The Principles of Chemistry, Volume I

by Dmitry Ivanovich Mendeleyev

Footnotes:

[1] In practice, the chemist has to continually deal with gases, and gases are often collected over water; in which case a certain amount of water passes into vapour, and this vapour mixes with the gases. It is therefore most important that he should be able to calculate the amount of water or of moisture in air and other gases. Let us imagine a cylinder standing in a mercury bath, and filled with a dry gas whose volume equals v, temperature t°, and pressure or tension h mm. (h millimetres of the column of mercury at 0°). We will introduce water into the cylinder in such a quantity that a small part remains in the liquid state, and consequently that the gas will be saturated with aqueous vapour; the volume of the gas will then increase (if a larger quantity of water be taken some of the gas will he dissolved in it, and the volume may therefore he diminished). We will further suppose that, after the addition of the water, the temperature remains constant; then since the volume increases, the mercury in the cylinder falls, and therefore the pressure as well as the volume is increased. In order to investigate the phenomenon we will artificially increase the pressure, and reduce the volume to the original volume v. Then the pressure or tension will be greater than h, namely h + f, which means that by the introduction of aqueous vapour the pressure of the gas is increased. The researches of Dalton, Gay-Lussac, and Regnault showed that this increase is equal to the maximum pressure which is proper to the aqueous vapour at the temperature at which the observation is made. The maximum pressure for all temperatures may be found in the tables made from observations on the pressure of aqueous vapour. The quantity f will be equal to this maximum pressure of aqueous vapour. This may be expressed thus: the maximum tension of aqueous vapour (and of all other vapours) saturating a space in a vacuum or in any gas is the same. This rule is known as Dalton's law. Thus we have a volume of dry gas v, under a pressure h, and a volume of moist gas, saturated with vapour, under a pressure h + f. The volume v of the dry gas under a pressure h + f occupies, from Boyle's law, a volume vh / h + f consequently the volume occupied by the aqueous vapour under the pressure h + f equals v - vh / h + f , or vf / h + f . Thus the volumes of the dry gas and of the moisture which occurs in it, at a pressure h + f, are in the ratio f : h. And, therefore, if the aqueous vapour saturates a space at a pressure n, the volumes of the dry air and of the moisture which is contained in it are in the ratio (n - f) : f, where f is the pressure of the vapour according to the tables of vapour tension. Thus, if a volume N of a gas saturated with moisture be measured at a pressure H, then the volume of the gas, when dry, will be equal to N H - f / H . In fact, the entire volume N must be to the volume of dry gas x as H is to H - f; therefore, N : x = H : H - f, from which x = N H - f / H . Under any other pressure—for instance, 760 mm.—The volume of dry gas will be xH / 760 , or H - f / 760 , and we thus obtain the following practical rule: If a volume of a gas saturated with aqueous vapour be measured at a pressure H mm., then the volume of dry gas contained in it will be obtained by finding the volume corresponding to the pressure H, less the pressure due to the aqueous vapour at the temperature observed. For example, 37·5 cubic centimetres of air saturated with aqueous vapour were measured at a temperature of 15·3°, and under a pressure of 747·3 mm. of mercury (at 0°). What will be the volume of dry gas at 0° and 760 mm.?

The pressure of aqueous vapour corresponding to 15·3° is equal to 12·9 mm., and therefore the volume of dry gas at 15·3° and 747·3 mm. is equal to 37·5 × 747·3 - 12·9 / 747·3 ; at 760 mm. it will be equal to 37·5 × 734·4 / 760 ; and at 0° the volume of dry gas will be 37·5 × 734·4 / 760 × 273 / 273 + 15·3 = 34·31 c.c.

From this rule may also be calculated what fraction of a volume of gas is occupied by moisture under the ordinary pressure at different temperatures; for instance, at 30° C. f = 31·5, consequently 100 volumes of a moist gas or air, at 760 mm., contain a volume of aqueous vapour 100 × 31·5 / 760 , or 4·110; it is also found that at 0° there is contained 0·61 p.c. by volume, at 10° 1·21 p.c., at 20° 2·29 p.c., and at 50° up to 12·11 p.c. From this it may be judged how great an error might be made in the measurement of gases by volume if the moisture were not taken into consideration. From this it is also evident how great are the variations in volume of the atmosphere when it loses or gains aqueous vapour, which again explains a number of atmospheric phenomena (winds, variation of pressure, rainfalls, storms, &c.)

