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Let A=SO3Aq; B=Na,OAq, and A'=H,C1,Aq; and let rrj.

See equation par. 230.
Then [Na2SO'Aq, H’Cl’Aq]=- $.3898-1.2352= -3383 :

observed, - 3364.

And

[Na2C1_Aq, SO3Aq]= +}.3898 - 3.2352=515: observed, 488.

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.

The differences between the observed and calculated numbers amount to less than I per million of the heat of neutralisation.

Hence, the avidity (affinity) of hydrochloric acid for soda is equal to that of nitric acid, and is twice as great as that of sulphuric acid for the same base!

Thomsen has determined the relative avidities (affinities) of many acids by this thermochemical method ; his results are given in the table on p. 441.

Thomsen then applies the theory of Guldberg and Waage to his results, and shews that the numbers obtained by experiment agree very well with those calculated by the use of equations deduced from this theory.

235. The following table contains Ostwald's results regarding the relative affinities of acids.

The numbers in column I are those obtained by the study of the inversion of sugar by various acids.

The numbers in column II are those obtained by the study of the decomposition of methylic acetate by water in presence of acids.

The numbers in column III are those obtained by the study of the decomposition of acetamide by water in presence of acids.

The numbers in column iv are those obtained by measuring the volume-changes which occur when various acids and bases are mixed in equivalent quantities.

The numbers in columns V and vi are those obtained by studying the action of dilute acids on calcium oxalate"; those

i loc. cit. p. 115.
Y loc. cit. pp. 118—-124.

3 The details of the investigation from which these numbers are obtained have not yet been published; the work has been conducted by one of Ostwald's pupils.

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Hydrochloric
Hydrobromic
Hydriodic
Nitric
Chloric
Sulphuric
Methyl sulphuric
Ethyl sulphuric
Propyl sulphuric
Isobutyl sulphuric
Amyl sulphuric
Ethyl sulphuric
Isethionic
Benzene sulphonic
Formic
Acetic
Propionic
Butyric
Isobutyric
Monochloracetic
Dichloracetic
Trichloracetic
Glycollic
Diglycollic
Lactic
Methoxyacetic
Ethoxyacetic
Methoxypropionic
Hydroxyisobutyric
Trichlorolactic
Pyruvic
Oxalic
Malonic
Glyceric
Succinic
Malic
Tartaric
Pyrotartaric
Racemic
Citric
Phosphoric
Arsenic

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135
117

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131 249 219

1

? The affinity of sulphuric acid appears less than that of its derivatives obtained by replacing hydrogen by indifferent, or even basic, radicles. But it is to be noted that 1 H,, is compared with SO,.OH.OCH, &c. If molecular quantities are

3

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in v represent the results of the use of normal solutions, and those in VI of 10 th normal solutions of acids.

The numbers in column I are regarded by Ostwald as the most trustworthy; the reaction employed is freer from secondary actions than any of the others. The numbers in column II are also very satisfactory; the reaction used (CH,.COO.CH,+HOH=CH .COOH+CH,OH)was simpler than any of those by which the numbers in the succeeding columns were obtained; the acids whose affinity-constants were sought for remained in the free state throughout the whole process, so that no complication could arise from the formation of acid salts, &c. such as occurred in the processes investigated in columns III to VI. There was only one secondary action, namely, that due to the presence of free acetic acid, and the influence of this could be partially eliminated in the calculations.

The two series of numbers obtained by employing the reaction of acids on solid calcium oxalate differ greatly, but the arrangement of the acids in accordance with their affinities is the same in both. The numbers obtained by using dilute acids (10 th normal), column VI, agree very well with those in column II, while the numbers deduced from observations with stronger solutions (normal), column V, agree better with those based on measurements of volume-changes, column IV; hence, Ostwald argues, the explanation before given regarding the combined action of water and acid on calcium oxalate is confirmed. When very dilute solutions of acids are employed, the water exerts an action on the solid salt independently of the acid, just as in the reaction from which the numbers in column II are obtained there is a twofold action, partly due to the water and partly to the acid. It will still be necessary to endeavour to separate these actions before numbers are obtained which represent the affinity-constants of the acids alone. From experiments not yet published, Ostwald thinks that the numbers obtained by studying the division of bases between two acids are affected by a source of error which to be compared, the observed numbers for sulphuric acid reactions must be doubled ; if this is done the affinity of this acid is 104'56.

