivalent weights while trying to determine the relative phlogiston content of metals was discussed in Sect. 22.5.
In his paper on the isolation of oxalic acid (Sect. 24.1), Scheele also used
stoichiometry in an ingenious method to determine the proper amount of sulphuric
acid required to decompose lead(II) oxalate to lead sulphate and oxalic acid without
adding an excess of sulphuric acid: [24]: he precipitated lead oxalate from potassium oxalate solution using lead acetate, noting the amount of lead acetate required.
He then measured the amount of sulphuric acid required to quantitatively precipitate
lead sulphate from this amount of lead acetate. Finally, he added the same amount
of sulphuric acid to his lead oxalate to liberate the oxalic acid quantitatively.
314
23 Bergman as an Analytical Chemist