Note 26 — Chapter XXI · CHROMIUM, MOLYBDENUM, TUNGSTEN, URANIUM, AND MANGANESE

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. If dt be the increment of time and dx the quantity of a substance changed in this space of time, then the fraction (or quotient) dx/dt will 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. that dx/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 when t = 0 and x = 0—that is, at the beginning of the experiment, from which the time t and quantity x of substance changed is counted. On integrating the preceding equation we obtain log(A/(A - x)) = kt, where k is a new constant, if we take ordinary (and not natural) logarithms. Hence, knowing A, x, and t, for each reaction, we find k, 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 that k = 0·0114; for example, t = 44, x = 68·4 (A = 100), whence kt = 0·5004 and k = 0·0114, (see also Chapter XIV., Note 3, and Chapter XVII., Note 25 bis).