UNIT OF MOLECULAR WEIGHT 35 the value of n has been attempted. At 0° and under a pressure of one atmosphere a single cubic centimetre of any given gas contains about 20 trillion particles or molecules. Divide the weight of a cubic centimetre of the gas by this number and we obtain the weight of a single particle. In the case of hydrogen, the lightest of all gases, a particle weighs 0·000,000,000,000,000,000,000,004 grammes, or one quadrillion particles of hydrogen weigh about 4 grammes. The particles of other gases weigh more in proportion as they are heavier than hydrogen. The minuteness of the molecular weights calculated in this way, but more especially their doubtful accuracy, has prevented the use of these absolute values, and the relative molecular weights suffice for the present. § 22. Unit of Molecular Weights.-The same reasons which led to the adoption of the atom of hydrogen as the unit of atomic weights caused hydrogen to be chosen as the standard of molecular weights. At first sight it would seem best to take the molecule of hydrogen=1 and compare the molecular weights of all other gases with this unit, i.e. represent their molecular weights by numbers indicating how many times heavier they are than hydrogen. This is certainly permissible, but it is much more convenient to compare the weights of the molecules, which are composed of atoms with the same standard by which the atomic weights were measured, so that the molecular weights may be directly represented as the sum of the atomic weights. In order to do this it is necessary to know what relation the molecular weight of hydrogen bears to its atomic weight. The molecular weight cannot be smaller, but it may be larger than the atomic weight, as the molecule may contain several atoms. We are compelled to assume that it contains more than one atom, as gaseous hydrogen compounds are known which only contain half as much hydrogen as is contained in the same volume of free hydrogen. As one volume of hydrogen combines with one volume of chlorine to form two volumes of hydrochloric acid, it follows, from Avogadro's law, that each particle of hydrogen and chlorine produces two particles or molecules of hydrochloric acid, as the two volumes of the latter gas contain, according to this hypothesis, twice as many particles as are contained in one volume of one of its constituents. And as a particle of hydrogen and a particle of chlorine can divide into two parts, it must consist of at least two atoms. It cannot contain less than two, but it may contain more; but there is no reason for assuming the existence of more than two atoms in the molecule until a compound is discovered which contains less than half its volume of hydrogen. The molecular weight of hydrogen is represented by § 23. Calculation of Molecular Weights. When the unit is chosen the calculation of the molecular weight of any other gaseous substance is extremely simple; for, according to § 21, The molecular weight of any gas is calculated by multiplying its density compared with air at the same temperature and pressure by 28.876. The relation is even more simple when the density is expressed in terms of hydrogen instead of air: This calculation yields the same results as the previous one, for the densities compared with air d are to the densities compared with hydrogen 8, as The densities of gases would no doubt be directly compared with that of hydrogen if it were not for the great experimental STANDARD OF DENSITY 37 difficulties involved. This is the reason why the comparison with air is, as a rule, preferred. The factors 14-438 and 28-876 in the preceding formulæ have a very simple meaning. The first number represents the specific gravity or density of dry atmospheric air in terms of hydrogen; the second number, which is double the first, represents the mean value of the molecular weights of its constituents. In the case of Oxygen. d=1.10563, 8=15.963, m=31-93. But according to Bunsen, 100 volumes of air contain Oxygen 20.96 volumes 79.04 "" Now, according to Avogadro's hypothesis, equal volumes of the two gases contain the same number of particles; therefore 10,000 particles of air contain But as oxygen is heavier than nitrogen, the average weight of a particle of air is m = 2096 × 31·93+7904 × 28·05 = 28.86. This result closely agrees with the value 28.876. This number has no real meaning, because no existing particle of air has this weight; but it may be conveniently used in molecular weight calculations, as the molecular weight of any given gas bears the same relation to this value as the density expressed in terms of air does to 1. § 24. Correction for Errors of Experiment.-The molecular weights calculated by either of these methods generally require correction. The determination of the densities of gases and vapours, like all other observations, are liable to errors of experiment, which in some cases are considerable. Another point to be noticed is, that the expansion of different gases by heat, and the relation of their volume to pressure, is almost but not absolutely identical. Hence it follows that if two gases exactly conform to Avogadro's law at a certain temperature and pressure they will no longer do so at any other temperature and pressure, as both gases will not change their volume to absolutely the same extent. Since the deviations are but small, we may use the method mentioned in the preceding paragraphs, in order to make a fairly accurate determination of the molecular weights, and then correct the values so obtained. The correction is effected by making use of the fact that each molecule is composed of atoms; its weight must consequently be equal to the sum of the weight of the atoms contained in it. The density of hydrochloric acid gas is found by experiment to be 1.247. Analysis proves that this gas contains 35-37 parts by weight of chlorine to 1 part by weight of hydrogen; therefore the molecular weight of this compound must either be m=1+35.37=36-37, or a simple multiple of this number, as less than a whole atom of hydrogen (1) cannot be present in the compound. The product of the density by 28.87 is dx 28.87 1.247 x 28.87=36·0, which agrees with the value calculated from the atomic weights; the difference is due to errors of experiment, and 36-37 must be held to be the correct molecular weight. = Marsh gas contains 2.9925 parts by weight of carbon to 1 part by weight of hydrogen. The molecular weight must be represented as m=n(1+2·9925) =n × 3·9925, in which n stands for a whole number (possibly n=1). The density compared with air=0.555, and the molecular weight will be approximately m' 28.87 x 0.555=16.02. This is roughly four times the smallest value possible; consequently the true value is m==4×3.9925=15·97=(4+11.97). The molecular weight consists of 4 parts by weight of hydrogen and 11.97 parts by weight of carbon. In this way the molecular weights of numerous substances which can be volatilised without decomposition have been determined. ATOMIC WEIGHTS DEDUCED FROM MOLECULAR WEIGHTS 39 § 25. Determination of Atomic Weights from Molecular Weights. As the atoms are indivisible particles (ǎToμo) a molecule cannot contain less than a whole atom. Hence the molecular weights of compounds offer special facilities for the determination of the atomic weights of the elements. The smallest quantity of an element which is found to exist, in the molecular weight of any of its compounds is the maximum value of the atomic weight. This smallest quantity must contain at least one atom; it may contain two, three, or more atoms. We are justified in regarding this smallest quantity as the atomic weight, if no good reasons exist for believing that this smallest quantity consists of more than one atom. It will be seen later on that methods are not wanting which prevent the possibility of errors of this kind. The following table comprises a list of those substances which contain the smallest quantity of the given elements in the molecular weights of their compounds. The first column contains the names of the compounds; the second, under d, the density compared with air; the third, the corrected molecular weights calculated from the densities; the fourth the amount of the element contained in the molecular weight; the fifth, the chemical equivalent; and finally the sixth contains the thermic equivalent of the element, if the element be known in the solid state. VAPOUR DENSITIES, MOLECULAR AND ATOMIC WEIGHTS |