RESIDUAL ANALYSES.
CALCULATION FROM RESIDUAL ANALYSES.
The increment in weight of the absorbers for water and carbon dioxide and the loss in weight of the oxygen cylinder give only an approximate idea of the amounts of carbon dioxide and water-vapor produced and oxygen absorbed during the period, and it is necessary to make correction for change in the composition of the air as shown by the residual analyses and for fluctuations in the actual volume. In order to compute from the analyses the total carbon-dioxide content of the residual air, it is necessary to know the relation of the air used for the sample to the total volume, and thus we must know accurately the volume of air passing through the gas-meter.
In the earlier apparatus 10-liter samples were used, and the volume of the respiration chamber was so large that it was necessary to multiply the values found in the residual sample by a very large factor, 500. Hence, the utmost caution was taken to procure an accurate measurement of the sample, the exact amounts of carbon dioxide absorbed, and water-vapor absorbed. To this end a large number of corrections were made, which are not necessary with the present type of apparatus with a volume of residual air of but about 1,300 liters, and accordingly the manipulation and calculations have been very greatly simplified.
While formerly pains were taken to obtain the exact temperature of the air leaving the gas-meter, with this apparatus it is unnecessary. When the earlier type of apparatus was in use there were marked changes in the temperature of the calorimeter laboratory and in the water in the meter which were naturally prejudicial to the accurate measurement of the volume of samples, but with the present control of temperature in this laboratory it has been found by repeated tests that the temperature of the water in the meter does not vary a sufficient amount to justify this painstaking measurement and calculation. Obviously, this observation also pertains to the corrections for the tension of aqueous vapor. It has been found possible to assume an average laboratory temperature and reduce the volume as read on the meter by means of a constant factor.
The quantity of air passing through the meter is so adjusted that exactly 10 liters as measured on the dial pass through it for one analysis. The air as measured in the meter is, however, under markedly different conditions from the air inside the respiration chamber. While there is the same temperature, there is a material difference in the water-vapor present, and hence the moisture content as expressed in terms of tension of aqueous vapor must be considered. This obviously tends to diminish the true volume of air in the meter.
Formerly we made accurate correction for the tension of aqueous vapor based upon the barometer and the temperature of the meter at the end of the period, but it has now been found that the reduction of the meter readings to conditions inside of the chamber can be made with a sufficient degree of accuracy by multiplying the volume of air passing through the meter by a fraction, (h-t)/h, in which h represents the barometer and t the tension of aqueous vapor at the temperature of the laboratory, 20° C. Since the tension of aqueous vapor at the laboratory temperature is not far from 15 mm., a simple calculation will show that there may be considerable variations in the value of h without affecting the fraction materially, and we have accordingly assumed a value of h as normally 760 mm., and the correction thus obtained is (760 - 15)/760 = 0.98, and all readings on the meter should be multiplied by this fraction.
On the one hand, then, there is the correction on the meter itself, which correction is +1.4 per cent (see page 75); and on the other hand the correction on the sample for the tension of aqueous vapor, which is -2.0 per cent, and consequently the resultant correction is -0.6 per cent. From the conditions under which the experiments are made, however, it is rarely possible to read the meter closer than ±0.05 liter, as the graduations on the meter correspond to 50 cubic centimeters. It will be seen, then, that this final correction is really inside the limit of error of the instrument, and consequently with this particular meter now in use no correction whatever is necessary for the reduction of the volume. The matter of temperature corrections has been taken up in great detail in an earlier publication, and where there are noticeable differences in temperature between the meter and the calorimeter chamber the calculation is very much more complicated.
For practical purposes, therefore, we may assume that the quantity of air passed through the meter, as now in use, represents exactly 10 liters measured under the conditions obtaining inside of the respiration chamber, and in order to find the total amount of water-vapor present in the chamber it is necessary only to multiply the weight of water found in the 10-liter sample by one-tenth of the total volume of air containing water-vapor.
The total volume of air which contains water-vapor is not far from 1,360 liters; consequently multiplying the weight of water in the sample by 136 gives the total amount of water in the chamber and the piping. The volume of air containing carbon dioxide is that contained in the chamber and piping to the first sulphuric-acid vessel plus 16 liters of air above the sulphuric acid and connections in the first porcelain vessel, and in order to obtain the amount of carbon dioxide from the sample it is only necessary to multiply the weight of carbon dioxide in the sample by 137.6.
Since in the calculation of the total amount of residual oxygen volumes rather than weights of gases are used, it is our custom to convert the weights of carbon dioxide and water-vapor in the chamber to volumes by multiplying by the well-known factors. The determination of oxygen depends upon the knowledge of the true rather than the apparent volume of air in the system, and consequently the apparent volume must be reduced to standard conditions of temperature and pressure each time the calculation is made. To this end, the total volume of air in the inclosed circuit (including that in the tension-equalizer, amounting to 1,400 liters in all) is reduced to 0° and 760 millimeters by the usual methods of computation. The total volume of air (which may be designated as V) includes the volumes of carbon dioxide, water-vapor, oxygen, and nitrogen. From the calculations mentioned above, the volumes of water-vapor and carbon dioxide have been computed, and deducting the sum of these from the reduced volume of air gives the volume of oxygen plus nitrogen. If the volume of nitrogen is known, obviously the volume of oxygen can be found.
At the beginning of the experiment, it is assumed that the chamber is filled with ordinary air. By calculating the amount of nitrogen in the chamber at the start as four-fifths of the total amount, no great error is introduced. In many experiments actual analyses of the air have been made at the moment of the beginning of the experiment. The important thing to bear in mind is that having once sealed the chamber and closed it tightly, no nitrogen can enter other than that admitted with the oxygen, and hence the residual amount of nitrogen remains unaltered save for this single exception. If care is taken to keep an accurate record of the amount of nitrogen admitted with the oxygen, the nitrogen residual in the chamber at any given time is readily computed. While from an absolute mathematical standpoint the accuracy of this computation can be questioned, here again we are seeking an accurate record of differences rather than an absolute amount, and whether we assume the volume of the air in the chamber to contain 20.4 per cent of oxygen or 21.6 per cent is a matter of indifference. It is of importance only to note the increases in the amount of nitrogen, since these increases represent decrease in the residual oxygen and it is with the changes in the residual oxygen that we particularly have to do.