If a gas is not saturated, then it is indispensable that the degree of moisture should be known in order to determine the volume of dry gas from the volume of moist gas. The preceding ratio gives the maximum quantity of water which can be held in a gas, and the degree of moisture shows what fraction of this maximum quantity occurs in a given case, when the vapour does not saturate the space occupied by the gas. Consequently, if the degree of moisture equals 50 p.c.—that is, half the maximum—then the volume of dry gas at 760 mm. is equal to the volume of dry gas at 760 mm. multiplied by h - 0·5f / 760 , or, in general, by h - rf / 760 where r is the degree of moisture. Thus, if it is required to measure the volume of a moist gas, it must either be thoroughly dried or quite saturated with moisture, or else the degree of moisture determined. The first and last methods are inconvenient, and therefore recourse is usually had to the second. For this purpose water is introduced into the cylinder holding the gas to be measured; it is left for a certain time so that the gas may become saturated, the precaution being taken that a portion of the water remains in a liquid state; then the volume of the moist gas is determined, from which that of the dry gas may be calculated. In order to find the weight of the aqueous vapour in a gas it is necessary to know the weight of a cubic measure at 0° and 760 mm. Knowing that one cubic centimetre of air in these circumstances weighs 0·001293 gram, and that the density of aqueous vapour is 0·62, we find that one cubic centimetre of aqueous vapour at 0° and 760 mm. weighs 0·0008 gram, and at a temperature t° and pressure h the weight of one cubic centimetre will be 0·0008 × h / 760 × 273 / 273 + t . We already know that v volumes of a gas at a temperature t° pressure h contain v × f / h volumes of aqueous vapour which saturate it, therefore the weight of the aqueous vapour held in v volumes of a gas will be

v x 0·0008 × f / 760 × 273 / 273 + t

Accordingly, the weight of water which is contained in one volume of a gas depends only on the temperature and not on the pressure. This also signifies that evaporation proceeds to the same extent in air as in a vacuum, or, in general terms (this is Dalton's law), vapours and gases diffuse into each other as if into a vacuum. In a given space, at a given temperature, a constant quantity of vapour enters, whatever be the pressure of the gas filling that space.

From this it is clear that if the weight of the vapour contained in a given volume of a gas be known, it is easy to determine the degree of moisture r = p / v × 0·0008 × 760 / t × 273 + t / 273 . On the is founded the very exact determination of the degree of moisture of air by the weight of water contained in a given volume. It is easy to calculate from the preceding formula the number of grams of water contained at any pressure in one cubic metre or million cubic centimetres of air saturated with vapour at various temperatures; for instance, at 30° f = 31·5, hence p = 29·84 grams.

The laws of Mariotte, Dalton, and Gay-Lussac, which are here applied to gases and vapours, are not entirely exact, but are approximately true. If they were quite exact, a mixture of several liquids, having a certain vapour pressure, would give vapours of a very high pressure, which is not the case. In fact the pressure of aqueous vapour is slightly less in a gas than in a vacuum, and the weight of aqueous vapour held in a gas is slightly less than it should be according to Dalton's law, as was shown by the experiments of Regnault and others. This means that the tension of the vapour is less in air than in a vacuum. The difference does not, however, exceed 5 per cent. of the total pressure of the vapours. This decrement in vapour tension which occurs in the intermixture of vapours and gases, although small, indicates that there is then already, so to speak, a beginning of chemical change. The essence of the matter is that in this case there occurs, as on contact (see preceding footnote), an alteration in the motions of the atoms in the molecules, and therefore also a change in the motion of the molecules themselves.

In the uniform intermixture of air and other gases with aqueous vapour, and in the capacity of water to pass into vapour and form a uniform mixture with air, we may perceive an instance of a physical phenomenon which is analogous to chemical phenomena, forming indeed a transition from one class of phenomena to the other. Between water and dry air there exists a kind of affinity which obliges the water to saturate the air. But such a homogeneous mixture is formed (almost) independently of the nature of the gas in which evaporation takes place; even in a vacuum the phenomenon occurs in exactly the same way as in a gas, and therefore it is not the property of the gas, nor its relation to water, but the property of the water itself, which compels it to evaporate, and therefore in this case chemical affinity is not yet operative—at least its action is not clearly pronounced. That it does, however, play a certain part is seen from the deviation from Dalton's law.