Rapid Method for Applying Vacuum Corrections to Weights
P. K.
Faure’ and J. A. Gledhill, Departments of Chemistry and Physics, Rhodes University, Grahamstown, South Africa
HEN a largg number of meigliings ware to be made in the course of precise work, the calculation of the corrections due to tlie buoyancy of the air becomes VCI are available to fac but they are usually based on a constant value for the density of the air and are often not sufficiently accurate. Other tables require several numerical steps before the correction can be found. Thacher’s nomographic chart ( 2 ) gives good results for sea-level conditions, but if it is extended to lower pressures for use a t elevated places the accuracy with which the corrcction can be found falls off rapidly, and its utility is limited by this. The accompanying chart has proved very rapid and satisfactory in use. The various areas give the correction (in percentage) to be applied to the apparent weight found in air under conditions of temperature and pressure such as are normally encountered; for other ranges of these variables the chart can easily be extended without loss of accuracy. The corrections for dilute aqueous solutions arc near to 0.1% and the process of applying them is then very simple, as tlie following esample s h o w .
ilpparent weight 930 324 grams of solution in air Air temperature, 22.0” C. Bir pressure, 710 mni. Hence correction, + 0 . 0 9 8 ~ ~ +0,1% = +0.936 gram -0.00270 = -0.019 gram Correction = +0.917 gram Corrected weight in vacuo 937 241 grams CONSTRUCTION O F CHART
The equation for the correction of weights in air t o their value in a vacuuni is ( 3 ) :
where W , is the weight in vacuo of a body of density db and is its apparent weight in air of density d, against weights of density d,. As Ti’, and TI’, are very nearly equal, Equation 1 may be reduced to
m,= W,(1 + C’)
(2)
where (3)
The density of air depends on the temPresent address, h’ational Rexearrh Council, Ottawa 2, Canada.
1304
ANALYTICAL CHEMISTRY
PRESSURE (mm.)
Chart for correction of weights for buoyancy of air For a b o d y of density 1 gram per cc. weighed against brass weights. Figure given is percentage of weight of body which must b e a d d e d to apparent weight in air. For body of density db, first multiply correction b y
(
- 0.1 351 ).
For weights not of brass, see text.
perature, pressure, and humidity ( 1 ) : da
273.16(P - 0.3i83Pa) 0.0012929- - ___(4) T 760
where T is the absolute temperature, P the barometric pressure, and P , the partial pressure of nater vapor in the atmosphere, both in millimeters of mercury. For a body of density 1 gram per cc. weighed against brass weights (d, = 8.4 grams per cc.), Equation 3 liecomes Ci = 0.881 d a (5) If the relative humidity is assunird t o be 50%, values of P , may be found from tables for various values of T, and it is then a simple matter to calculate from Equations 4and 5 the values of P which correspond t o suitably chosen values of C:. On plotting these values of P against T and joining the points, the chart is completed. It is thus, in effect, a chart showing lines of constant air density which givc a constant value of C1 according to Equation 5. For brass weights and bodies of density db other than 1 gram per r e . it is easily shown that the correction fartor is given by
C may be evaluated quickly from C1with a slide-rule left a t the correct setting, once the factor has been evaluated for a substance of a particular density. For weights of density d, and a body of density 1 gram per cc., the correction is
c,
=
c1x
(
1.1351 1
-
d3 -
which is uscful if the m-eights are made of materials othcr than brass. Calculation s h o w that, for bodies of density 1 gram per cc. or greater, the effect of changes in the relative humidity of the air on the corrections read off from tlie chart is not more than 0.0005% of tlie weight of the body a t temperatures below 20” C., and never exceeds 0.0017, throughout the 11-hole range covered by tlie chart. Thus the relativc humidity is not requirpd esccpt in work of tlie highest precision. LITERATURE CITED
(1) “Handbook of Chemistry and Physics,” 30th rd., p. 1697, Chemical
Rubber Publishing Co., Cleveland, Ohio, 194i. (’1) Thacher, H. C., ISD. E~uo.CHEII., ANAL.ED.16, 275 (1911).
(:3)
Vogel, .4. I., “Text Book of Quantitative Inorganic Analysis,” p. 165. Inngmmis, Giecn, London, 1951,
