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# Determining the Density of Aqueous Vapour

It is not easy to arrange experiments to determine directly, with sufficient accuracy, the diminution in pressure of a mass of air when all moisture shall have been abstracted without alteration of volume, but we may attack the problem indirectly. Let us suppose that we determine the weight in grammes of the moisture which is contained in a cubic metre of the air as we find it at the temperature t and with a barometric pressure H.

Then this weight is properly called the actual density of the aqueous vapour in the air at the time, in grammes per cubic metre. Let this be denoted by d, and let us denote by δ the specific gravity of the aqueous vapour referred to air at the same pressure e and the same temperature t, and moreover let w be the density of air at 0°C and 760 mm pressure expressed in grammes per cubic metre. Then the density of air at the pressure e and temperature t, also expressed in grammes per cubic metre, is equal to ew/760/(1+at), where a = coefficient of expansion of gases per degree centigrade, and therefore

Now w is known to be 1293 and a = 0.00366;

If, therefore, we know the value of δ for the conditions of the air under experiment, we can calculate the tension of the vapour when we know its actual density. Now, for water vapour which is not near its point of saturation δ is equal to 0.622 for all temperatures and pressures. It would be always constant and equal to 0.622 if the vapour followed the gaseous laws up to saturation pressure. That is however, not strictly the case, and yet Regnault has shown by a series of experiments on saturated air that the formula

suffices to give accurately the tension when d is known, even for air which is saturated, or nearly so, with vapour.

We have still to show how to determine d. This can be done if we cause, by means of an aspirator, a known volume of air to pass over some substance which will entirely absorb from the air the moisture and nothing else, and determine the increase of weight thus produced. Such a substance is sulphuric acid with a specific gravity of 1.84. To facilitate the absorption, the sulphuric acid is allowed to soak into small fragments of pumice contained in a U-tube. The pumice should be first broken into fragments about the size of a pea, then treated with sulphuric acid and heated to redness, to decompose any chlorides, &c., which may be contained in it. The U-tubes may then be filled with the fragments, and the strong sulphuric acid poured on till the pumice is saturated; but there must not be so much acid that the air, in passing through, has to bubble, as this would entail a finite difference of pressure on the two sides before the air could pass.

Phosphoric anhydride may be used instead of sulphuric acid, but in that case the tubes must be kept horizontal. Chloride of calcium is not sufficiently trustworthy to be used in these experiments as a complete absorbent of moisture.

The arrangement of the apparatus, the whole of which can be put together in any laboratory, will be understood by the fig. 22. As aspirator we may use any large bottle, A, having, besides a thermometer, two tubes passing airtight through its cork and down to the bottom of the bottle. One of these tubes is bent as a syphon and allows the water to run out, the flow being regulated by the pinch-cock T; the other tube is for the air to enter the aspirator; its opening being at the bottom of the vessel, the flow of air is maintained constant and independent of the level of the water in the bottle.

The vessel B, filled with fragments of freshly fused chloride of calcium, is provided with two tubes through an airtight cork, one, connected with the aspirator, passing just through, and the other, connected with the drying tube D, to the bottom of the vessel This serves as a valve to prevent any moisture reaching the tubes from the aspirator. The most convenient way of connecting up drying tubes is by means of mercury cups, consisting of short glass tubes with a cork bottom perforated for a narrow tube; over this passes one limb of an inverted U-tube, the other limb of which is secured to one limb of the drying tube either by an india-rubber washer with paraffin or, still better, by being thickened and ground as a stopper. A glance at the figure will show the arrangement. The drying tubes can then be removed and replaced with facility, and a perfectly airtight connection is ensured. The space in the little cups, M, M, M, M, between the narrow tubes and the limbs of the inverted U's is closed by mercury. Care must be taken to close the ends of the inverted U's with small bungs during weighing, and to see that no globules of mercury are adhering to the glass. The connecting tubes c between the drying tubes should be of glass and as short as possible.

Two drying tubes must be used, and weighed separately before and after the experiment; the first will, when in good order, entirely absorb the moisture, but if the air is passed with too great rapidity, or if the acid has become too dilute by continued use, the second tube will make the fact apparent A thermometer, x, to determine the temperature of the air passing into the tubes is also necessary.

To take an observation, the tubes are weighed and placed in position, the vessel A filled with water, the syphon tube filled, and the tube at the end of the drying tubes closed by means of a pinch-tap. Then, on opening the tap at T, no water should flow out; if any does there is some leak in the apparatus which must be made tight before proceeding further. When assured that any air supplied to the aspirator will pass through the drying tubes, the observation may be begun. The water is run out slowly (at about the rate of 1 litre in ten minutes) into a litre flask, and when the latter is filled up to the scratch on the neck it is removed and weighed, its place being taken by another flask, which can go on filling during the weighing of the first. This is repeated until the aspirator is empty, when, the weight of the empty flasks being ascertained, the total weight of water thus replaced by air can be found. The height H of the barometer must be determined at the beginning and end of the experiment. During the observation the thermometer x must be read every ten minutes, and the mean of the readings taken as the temperature t of the entering air; the thermometer in the aspirator must be read at the end of the experiment; let the reading be t'. If the aspirator A is but small, it can be refilled and the experiment repeated, and we may of course determine, once for all, the volume of water which can be run out of the aspirator when filled up to a certain mark in the manner thus described; but as an exercise it is better to re-determine it for each experiment.

From the weight of water run out, with the assistance of Table 32 (Lupton, p. 28) we can determine the volume v of air taking the place of the water in the aspirator, v being measured in cubic metres. This air is evidently saturated with water at the temperature t'; its pressure is the barometric pressure, and therefore the pressure of the dry air in it is H-et, et being the saturation tension at t'. When it entered the drying tubes this air had a pressure H-e, and its temperature was t,e being the tension whose value we are seeking. The volume of the air was, therefore, then

Hence, if w be the increase of weight of the drying tubes in grammes, we shall have for d the actual density of the moisture in the air;

We thus obtain the quantity d; substituting its value from equation (1) above, we get

or

Experiment. - Determine the density of the aqueous vapour in the air, and also its tension.

Enter results thus : -

Last Update: 2011-03-27