23.2 Quantitative Analysis
By the time Bergman was appointed professor of chemistry, the idea of conservation of mass in chemical processes was not yet universally accepted, and much
less the idea of stoichiometry, i.e. that a certain amount of a particular acid, for
example, needed a certain amount of a base for neutralisation. Chemists had to use
trial and error to find the correct ratios for mixing of starting materials in chemical
reactions. Sometimes, they came quite close, as, for example, when Basil Valentine
(Basilius Valentinus) prepared metallic antimony by reducing antimony(III) sulphide with iron in his 1604 book Triumph Wagen Antimonii (Triumphant Chariot
of Antimony). He used two parts of Sb 2 S 3 and one part of Fe; the true stoichiometric
ratio is 2:0.98. The term stoichiometry was coined by Jeremias Benjamin Richter
(1762–1807), who explained the relationships between the amounts of substances
in chemical reactions in mathematical terms in his book Anfangsgründe der
Stöchymometrie (Introduction to Stoichiometry) 1792–1794. Still, the concept was
not generally accepted until about 1805 and the controversy between French
chemists Joseph Proust and Claude Louis Berthollet (1748–1822).
There are rare examples of the use of stoichiometry as early as in the seventeenth
century, e.g. by van Helmont, Kunckel and Homberg [16]. Bergman referred to an
experiment by van Helmont where he fused a weighed amount of silica (hydrated
SiO 2 ) with alkali to form an alkali silicate. The same amount of silica was precipitated from the silicate solution by acids [17]. Homberg determined the concentrations of mineral acids in 1699 by determining the weight of alkali carbonate
needed to neutralise the acid [18]. Henry Cavendish was another early pioneer of
stoichiometry. In a paper dealing with water analysis, he introduced the word
equivalent in 1767, writing “[…] as much fixed alkali [sodium or potassium carbonate], as was equivalent to 48 8/10 grains of calcareous earth [CaO]” [19]. For
Bergman and Scheele, it seems that the concept of stoichiometry was so natural that
they never discussed the matter, while Wallerius was a fierce opponent.
Bergman was familiar with at least the work of Homberg[20] and in his notes to
The Chemical Lectures of H.T. Scheffer, published in 1775, he presented a table of
the weights of sulphuric acid, nitric acid, hydrochloric acid and carbonic acid
needed to neutralise 100 parts of sodium hydroxide and 100 parts of potassium
hydroxide, respectively [21]. Alkali metal hydroxides are very hygroscopic and also
absorb carbon dioxide from the air, which made the experiment complicated.
Bergman removed moisture by heating the hydroxides, but they would still be
contaminated with carbonate. Thus, Bergman dissolved the hydroxide in the minimum amount of water in a bottle (A) and closed it with a cork. The acid was put in
a smaller bottle (B), and the two bottles were weighed; the weight of the hydroxide
bottle being a and the weight of the acid bottle b.
3 Small portions of the acid were
added to the base until the solution was neutral, and the bottles weighed again, the
weights now being a and b, respectively. For a completely pure hydroxide, a-a
3
With his mathematical and physical education, Bergman expressed himself in this algebraic
manner whenever possible.
23.2 Quantitative Analysis
313
By the time Bergman was appointed professor of chemistry, the idea of conservation of mass in chemical processes was not yet universally accepted, and much
less the idea of stoichiometry, i.e. that a certain amount of a particular acid, for
example, needed a certain amount of a base for neutralisation. Chemists had to use
trial and error to find the correct ratios for mixing of starting materials in chemical
reactions. Sometimes, they came quite close, as, for example, when Basil Valentine
(Basilius Valentinus) prepared metallic antimony by reducing antimony(III) sulphide with iron in his 1604 book Triumph Wagen Antimonii (Triumphant Chariot
of Antimony). He used two parts of Sb 2 S 3 and one part of Fe; the true stoichiometric
ratio is 2:0.98. The term stoichiometry was coined by Jeremias Benjamin Richter
(1762–1807), who explained the relationships between the amounts of substances
in chemical reactions in mathematical terms in his book Anfangsgründe der
Stöchymometrie (Introduction to Stoichiometry) 1792–1794. Still, the concept was
not generally accepted until about 1805 and the controversy between French
chemists Joseph Proust and Claude Louis Berthollet (1748–1822).
There are rare examples of the use of stoichiometry as early as in the seventeenth
century, e.g. by van Helmont, Kunckel and Homberg [16]. Bergman referred to an
experiment by van Helmont where he fused a weighed amount of silica (hydrated
SiO 2 ) with alkali to form an alkali silicate. The same amount of silica was precipitated from the silicate solution by acids [17]. Homberg determined the concentrations of mineral acids in 1699 by determining the weight of alkali carbonate
needed to neutralise the acid [18]. Henry Cavendish was another early pioneer of
stoichiometry. In a paper dealing with water analysis, he introduced the word
equivalent in 1767, writing “[…] as much fixed alkali [sodium or potassium carbonate], as was equivalent to 48 8/10 grains of calcareous earth [CaO]” [19]. For
Bergman and Scheele, it seems that the concept of stoichiometry was so natural that
they never discussed the matter, while Wallerius was a fierce opponent.
Bergman was familiar with at least the work of Homberg[20] and in his notes to
The Chemical Lectures of H.T. Scheffer, published in 1775, he presented a table of
the weights of sulphuric acid, nitric acid, hydrochloric acid and carbonic acid
needed to neutralise 100 parts of sodium hydroxide and 100 parts of potassium
hydroxide, respectively [21]. Alkali metal hydroxides are very hygroscopic and also
absorb carbon dioxide from the air, which made the experiment complicated.
Bergman removed moisture by heating the hydroxides, but they would still be
contaminated with carbonate. Thus, Bergman dissolved the hydroxide in the minimum amount of water in a bottle (A) and closed it with a cork. The acid was put in
a smaller bottle (B), and the two bottles were weighed; the weight of the hydroxide
bottle being a and the weight of the acid bottle b.
3 Small portions of the acid were
added to the base until the solution was neutral, and the bottles weighed again, the
weights now being a and b, respectively. For a completely pure hydroxide, a-a
3
With his mathematical and physical education, Bergman expressed himself in this algebraic
manner whenever possible.
23.2 Quantitative Analysis
313