302 EQUIVALENTS, CHEMICAL 



tho stops by which tho doctrine of equivalents was gradually developed ; but it is 

 proper that we should indicate some of the methods by which tho equivalents uf ele- 

 ments and compounds are ascertained and demonstrated to bo correct. But boforo 

 proceeding, it is necessary to define tho term ' equivalent.' This is not easy to do, 

 because the theoretical ideas of all chemists are not the same. Suppose, for ox- 

 ample, tho constitution of water wore to be taken as the starting point. On submit t ing 

 it to the action of the pile, it is immediately observed that the ratio of tho two 

 gases evolved is as 1 to 2. One chemist will at onco assume that water is a simple 

 binary compound of ono equivalent of each of its constituents. But this involves the 

 assumption that tho gaseous volume of the equivalent of hydrogen is twice that of 

 oxygen. Tho other chemist assuming that one volume of a gas represents ;ui equiva- 

 lent, considers water to be a ternary compound, having tho formula 1I 2 0. It is plain 

 that the atom of hydrogen will have only half tho value on tho second hypothesis tli.it 

 it will on the first, or, what comes to the same thing, the atom of oxygen will be 

 twice as groat. If. with some chemists, wo consider the volumes of tho gases to repre- 

 sent atoms or equivalents, then, water consisting of two volumes of hydrogen and ono 

 volume of oxygen, and as by weight water contains 8 parts of oxygen to 1 part of 

 hydrogen, it is plain that 8 parts of oxygen by weight will represent 1 equivalent, 

 and 1 part by weight of hydrogen will represent 2 equivalents. Consequently 1 

 equivalent of hydrogen will weigh '5. But to avoid fractional numbers it will (on 

 those assumptions) be more convenient to write the equivalent of hydrogen = ] , and 

 oxygen 16. - In this country it has, until recently, been usual to consider the atom of 

 hydrogen as occupying twice the space in the gaseous state of that of oxygen. The 

 atomic weights being, therefore, oxygen 8 and hydrogen 1. 



We have said that it is by no means easy to define an equivalent. The difficulty 

 arises not merely from the different aspects under which theoretical chemists regard 

 the elements and their compounds, but also from the practical difficulties attending 

 the determination of the true constitution of some substances. Thus tho equivalent 

 of bismuth is assumed by some to be 71 and by others 213 ; the oxide in tho ono 

 case becomes BiO, in the other BiO 3 ; the first equivalent being only one-third as 

 great as the second. But, it is to be observed, the variations in the theoretical views 

 of chemists are of no consequence, so long as we clearly comprehend the nature of 

 those variations. The relative values or proportions are the same in all cases. It is, 

 in fact, somewhat the same as if one class regarded the avoirdupois pound as made up 

 of 16 ounces, each ounce weighing 437*5 grains, and the other considered it as con- 

 sisting of 8 ounces, each ounce containing 875'0 grains. 



In order to clearly understand the nature of the equivalents as received in this 

 country, it is necessary to remember that there are three relations of volume amongst 

 gases, namely, one, two, and four volumes. The first relation applies solely to 

 elementary gases. The two others apply to elements and compounds. [It is true that 

 the vapour-densities of pontachloride of phosphorus, chloride of ammonium, and, 

 perhaps, one or two other substances, appear to differ from this rule, but it is probable 

 that, like sulphur, the vapour densities require to be determined under special condi- 

 tions of temperature or pressure.] In the table of equivalents the density of the 

 vapours of those substances which are capable of assuming the gaseous states are so 

 placed that the number obtained by experiment may be compared with that deduced 

 from theoretical considerations. In the following table tho vapour-volumes or com- 

 bining measures of some of the more important elements are given. We sh;ill sue 

 presently the practical value of the information contained in it : 



Combining 

 Element Measure 



Hydrogen 



Chlorine . 



Bromine . 



Iodine 



Fluorine (hypothetical] 



Nitrogen . 



two volumes 

 do. 

 do. 

 do. 

 do. 

 do. 



Combining 

 Element Measure 



Oxygen 



Sulphur 



Selenium . 



Phosphorus 



Arsenic 



Carbon 



one volume 

 do. 

 do. 

 do. 

 do. 

 do. 



It must bo remembered, that all volatile compounds possess four- volume formula, 

 except a few, which in this country are always written as if possessing a condensation 

 to two volumes ; such are carbonic acid, carbonic oxide, sulphurous acid. &c. With 

 the above information it will be easy for any person to calculate tho density of any 

 vapour or gas by the aid of tho following dim-lions : 



To obtain the density of any vapour or gas having a condensation to four v<- 

 such as most organic or inorganic compounds. Multiply half tho density <>t h\- 

 by tho atomic weight of tho vapour or gas. EXAM IM.K: Find the density of tho 

 vapour of hydrobromic acid. The atomic weight of hydrobromk acid is yi. The 



