PREFACE.. TABLE OF CONTENTS Decomposition of Mercuric Oxide - Metathesis Between Barium Chloride and Sodium Sulphate - Factors - Percentage Composition - Equiva- Reamur-Absolute - Calorie - British Ther- mal Unit Specific Heat - Heat of Fusion - Heat of Vaporization Heat of Combustion. - Temperature Conversions - Thermo chemis- Solids Lighter Than Water-Specific Gravity of Powders - Pyknometer Methods Sinker Methods - Constant Weight Hydrometers - Con- stant Volume Hydrometers — Hydrometers — Beaumé Hydrometer — Conversion of Beaumé into Specific Gravity - Conditions of Tempera- PAGE Boyle's Law - Charles' Law — Gas Thermometer-Laws of Boyle and Charles' Combined - Standard Conditions Correction of the Barom- eter - Moist Gasses - Gay-Lussac's Law - Atomic and Molecular Weights - Vapor Density — Graham's Law - Volume Occupied by a Gram Molecule of a Gas — Measurement of Vapor Density — Deviations from Gas Laws — Volume of Gas from Weight in Grams — Volume of Gas from Weight in Ounces — Weights in Vacuo — United States Unit of Atomic Weight — Valence, Atomic Weight and Combining Weight — Atomic Weight from Analysis — Determination of Atomic Weight — Law of Dulong and Petit — Atomic Weight from Analysis, Complex Cases -Molecular Weight from Solution Constants Molecular Weight of Organic Acid — Molecular Weight of Organic Base Formula of a Com- pound - Formula from Percentage Composition —- Formulas of Minerals Single Factor Solutions - Methods of Standardization — Equivalent Values - Factor Weights for Volumetric Solutions - Normal Solu- tions - Simplification of Calculation — Calculation of Normality— Back Titrations — Indirect Analysis — Titration of Mixed Acid — Two Indicator Titrations — Titration of Oleum — Adjustment of Strength CHAPTER I APPROXIMATE NUMBERS Approximate Numbers. Most of the numbers handled by the chemist are the result of experimental determination and consequently are approximate only. An abstract number is the result of a logical process while a number obtained by measurement employing an appropriate unit is approximate. The number of individual weights in a box may readily be counted and the result accurately expressed, but if these weights are used to determine the weight of an object, the result is approximate only, and depends upon the accuracy with which the weights are calibrated, the sensitiveness of the balance and other considerations. There is some error, large or small, depending upon conditions, and this error is called the experimental error, or the error of measurement. For example, suppose a substance is weighed on a balance sensitive to a milligram only, and that equilibrium is established with 1.628 g. as a counterpoise. Should this same object be weighed on a more sensitive balance, say one sensitive to a tenth of a milligram, it cannot be predicted that it will weigh 1.6280 g., in fact, it may weigh anything between 1.6275 and 1.6285 g. These are the limits of deviation. The error in weighing on a balance sensitive to a milligram may be less than this; it can only be said with certainty that the error does not exceed half a miligram, i.e., 0.0005 g. Such experimentally determined magnitudes we call approximate num bers. A number expressing some multiple of a unit determined experimentally or by comparison, or derived, always contains some error, which is great or small according to the difficulty or delicacy of the operation by which it was determined; hence there must be some figure in the result beyond which there is some uncertainty. In atomic weight tables, the element iodine will be found stated to six significant figures (126.932),1 while many of the other elements are given only to 1 Significant figures are used to designate magnitudes, one or more of which may be used. One mile is 5280 feet, the number of significant figures in this case being four. A circle is divided into degrees and minutes, there being 60 degrees, each degree of which is further subdivided into 60 minutes, making 21600 minutes in all. This latter magnitude is one of five significant figures. Zeros in the above illustrations are significant but when used to indicate the location of the decimal point are not counted as significant figures. Thus, the speed of light, given as 186,000 miles per second, has three significant figures, the final zeros merely serving three or four, as for instance, Beryllium (9.02) or Boron (10.82). The reason for this is that iodine, a very important element, has been very carefully studied and also because of some of the properties of its compounds such as the stability, definiteness, and insolubility of its silver salt through which its atomic weight is determined. 1 By convention, when a number expresses a multiple of some unit which has been experimentally determined, or derived, it is customary that the last figure given is the last figure known with any degree of certainty. Thus, iodine is given as having an atomic weight of 126.932; this means that the atomic weight is accurately known as far as the nearest one thousandth of a unit. From the figure given it may be understood that its value is 126.932 ± 0.0005. In this case then± 0.0005 is the maximum apparent error of the atomic weight of iodine. If the atomic weight of iodine were known with certainty to the one ten thousandth of a unit, then the atomic weight might be expressed as 126.9320. The consequences following from the nature of approximate numbers may be illustrated by examples. Supposing it is required to obtain the molecular weight of crystallized aluminum sulphate: Al2(SO4)3.18H2O. The atomic weight of aluminum is given as 26.97 which shows that the atomic weight of this element is known accurately only as far as the hundredth of a unit; there is then no knowledge of the atomic weight of this element to the thousandths of a unit, for if it were known with this degree of precision, the thousandths value of this place would have to indicate the position of the decimal point. The ash of a certain size and grade of filter paper may be given as 0.00042 g., the zeros merely serving to indicate the position of the decimal point, there being only two significant figures. 1 Logarithms have been employed in the solution of problems in this book, except where the operation was very simple. In such cases the 10" Mannheim slide rule was used. The author would strongly recommend this simple device for the checking of results in the laboratory. It cannot be used exclusively, as the accuracy of the rule is only to three figures in the higher numbers. The mantissa only of a logarithm may be used, neglecting the characteristic, the position of the decimal point being determined by inspection. A chemists' slide rule, manufactured by Keuffel & Esser and devised by the author is now on the market. It is designed to facilitate the computation of such problems as are found in this book and is recommended to students, as by its use much time is saved in calculating the answers to the problems. |