Part 9

Weight, Weight, Temperature. Gram. Temperature. Gram.

0° 0.999871 21° 0.998047 1° 0.999928 22° 0.997826 2° 0.999969 23° 0.997601 3° 0.999991 24° 0.997367 4° 1.000000 25° 0.997120 5° 0.999990 26° 0.996866 6° 0.999970 27° 0.996603 7° 0.999933 28° 0.998331 8° 0.999886 29° 0.995051 9° 0.999824 30° 0.995765 10° 0.999747 31° 0.995401 11° 0.999655 32° 0.995087 12° 0.999549 33° 0.994765 13° 0.999430 34° 0.994436 14° 0.999299 35° 0.994098 15° 0.999160 36° 0.993720 16° 0.999002 37° 0.993370 17° 0.998841 38° 0.993030 18° 0.998654 39° 0.992680 19° 0.998460 40° 0.992330 20° 0.998259

From the table and the weight of water found, the volume of the pyknometer is easily calculated.

Example.—Let the weight of water found be 11.72892 grams, and the temperature 20°. Then the volume of the flask is equal to 11.72892 ÷ 0.998259, viz., 11.95 cubic centimeters.

=50. Use of Pyknometer at High Temperatures.=—It is often found desirable to determine the density of a liquid at temperatures above that of the laboratory, e. g., at the boiling-point of water. This is easily accomplished by following the directions given below:

Weight of Flask.—Use a small pyknometer of from twenty-five to thirty cubic centimeters capacity. The stopper should be beveled to a fine edge on top and the lower end should be slightly concave to avoid any trapping of air. The flask is to be thoroughly washed with hot water, alcohol and ether, and then dried for some time at 100°. After cooling in a desiccator the weight of the flask and stopper is accurately determined.

Weight of Water.—The flask in an appropriate holder, Fig. 28, conveniently made of galvanized iron, is filled with freshly boiled and hot distilled water and placed in a bath of pure, very hot distilled water, in such a way that it is entirely surrounded by the liquid with the exception of the top.

The water of the bath is kept in brisk ebullition for thirty minutes, any evaporation from the flask being replaced by the addition of boiling distilled water. The stopper should be kept for a few minutes before use in hot distilled water and is then inserted, the flask removed, wiped dry, and, after it is nearly cooled to room temperature, placed in the balance and weighed when balance temperature is reached. A convenient size of holder will enable the analyst to use eight or ten flasks at once. The temperature at which water boils in each locality may also be determined; but unless at very high altitudes, or on days of unusual barometric disturbance the variations will not be great, and will not appreciably affect the results.

=51. Alternate Method of Estimating the Weight of Water in Flasks.=—Formulas for calculating the volume V, in cubic centimeters, of a glass vessel from the weight P of water at the temperature t contained therein, and the volume Vʹ at any other temperature t’ are given by Landolt and Börnstein. They are as follows:

p V = P --- d

p Vʹ = P ---- [1 + γ(tʹ- t)] d

p = weight (in brass weights) of one cubic centimeter H₂O in vacuo. This is so nearly one gram that it will not affect the result in the fifth place of decimals and may therefore be disregarded. Hence the formula stands:

1 Vʹ = P ---- [1 + γ(tʹ-t)]; in which d

d = density of water at temperature t.

γ = 0.000025, the cubical expansion coefficient of glass.

From this volume the weight of the water may be readily obtained by referring to tables 13, 14 and 15a in Landolt and Börnstein’s book.

=52. Example Showing Determination of Specific Gravity of a Fat.=—The flask is emptied of its water, rinsed with alcohol and ether, and dried again for a few minutes at 100°. It is then filled with the dry, hot, fresh-filtered fat, which should be entirely free from air bubbles.

The stoppered flask is then replaced in the water-bath, kept for thirty minutes at the temperature of boiling water, removed, and treated as above. The weight of fat having been determined, the specific gravity is obtained by dividing it by the weight of water previously found.

Example. Grams. Weight of flask, dry 10.0197 Weight of flask, plus water 37.3412 Weight of water 27.3215 Weight of flask, plus fat 34.6111 Weight of fat 24.5914

Specific gravity = 24.5914 ÷ 27.3215 = 0.90008.

The weight of the flask dry and empty and the weight of water at 99° to 100° contained therein may be used constantly if great care be taken in handling and cleaning the apparatus.

Example. Grams. Weight of flask, dry and empty 10.0028 Weight of flask after three weeks’ use 10.0030

=53. Determination of Density by the Hydrostatic Balance.=—While the pyknometer is useful in control work and in fixing standards of comparison, it is not used extensively in practical work. Quicker methods of determination are desired in such work, and these are found in the use of other forms of apparatus. A convenient method of operation consists in determining the weight of a sinker, whose exact weights in air and in pure water of a definite temperature, have been previously determined. The instrument devised by Mohr and modified by Westphal, is based upon that principle, and is extensively used in practical work. The construction of this apparatus and also that of the pyknometers and areometers is shown in the illustrations, figures 29 and 30.

The weight of the sinker is so adjusted that the index of the balance arm marks zero when the sinker is wholly immersed in pure water at the standard temperature. The density of a solution of sugar at the same temperature, is then determined by placing the rider-weights on the divided arm of the balance, until the index again marks zero. The density can then be read directly from the position of the weights in the arm of the balance or calculated therefrom.

=54. The Areometric Method.=—The most rapid method of determining the density of a solution and the one in most common use, is based on the distance to which a heavy bulb with a slender graduated stem will sink therein. An instrument of this kind is called an areometer. Many forms of this instrument are employed but they all depend on the same principle and differ only in the manner of graduation. The one of widest application has the stem graduated in such a manner as to give directly the specific gravity of the solution in which it is placed.

Others are made with a special graduation giving directly the percentage of solid matter in the solution. These instruments can be used only for the special purposes for which they are constructed. Other forms are provided with an arbitrary graduation, the numbers of which by appropriate tables can be converted into expressions of specific gravity or of per cents of dissolved matters. It is not practicable to give here, a discussion of the principles of the construction of areometers. The two which are commonly used, are the baumé hydrometer and the balling or brix spindle.

In the baumé instrument the zero of the scale is fixed at the point marked by the surface of distilled water at 15°, and the point to which it sinks in pure monohydrated sulfuric acid at the same temperature is marked 66, corresponding to a specific gravity of 1.8427.

The specific gravity corresponding to any degree of the scale, may be calculated in the absence of a table giving it, by the following formula