[25]For rapid and accurate determinations of this kind, advantage is taken of those methods of chemical analysis which are known as ‘titrations’ (volumetric analysis), and consist in measuring the volume of solutions of known strength required for the complete conversion of a given substance. Details respecting the theory and practice of titration, in which potassium permanganate is very frequently employed, must be looked for in works on analytical chemistry.[26]The measurements of velocity and acceleration serve for determining the measure of forces in mechanics, but in that case the velocities are magnitudes of length or paths passed over in a unit of time. The velocity of chemical change embodies a conception of quite another kind. In the first place, the velocities of reactions are magnitudes of the masses which have entered into chemical transformations; in the second place, these velocities can only be relative quantities. Hence the conception of ‘velocity’ has quite a different meaning in chemistry from what it has in mechanics. Their only common factor is time. Ifdtbe the increment of time anddxthe quantity of a substance changed in this space of time, then the fraction (or quotient)dx/dtwill express the rate of the reaction. The natural conclusion, come to both by Harcourt and Esson, and previously to them (1850) by Wilhelmj (who investigated the rate of conversion, or inversion, of sugar in its passage into glucose), consists in establishing that this velocity is proportional to the quantity of substances still unchanged—i.e.thatdx/dt= C(A -x), where C is a constant coefficient of proportionality, and where A is the quantity of a substance taken for reaction at the moment whent= 0 andx= 0—that is, at the beginning of the experiment, from which the timetand quantityxof substance changed is counted. On integrating the preceding equation we obtain log(A/(A -x)) =kt, wherekis a new constant, if we take ordinary (and not natural) logarithms. Hence, knowing A,x, andt, for each reaction, we findk, and it proves to be a constant quantity. Thus from the figures cited in the text for the reaction 2KMnO4+ 108C2H2O4+ 14MnSO4, it may be calculated thatk= 0·0114; for example,t= 44,x= 68·4 (A = 100), whencekt= 0·5004 andk= 0·0114, (see alsoChapter XIV., Note3, and Chapter XVII., Note25 bis).[27]The researches made by Hood, Van't Hoff, Ostwald, Warder, Menschutkin, Konovaloff, and others have a particular significance in this direction. Owing to the comparative novelty of this subject, and the absence of applicable as well as indubitable deductions, I consider it impossible to enter into this province of theoretical chemistry, although I am quite confident that its development should lead to very important results, especially in respect to chemical equilibria, for Van't Hoff has already shown that the limit of reaction in reversible reactions is determined by the attainment of equal velocities for the opposite reactions.
[25]For rapid and accurate determinations of this kind, advantage is taken of those methods of chemical analysis which are known as ‘titrations’ (volumetric analysis), and consist in measuring the volume of solutions of known strength required for the complete conversion of a given substance. Details respecting the theory and practice of titration, in which potassium permanganate is very frequently employed, must be looked for in works on analytical chemistry.
[25]For rapid and accurate determinations of this kind, advantage is taken of those methods of chemical analysis which are known as ‘titrations’ (volumetric analysis), and consist in measuring the volume of solutions of known strength required for the complete conversion of a given substance. Details respecting the theory and practice of titration, in which potassium permanganate is very frequently employed, must be looked for in works on analytical chemistry.
[26]The measurements of velocity and acceleration serve for determining the measure of forces in mechanics, but in that case the velocities are magnitudes of length or paths passed over in a unit of time. The velocity of chemical change embodies a conception of quite another kind. In the first place, the velocities of reactions are magnitudes of the masses which have entered into chemical transformations; in the second place, these velocities can only be relative quantities. Hence the conception of ‘velocity’ has quite a different meaning in chemistry from what it has in mechanics. Their only common factor is time. Ifdtbe the increment of time anddxthe quantity of a substance changed in this space of time, then the fraction (or quotient)dx/dtwill express the rate of the reaction. The natural conclusion, come to both by Harcourt and Esson, and previously to them (1850) by Wilhelmj (who investigated the rate of conversion, or inversion, of sugar in its passage into glucose), consists in establishing that this velocity is proportional to the quantity of substances still unchanged—i.e.thatdx/dt= C(A -x), where C is a constant coefficient of proportionality, and where A is the quantity of a substance taken for reaction at the moment whent= 0 andx= 0—that is, at the beginning of the experiment, from which the timetand quantityxof substance changed is counted. On integrating the preceding equation we obtain log(A/(A -x)) =kt, wherekis a new constant, if we take ordinary (and not natural) logarithms. Hence, knowing A,x, andt, for each reaction, we findk, and it proves to be a constant quantity. Thus from the figures cited in the text for the reaction 2KMnO4+ 108C2H2O4+ 14MnSO4, it may be calculated thatk= 0·0114; for example,t= 44,x= 68·4 (A = 100), whencekt= 0·5004 andk= 0·0114, (see alsoChapter XIV., Note3, and Chapter XVII., Note25 bis).
[26]The measurements of velocity and acceleration serve for determining the measure of forces in mechanics, but in that case the velocities are magnitudes of length or paths passed over in a unit of time. The velocity of chemical change embodies a conception of quite another kind. In the first place, the velocities of reactions are magnitudes of the masses which have entered into chemical transformations; in the second place, these velocities can only be relative quantities. Hence the conception of ‘velocity’ has quite a different meaning in chemistry from what it has in mechanics. Their only common factor is time. Ifdtbe the increment of time anddxthe quantity of a substance changed in this space of time, then the fraction (or quotient)dx/dtwill express the rate of the reaction. The natural conclusion, come to both by Harcourt and Esson, and previously to them (1850) by Wilhelmj (who investigated the rate of conversion, or inversion, of sugar in its passage into glucose), consists in establishing that this velocity is proportional to the quantity of substances still unchanged—i.e.thatdx/dt= C(A -x), where C is a constant coefficient of proportionality, and where A is the quantity of a substance taken for reaction at the moment whent= 0 andx= 0—that is, at the beginning of the experiment, from which the timetand quantityxof substance changed is counted. On integrating the preceding equation we obtain log(A/(A -x)) =kt, wherekis a new constant, if we take ordinary (and not natural) logarithms. Hence, knowing A,x, andt, for each reaction, we findk, and it proves to be a constant quantity. Thus from the figures cited in the text for the reaction 2KMnO4+ 108C2H2O4+ 14MnSO4, it may be calculated thatk= 0·0114; for example,t= 44,x= 68·4 (A = 100), whencekt= 0·5004 andk= 0·0114, (see alsoChapter XIV., Note3, and Chapter XVII., Note25 bis).
[27]The researches made by Hood, Van't Hoff, Ostwald, Warder, Menschutkin, Konovaloff, and others have a particular significance in this direction. Owing to the comparative novelty of this subject, and the absence of applicable as well as indubitable deductions, I consider it impossible to enter into this province of theoretical chemistry, although I am quite confident that its development should lead to very important results, especially in respect to chemical equilibria, for Van't Hoff has already shown that the limit of reaction in reversible reactions is determined by the attainment of equal velocities for the opposite reactions.
[27]The researches made by Hood, Van't Hoff, Ostwald, Warder, Menschutkin, Konovaloff, and others have a particular significance in this direction. Owing to the comparative novelty of this subject, and the absence of applicable as well as indubitable deductions, I consider it impossible to enter into this province of theoretical chemistry, although I am quite confident that its development should lead to very important results, especially in respect to chemical equilibria, for Van't Hoff has already shown that the limit of reaction in reversible reactions is determined by the attainment of equal velocities for the opposite reactions.