Art. LIX.—The Effect on Temperature of Molecular Association and Dissociation.
[Read before the Philosophical Institute of Canterbury, 6th September, 1905]
In this paper it is proposed to show that in certain chemical reactions much of the temperature-change may be due to a source overlooked in Berthelot's fundamental proposition as stated in 1879— viz., “The heat disengaged in any reaction is a measure of the chemical and physical work done in that reaction.” In recent criticism of Berthelot's proposition this source appears to remain unnoticed.
According to the kinetic theory the temperature of any given gas is proportional to the mean square of the molecular velocity, and for different gases the temperature is proportional to the average kinetic energy of translation of the molecules.
If we mix equal volumes of two different gases without any temperature-change resulting it can be shown that mnv2 = m, nv,2, where m and v represent the mass and average velocity of the molecules in the one, and m, and v, the corresponding quantities in the other, gas. That is to say, at the same temperature the average kinetic energy of translation of all gaseous particles must be the same whatever be their masses.
If we have two gases with molecular masses of m and m/2 respectively, then, where their average molecular velocities are equal, their respective kinetic energies are as 2 : 1, and their respective absolute temperatures therefore as 2 : 1. Let us apply this, in the first instance, to those numerous cases in which gaseous molecules when heated split up into two or more parts, reassociating on cooling—e.g., water, carbon-dioxide, ammonium-chloride, nitrogen-peroxide, &c. The dissociation absorbs heat, while the reassociation, promoted by cooling, gives out heat.
Consider the case of N2O4—nitrogen-peroxide : If this gas be heated above O°C. some of the molecules split into two parts, as is shown by the lessened density. Disregarding any work done in bringing about this disruption, and further neglecting, for the present, any change in the internal energy of the molecule, we may fairly assume that the sum of the kinetic energies of translation of the two parts must be equal to the kinetic energy of translation of the original molecule. But each part is now an independent molecule, having half the kinetic energy of translation of the molecules around it. So mv2 has become 2 × m/2 v2, and therefore each NO2 molecule in impact with the rest will have its velocity increased, and will not be in equ-
librium until its original velocity is doubled; for m/2v,2 to be equal to mv2, v,2 must be equal to 2v2. In other words, heat will be absorbed by the dissociation. Each molecule that dissociates is thereby reduced to half its original absolute temperature, if the term “temperature” can be applied to individual molecules.
The internal energy neglected above may be a disturbing factor. If the sum of the internal energies of the two new molecules is less than that of the original molecule, the difference will be added to the external translation energy, and the fall of temperature may be less than given above.
As for the quantity of heat which appears or disappears in any given case, this will obviously depend upon the initial temperature, increasing and decreasing with it. For instance, in the oxidation of CO into CO2 the number of molecules decreases by one-third, the kinetic energy of the vanished molecules is divided amongst those which are left, and hence, neglecting any heat produced by chemical attraction, or absorbed as internal energy in the more complex new molecules, the temperature will rise one-third. Supposing the initial temperature to be 600° C., the final temperature will thus be 800°, a rise of 200° which does not represent any chemical or physical work done in the reaction. If by the use of catalytic agents or otherwise the reaction could be carried out at a temperature of 60° the rise would be 20° only. If, on the other hand, the reaction could take place in an arc lamp at, say, a temperature of 3,000° C., the rise of temperature would be 1,000°. The quantities of heat disengaged would be proportional to the temperature-rise. Hence it would appear that heats of combustion of gases, in all cases where the number of molecules alters, should vary with the initial temperature of the experiment, and should be affected also by any rise of temperature during the experiment. A difficulty in calculating the amount of this effect in any given case may arise in this way : In reactions accelerated by heat those molecules with velocities above the average may suffer change more readily than the rest, introducing an uncertainty as to the true initial temperature.
If a gaseous molecule could be split up into parts small enough, the temperature of these parts might be reduced nearly to absolute zero without any reduction of molecular velocity. Supposing, for example, the alpha particle separated from a molecule, of radium at O° C. to have a mass of 1/100 of the original molecule, and to split off without gaining or losing velocity, its kinetic energy would be 1/100 of that of the original molecule, and would correspond to a temperature of 2·73° absolute. It would appear, then, if association or dissociation could be carried on sufficiently far in a given mass, the temperature of that mass may alter to any extent, its kinetic energy remaining the same. As,
approximately, the specific heat of gases under constant pressure is inversely proportional to their densities, any dissociation should proportionately increase the specific heat.
Reasoning similar to the foregoing can be applied to liquids, though with less certainty, perhaps also to solids. Assuming it to be thus applicable, and neglecting the internal-energy factor, the following relations should hold:—
1. Whenever, in a given mass undergoing chemical change, there is an increase or decrease in the number of molecules, there is a proportionate decrease or increase of the absolute temperature.
2. The temperature of a given mass may be altered apart from external conditions, thus : (a) by conversion of potential energy of chemical affinity into kinetic energy, and vice versa; (b) by conversion of internal energy of a molecule into external energy, or vice versa; (c) by association or dissociation of molecules, including ionization; (d) by dissociation of atoms, as in radium.
3. The temperature of a given mass remains proportional to the sum total of the kinetic energy of translation of its particles only so long as the number of particles remains constant.
4. Evolution of heat in a chemical reaction is not necessarily synonymous with production of energy, but may be due merely to the distribution of the original energy amongst a greater or smaller number of molecules.
displays of light and heat so familiar in cases of chemical combination suggest the idea that chemical actions take place only when heat is evolved by them. This idea was given definite expression by Thomsen, and later by Berthelot, thus : “Substances which can act chemically upon one another tend, when left freely to their mutual action, to produce that system which is formed with the greatest evolution of heat.” This statement, however, has been found to be much too general, and is no longer defended in its entirety, many cases being known in which heat-absorbing reactions occur spontaneously. On examining some of these endothermic reactions, however, it will be found that there is quite a possibility that they are really exothermic after all, so far as the chemical reactions are concerned. Some, if not all, of the apparent loss of heat is obviously due to increase in the number of molecules—e.g., solid Glauber's salt mixed with concentrated hydrochloric acid liquefies spontaneously, and cools down many degrees. On writing the equation a large increase in the number of particles becomes evident— Na2SO4. 10 H2O+ 2HCl =2 NaCl+H2SO4+10 H2O. Allowing for ionization, there is an increase of particles in the ratio of about 17 to 5. Hence, even though the transformation be far from complete,
there is a considerable increase in the number of molecules, or ions and molecules, and therefore a considerable decrease in temperature, quite apart from that due to chemical energies.
In connection with Van't Hoff's finding that the principle of maximum work stated by Berthelot is the more nearly correct the nearer the temperature of reaction is to absolute zero, and that at absolute zero it would be correct, it is perhaps worth pointing out as a coincidence that the apparent heat-changes due to formation or disappearance of molecules become proportionately less as the temperature of reaction is lowered, and vanish at absolute zero.
If the temperature of solids is proportional to their molecular kinetic energies, then, neglecting the internal -energy factor, the capacity for heat of equal numbers of molecules should be the same irrespective of their masses. Hence the specific heat of solids (other things being equal) should be inversely proportional to their molecular weights. The specific heats of the solid elements, however, are proportional to their atomic weights, which suggests that the solid elements with normal specific heats have the same number of atoms per molecule.