In the case of gases we distinguish the specific heat at a constant pressure c′ (we designated this quantity above by Q), and at a constant volume c. It is evident that the relation between the two specific heats, k, judging from the above, is the ratio of Q to K, or equal to the ratio of 2·45n + 2 to 2·45n. When n = 1 this ratio k = 1·8; when n = 2, k = 1·4, when n = 3, k = 1·3, and with an exceedingly large number n, of atoms in the molecule, k = 1. That is, the ratio between the specific heats decreases from 1·8 to 1·0 as the number of atoms, n, contained in the molecule increases. This deduction is verified to a certain extent by direct experiment. For such gases as hydrogen, oxygen, nitrogen, carbonic oxide, air, and others in which n = 2, the magnitude of k is determined by methods described in works on physics (for example, by the change of temperature with an alteration of pressure, by the velocity of sound, &c.) and is found in reality to be nearly 1·4, and for such gases as carbonic anhydride, nitric dioxide, and others it is nearly 1·3. Kundt and Warburg (1875), by means of the approximate method mentioned in Note [29], Chapter VII., determined k for mercury vapour when n = 1, and found it to be = 1·67—that is, a larger quantity than for air, as would be expected from the above.
It may be admitted that the true atomic heat of gases = 2·43, only under the condition that they are distant from a liquid state, and do not undergo a chemical change when heated—that is, when no internal work is produced in them (B = 0). Therefore this work may to a certain extent be judged by the observed specific heat. Thus, for instance, for chlorine (Q = 0·12, Regnault; k = 1·33, according to Straker and Martin, and therefore K = 0·09, MK = 6·4), the atomic heat (3·2) is much greater than for other gases containing two atoms in a molecule, and it must be assumed, therefore, that when it is heated some great internal work is accomplished.
In order to generalise the facts concerning the specific heat of gases and solids, it appears to me possible to accept the following general proposition: the atomic heat (that is, AQ or QM/n, where M is the molecular weight and n the number of molecules) is smaller (in solids it attains its highest value 6·8 and in gases 3·4), the more complex the molecule (i.e. the greater the number (n) of atoms forming it) and so much smaller, up to a certain point (in similar physical states) the smaller the mean atomic weight M/n.
[8] As an example, it will be sufficient to refer to the specific heat of nitrogen tetroxide, N2O4, which, when heated, gradually passes into NO2—that is, chemical work of decomposition proceeds, which consumes heat. Speaking generally, specific heat is a complex quantity, in which it is clear that thermal data (for instance, the heat of reaction) alone cannot give an idea either of chemical or of physical changes individually, but always depend on an association of the one and the other. If a substance be heated from t0 to t1 it cannot but suffer a chemical change (that is, the state of the atoms in the molecules changes more or less in one way or another) if dissociation sets in at a temperature t1. Even in the case of the elements whose molecules contain only one atom, a true chemical change is possible with a rise of temperature, because more heat is evolved in chemical reactions than that quantity which participates in purely physical changes. One gram of hydrogen (specific heat = 3·4 at a constant pressure) cooled to the temperature of absolute zero will evolve altogether about one thousand units of heat, 8 grams of oxygen half this amount, whilst in combining together they evolve in the formation of 9 grams of water more than thirty times as much heat. Hence the store of chemical energy (that is, of the motion of the atoms, vortex, or other) is much greater than the physical store proper to the molecules, but it is the change accomplished by the former that is the cause of chemical transformations. Here we evidently touch on those limits of existing knowledge beyond which the teaching of science does not yet allow us to pass. Many new scientific discoveries have still to be made before this is possible.
[9] As if NaH = Mg and KH = Ca, which is in accordance with their valency. KH includes two monovalent elements, and is a bivalent group like Ca.
[10] Sodium carbonate and other carbonates of the alkalis give acid salts which are less soluble than the normal; here, on the contrary, with an excess of carbonic anhydride, a salt is formed which is more soluble than the normal, but this acid salt is more unstable than sodium hydrogen carbonate, NaHCO3.
[11] The formation of dolomite may be explained, if only we imagine that a solution of a magnesium salt acts on calcium carbonate. Magnesium carbonate may be formed by double decomposition, and it must be supposed that this process ceases at a certain limit (Chapter [XII].), when we shall obtain a mixture of the carbonates of calcium and magnesium. Haitinger heated a mixture of calcium carbonate, CaCO3, with a solution of an equivalent quantity of magnesium sulphate, MgSO4, in a closed tube at 200°, and then a portion of the magnesia actually passed into the state of magnesium carbonate, MgCO3, and a portion of the lime was converted into gypsum, CaSO4. Lubavin (1892) showed that MgCO3 is more soluble than CaCO3 in salt water, which is of some significance in explaining the composition of sea water.
[12] The undoubted action of lime in increasing the fertility of soils—if not in every case, at all events, with ordinary soils which have long been under corn—is based not so much on the need of plants for the lime itself as on those chemical and physical changes which it produces in the soil, as a particularly powerful base which aids the alteration of the mineral and organic elements of the soil.
[13] Sodium and potassium only decompose magnesium oxide at a white heat and very feebly, probably for two reasons. In the first place, because the reaction Mg + O develops more heat (about 140 thousand calories) than K2 + O or Na2 + O (about 100 thousand calories); and, in the second place, because magnesia is not fusible at the heat of a furnace and cannot act on the charcoal, sodium, or potassium—that is, it does not pass into that mobile state which is necessary for reaction. The first reason alone is not sufficient to explain the absence of the reaction between charcoal and magnesia, because iron and charcoal in combining with oxygen evolve less heat than sodium or potassium, yet, nevertheless, they can displace them. With respect to magnesium chloride, it acts on sodium and potassium, not only because their combination with chlorine evolves more heat than the combination of chlorine and magnesium (Mg + Cl2 gives 150 and Na2 + Cl2 about 195 thousand calories), but also because a fusion, both of the magnesium chloride and of the double salt, takes place under the action of heat. It is probable, however, that a reverse reaction will take place. A reverse reaction might probably be expected, and Winkler (1890) showed that Mg reduces the oxides of the alkali metals (Chapter XIII., Note [42]).
[14] Commercial magnesium generally contains a certain amount of magnesium nitride (Deville and Caron), Mg3N2—that is, a product of substitution of ammonia which is directly formed (as is easily shown by experiment) when magnesium is heated in nitrogen. It is a yellowish green powder, which gives ammonia and magnesia with water, and cyanogen when heated with carbonic anhydride. Pashkoffsky (1893) showed that Mg3N2 is easily formed and is the sole product when Mg is heated to redness in a current of NH3. Perfectly pure magnesium may be obtained by the action of a galvanic current.