MOLECULES AND ATOMS 327 



vapour density, or molecular weight and composition. The vapour 

 density D= For instance, the formula of ethyl ether is C 4 H IO O, 



corresponding with the molecular weight 74, and the vapour density 

 37, which is the fact. Therefore, the density of vapours and gases has 

 ceased to be an empirical magnitude obtained by experiment only, 

 and has acquired a rational meaning. It is only necessary to remember 

 that 2 grams of hydrogen, or the molecular weight of this primary 

 gas in grams, occupies, at and 760 mm. pressure, a volume of 22'3 

 litres (or 22,300 cubic centimetres), in order to directly determine the 

 weights of cubical measures of gases and vapours from their formulae, 

 because the molecular weights in grams of all other vapours at and 

 760 mm. occupy the same volume, 22*3 litres Thus, for example, in the 

 case of carbonic anhydride, CO 2 , the molecular weight M=44, hence 44 

 grams of carbonic anhydride at and 760 mm. occupy a volume of 

 22'3 litres consequently, a litre weighs 1-97 gram. By combining the 

 laws of gases Gay-Lussac's, Mariotte's, and Avogadro-Gerhardt's we 

 obtain 23 a general formula for gases 



where 8 is the weight in grams of a cubic centimetre of a vapour or gas 

 at a temperature t and pressure p (expressed in centimetres of mer- 

 cury) if the molecular weight of the gas=M. Thus, for instance, at 

 100 and 760 millimetres pressure (i.e. at the atmospheric pressure) 

 the weight of a cubic centimetre of the vapour of ether (M=74) is 

 =0-0024. 24 



25 This formula (which is given in my work on ' The Tension of Gases,' and in a 

 somewhat modified form in the ' Comptes Rendus,' Feb. 1876) is deduced in the following 

 manner. According to the law of Avogadro-Gerhardt, M = 2D for all gases, where M is' 

 the molecular weight and D the -density referred to hydrogen. But it is equal to the 

 weight s of a cubic centimetre of a gas in grams at and 76 cm. pressure, divided by 

 0'0000898, for this is the weight in grams of a cubic centimetre of hydrogen. But the 

 weight 8 of a cubic centimetre of a gas at a temperature t and under a pressure p 

 (in centimetres) is equal to P/76 (1 + at). Therefore, s = s.76' (1 + at)p; hence D =a 

 76.S (1 + at) '0'0000898p, whence M = 152s (1 + at)/0-0000898p, which gives the above expres- 

 sion, because I/a = 278, and 152 multiplied by 273 and divided by 0-0000898 is nearly 6200. 

 In place of s, m/v may be taken, where m is the weight and v the volume of a vapour. 



34 The above formula may be directly applied in order to ascertain the molecular 

 weight from the data; weight of vapour m grins., its volume v c.c., pressure p cm., and 

 temperature <; for. ^ = the weight of vapour m, divided by the volume v, and conse- 

 ^uently M = 6,200m. (273 + t)[pv Therefore, instead of the formula (see Chapter II., 

 Note 84), j?v = R(273 + <), where R varies with the mass and nature of a gas, we may 

 apply the formula ^t> = 6,200(?n/M) (278 + <). These formulas simplify the calculations 

 in many cases. For example, required the volume v occupied by 5 gnns. of aqueous 

 vapour at a temperature t = 127 and under a pressure p 76 cm. According to the 

 formula M = 6,200 m (273 4- t)/pv, we find that v = 9,064 c.c., as in the case of water 

 M = 18, m in this instance = 5 gnns. (These formulw, however, like the laws of gases, 

 are only approximate.) 