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makes the stronger acids appear stronger, and the weaker acids weaker, than they really are (loc. cit. (2) 29. 403).

The results obtained by thermochemical methods are presented in the following table.

100

RELATIVE AFFINITIES (avidities) OF ACIDS. (THOMSEN?.)
Acid.

Acid.
Nitric

Oxalic

24
Hydrochloric 100

Orthophosphoric 13
Hydrobromic

89

Monochloracetic 9
Hydriodic

79

Hydrofluoric 5
Sulphuric

49
Tartaric

5
Selenic

45
Citric

5
Trichloracetic

36
Acetic

3

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236. We have already seen that from his volumetric experiments on the division of a base between two acids, Ostwald concluded that the true relative affinities of hydrochloric, nitric, and sulphuric acids are independent of the nature of the base (see ante, par. 223). If this holds good for all acids, the conclusion is arrived at that the relative affinities of bases are independent of the nature of the acids on which they react.

Stating the absolute affinity of an acid A, for a base, C, in the form f(A,C), the statement just made may be put thus

(A,C)= (A), V (C): that is, the affinity between an acid and a base is the product of the specific affinity-constant of the acid, and the specific affinity-constant of the base ?.

This conclusion is confirmed, on the whole, by Thomsen's thermochemical researches. It was mentioned in pars. 222—3 that Ostwald had developed Guldberg and Waage's fundamental equation for finding the velocity of a chemical change,

a

3

1 loc. cit. 1. 308. The numbers given by Thomsen are calculated for equiva. lent weights of the various acids (e.g. for HCl, 1H,SO,, } Hz.C H,O,, &c.), except in the case of phosphoric acid ; the number given in the table for this acid is taken from L. Meyer (Die modernen Theorien, p. 489). The chapter on Chemische Massenwirkung in L. Meyer's book should be studied in conjunction with the preceding paragraphs (203-235).

2 Ostwald, loc. cit. (2) 16. 423.

so as to separate the factors k and k' (in reactions between acids and bases) into two parts, one depending solely on the nature of the acid and the other solely on the nature of the base, and that he had thence deduced the conclusion that the affinity-constants of acids are proportional to the square roots of the velocities of the reactions brought about by them.

Reviewing the whole of the work on affinity which has passed before us, we are I think justified in assenting to Ostwald's conclusion that the specific intensity of any action brought about by an acid is conditioned by the value of the affinity of that acid; or as it is put by Ostwald in another paper (loc. cit. (2) 29. 57), the affinity-values of the acids appear as constants which quantitatively condition the chemical actions of these acids. The numbers hitherto obtained representing the relative magnitudes of these affinities can be regarded only as approximate; no reaction has yet been found entirely free from secondary changes, nor has it been possible completely to eliminate the influence of these secondary changes in making the necessary calculations. Nevertheless we may use the numbers given by Ostwald, more especially those derived from his study of the accelerating action of various acids on the decomposition of methylic acetate by water, and on the inversion of sugar solutions, in endeavouring to find the velocities, and final states of equilibrium of many chemical reactions.

237. Guldberg and Waage did not attempt to do more than find the coefficients of affinity of various reactions. In their use of the expression, a coefficient of affinity is the resultant of the actions of many forces; Ostwald has analysed this quantity, and has endeavoured to assign to each member of the changing system a definite number which represents the share of the total result belonging to that constituent. As each element has a definite atomic weight, and each atom has a definite valency, and as these numbers sum up a great deal of information regarding the properties of the element and its compounds when looked at from a statical point of view; so each chemical substance appears to have a definite

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