tion in a certain sense, and those which are reversible. For the first, the general type of equation will evidently be :
^5= k (a — x) (b - x) (c - x)
at
��For the second, the momentary course of the reaction is the result of the difference in the speeds of the two reverse actions, so that
_5 = h (a - x) (6 — a?) (c— x) — k x (a x 4- x) (b x + x) (c x +x), ctt
a, b, c; a u b l9 and c x denoting as before the initial masses of the substances which constitute the two opposite systems.
The integration of these equations is always possible ; moreover, it is generally simplified by the choice of the initial masses. Thus in order to apply the calculus to the experimental results obtained by Berthelot and P6an de Saint- Oilles (acetic acid and alcohol), Guldberg and Waage took up the simplified case in which a = b = 1 and a x = b x = 0. The speed equation then becomes
^= k (1 - xf - k x x\ at
The constants k and k x are in the same ratio here as in
Avidity and Speed Coefficient
To complete the study of the equilibria and speeds of reaction we must examine in how far these two methods of investigation lead to concordant results. Tables, drawn up by Thomsen and Ostwald, have already been given, showing the relative avidity of acids. Let us now see if the different acids, in such catalytic transformations as those mentioned above, exert an influence proportional to
1 The transformation of 7-oxybutyric acid into water and lactone (and also inversely) is another example of the same kind (P. Henry).
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