137. The combustion of two drams of a substance caused the temperature of 9 ounces of water to be raised 15.43° F. (a) What is the calorific value in the British system? (b) In Calories? (16 drams = 1 oz. avoirdupois.) Ans. (a) IIII B.T.U. Ans. (a) 293.578 Cal., 139. In the reaction convert the heat liberated into Calories. 140. When Rhombic sulphur is burned in oxygen, heat is liberated according to the reaction S+ O2 = SO2 + 71,000 cal. What is the heat evolved per gram of sulphur? Ans. 2,245 cal. 141. Gaseous hydrogen and chlorine are combined to form gaseous hydrogen chloride When the resultant hydrogen chloride is dissolved in sufficient water, HCl + Aq = HCl aq + 72 J., calculate the heat of formation of dissolved hydrochloric acid from its elements. Ans. 164 J. 142. From the reactions H2+ Cl2 + 302 + Aq = 2HClO3 aq + 2 x 100 J., H2 +Cl2 calculate the heat evolved in oxidation by means of chloric acid HClO3 aq= HCl aq + 30 143. Being given the equations Ans. 64 J. CH4 + 2O2 = CO2 + 2H2O(vap.) + 193,502 cal., CHAPTER V SPECIFIC GRAVITY For the principles underlying this subject the student is referred to a text book on Physics. The absolute density of a substance is the weight of a unit volume. In the Metric system the absolute density is the weight in grams of a cubic centimeter of the substance, while in the British system the absolute density would be the weight in pounds of a cubic foot of the substance. One of the great advantages of the Metric system aside from the decimal system of notation is the connection between the unit of volume and the unit of mass. The unit of mass in the metric system, the gram, was taken to be the mass of one cubic centimeter of water at its greatest density, 4° C.1 One cubic foot of water weighs 62.37 pounds, hence this is the absolute density of water in the British system. The weight of a cubic centimeter of water being one gram, it follows that in the metric system the density of water is unity, or one. The relative density, or to use a synonymous term, specific gravity, is the ratio of weight of a given volume of a substance referred to the weight of the same volume of some other substance taken as standard (unity). The substance of reference for solids and liquids is water. In the case of gases the substance of reference is commonly air, oxygen or hydrogen.2 In the metric system, for solids and liquids, density, relative density and specific gravity are synonymous terms, the relationship between density, mass and volume being 1 This is not exactly realized, the volume of a kilogram of water at 4° C. is 1.000027 liters, hence the volume of one gram of water is 1.000027 c.c. The error is so small that it may be disregarded. See page 105. 2 This will be taken up again in Chapter VI on Gases. Specific Gravity of Body Heavier than and Insoluble in Water. The relative density, or specific gravity, is determined according to the following formula, let W = weight of the body in air,1 Ww= weight of an equal volume of water at 4° C., then Wo Ww= Wb - Wo', in which W. Wo' is the loss in weight in water of a substance heavier than water (i.e., the body is wholly immersed). Hence so, to obtain the relative density (or specific gravity), it is only necessary to weigh the substance in air and in water and solve by the formula. To obtain the relative density when the body is weighed in water at some other temperature than 4° C., say to C., then The Specific Gravity of a Solid Substance Lighter than Water is obtained by means of a sinker attached to the solid; the combination being of a relative density greater than water so that it will sink. Let W,' weight of the sinker in water, 8 = 8+6 weight of the sinker with body attached in water. W's = In practice such a determination is most easily carried out by weighing the light substance in air and then weighing the light substance in air 1 The subscripts are used in an endeavor to assist in identification of the various weighings, etc. Strictly, this weight should be corrected to weight in vacuo. The reduction of the weight in air to the weight in vacuo is treated on pages 104-105 of this book. 2 "A body wholly or partly immersed in a fluid (liquid or gas) is buoyed up with a force which is equal to the weight of the volume of the fluid which the body displaces." A Text-Book of Physics, by Duff. suspended from the hook with the sinker attached to it by a slender thread (the sinker being immersed in water) and taking the weight of this combination. Finally, the weight of both the substance and sinker in water is taken. Let Then 8 [W2+W.'] = weight of body in air and sinker in water, W's 8+b= The Specific Gravity of Powders is determined by using a specific gravity bottle, flask or pyknometer. The empty bottle is weighed, then filled with water and weighed again. This gives the weight of water held by the bottle. The bottle is emptied and dried and a convenient amount of powder introduced when the bottle and powder are weighed. This gives the weight of the powder. The bottle containing the powder is now filled to the mark and weighed again. Let W = weight of powder taken, Ww+= weight of flask full of water, Wo++ weight of powder, flask and water. = Pyknometer Method for Liquids. The relative density of liquids cannot be obtained by the means outlined above. An obvious method is to compare the weight of a given volume of the liquid in question with the weight of the same volume of water; account being always taken of the temperatures of the two liquids. Then, letting This method is used when extremely accurate results are desired. Sinker Method for Liquids. — The principle of Archimedes states that a body is buoyed up by an amount equal to the weight of liquid displaced. Knowing the amount of this buoyancy in water and in the liquid the specific gravity of which is to be found, the specific gravity of the liquid can be calculated. The buoyancies are measured by the losses in weight of a solid body in the liquid of unknown density and in water respectively. Any solid (usually a metal) of a specific gravity such that it will sink in both liquids and is not acted upon by either of the liquids will suffice. Let W = weight of the solid body in air, Wo' weight of the solid body in water, = Wo" = weight of the solid body in the liquid whose density is to be Constant Weight Hydrometers. - Another method which is based upon the principle of Archimedes is that a body lighter than a liquid in which it is immersed sinks until it displaces an amount of liquid equal to its own weight. Let A area of cross section of a cylindrical floating body, h = depth to which the cylinder sinks in water, Wwweight of water displaced. In the metric system, the unit of weight, the gram, being the weight of one cubic centimeter of water (at 4° C.), then if A and h are measured in square and linear centimeters respectively, Ah represents a volume of water displaced which is numerically equal to the weight in grams of water displaced. That is If the same cylinder is next placed in a liquid of a different density, it will sink to such a depth that it displaces an amount of liquid equal to its own weight. Let d = the density of this liquid, h' = the depth to which the cylinder sinks in the liquid, Wi = the weight of liquid displaced. The liquid displaced is W1 = Ah'd. Then as equal weights of the liquids are displaced (this is the method of the constant weight hydrometer), Ww = W1, and as the density of water is unity, then In words, the depth to which a cylindrical floating body will sink is inversely proportional to the density of the liquid in which it is im |