3 5 THE APPLIC'ATIOX O F GRAPHIC 3IETHODS IX C ERThl S C H 1;b lI C -1L 8 TT-DI E:S,
T h e graphic methods so generally applied in the different branches of science possess the great advantage of representing physically t o tlie e y l;t\vs deduced f r o m the observation of certain plienoineiia or metap1iysic:il conceptioiis, laws generaill- expressed by complicated ecl~iatio~is of which the solution would involve.impracticable c;tIciilatioiie. In it general rnanlier, the more coniplicatecl aiid difficult of conception bj- oiir mind is a physical lam, the liiglicr is tlie degree of the equation or ernlhical formula mliicli ernbodies it. U-lieii 2tpplied t o tlie study, of tlie laws of gritvitat,ion for i i i s t ; i i i c ~ . t o ti uote :t well k11ow1i ixample, this graphic method furr i i s h c t h ciirvos from which can bc ;it once calculated by measiiie111cz11 t s 011 :I diagram, the 1)riucipal dilttit of :t given qiiestion. '.l'ruiisported t o the domain of chemistry the method is f o u n d yery m e f i i l for t h e solution of nimy 1JrObIemS. The curve of solubility of certain salts of which tlie solubility varies wit,li the temperature furiiislies i t t once the a m o u n t of such salts in solntioii in water a t different temperatures. \\-lieu sitline solntioiis arc used for certaiii specific p r p o s w siniihr ciii'ves constructed froiii ttctu:tl oljserv.atioiis of the densities of different saturations or the degree tliey sliow with x givcii areometer, can give readily the amount of the salt t o be dissolved in a certain amount of water to obtain the density required, or
If we pass from these simple examples to curves representing certain conceptions of the intimiite constitution of matter, tlie use of graphic methods proves equally advantageous. A curve reproducing the results of certain observations may
GRAPHIC METHODS I X CERTAIN CHEMICAL STUDIES.
129’
and will often present ‘(breaks” or solutions of continuity, and a consideration of these missing parts may prove the means of discovering the probable properties of an unknown compound, which, graphically, would find its place a t such a point. We may mention as an esample the well known ciirve of Mendelejeff, embodying a classification of the elements. Without entering into a discussion of the question if this curve does really or not represent a natural classificatiou of the elements, it is well known that by the consideration of some missing points of the curve, i t has been possible for Mendelejeff to foresee that the “ g a p ” observed at certain points would have to be filled by an element which, by its position between certain others of which the properties were known ought to possess certain characters of atomic weight, specific gravity, and even chemical affinities which t h e subsequent discovery of such an element has emphatically confirmed. In other cases these curves may serve as affording a eorroboration, a control, of certain assertions generally admitted, and even if usefnl only to that extent, they would be very valuable. We have thought that in this line of investigation i t might prove interesting to submit the results of some personal researches. If the molecular weight W of a compound be divided by its specific gravity D, the quotient expresses the molecular volume of the compound
V=-
w D
and thisratio of the molecular weight to the specific gravity can be easily computed in each particular case. Of the nature of the atoms we do not know much, we are not in this respect any more advanced than the Greek philosophers were twenty centuries ago, we havc no definite ideas of their shape, we do not know if their number is limited. We admit that under certain circumstances they can assume an individuality and form molecules which we consider as the smallest conceivable parts of matter which can pass into or out of combination ; we admit also, that these molecules affect the spherical form, from which, i t can be inferred that a compound constituted by such molecules separated by intermolecular spaces will affect also a spherical form.
GRAPHIC METHODS IN CERTAIN CHEMICAL STUDIES.
131
The graphic consideration of these molecular volumes for certain class of compounds give rise to interesting deductions. If, for instance, we consider the primary alcohols and their derivates, aldehydes, acids, ethers, we know that, in each series of these conipounds, the molecolar weights proceed by regular and equal increments by the addition to the preceding term of the series of the niolecular weight of the radicle which heads it. If we carry then on a horizontal line, taken at8 the axis of abcissae and at a proper scale, these equal increments from an assumed point 0, and applying to each compound the proper molecular weight W, represented by a corresponding abcissa, we erect a t each point, thus determined in the axis A S of abcissae, a perpendicular ; by carrying on these ordiuates the lengths measured a t the same or any other scale assumed, for clearness of diagram, which represent the calculated molecular volunies V in each case and joining the points by a continuous curve we will obtain a curve which will be the graphical representation of the law by which, so to speak, we pass from one compound to the other. If it happens t h a t certain of these compounds be unknown, the curve a t the corresponding point (or the ordinate) will present a “gap,” but the general curvature assumed will allow us to trace it, with a sufficient approximation, by joining the points corresponding to the term or terms of the series preceding and following the missing compound or compounds and we shall be able, by actual measurements of the missing ordinates thus supplied, to foresee very closely the physical characters of the missing term. These molecular volumes being generally represented by numbers rather large may render the construction of the diagram on a scale sufficiently large rather difficult. They can be advan. tageously replaced by such quantities, proportional to them, as can be readily calculated, the volumes being known, for instance, the corresponding radii of the spheres which represent the molecular volumes.
and
3 -/
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G R A P H I C METHODS IS C ERTA IK CHEMICAL hTUD,IES.
We have calculated such radii for the primary alcohols, their ethers, aldehydes and acids for the compounds of which the moiecular weights IT and specific gravities D are giieu below. calculitting and tabulating first tlie molecular roliimcs from which the corresponding radii were deduced. and for each series or gronp of compounds we have constructed t h c special corresponding curve by carrying, as explained abow, a + ;ibeiss:te tlic respective molecular weights in each case and as ordinates at each point tli tis cletermined on the line of abcissae the calculstetl radii of tlie spheres corresponding to the different molerolar volumes. \LC OR 0 I,.
3
IT 32 46 60
74 81
102 11G 130 144
158 I??
C H,O Gas.
c, H, 0
C,, He 0 C4 H8 0 C j H,,O c6H120 (3, H,,O
C8HleO C, Hl8U? C,,Hz,O ? C,,H,,O
44 5s '72
SG 100
2.110
0. SO98 0.812 * d?O .E4 .83 .I3312 .838 ,tis75 .ti415 .8389 .a268
.so;
.13 *
834
, t;?2
?. 38.;
2.593 2 . 77s 3.939 3. 082 3 ?O!t 3.33:; 3.444 n . 5 5.i 3.6'7.5
54.5229 69.8795 86.3309 104.6228
,842 .827 0.82
118. ,648
114 128
170
.85
'!00.00
137.8476 156.0975
3.627
GRAPHIC! METHODS IN CERTAIN CHEMICAL STUDIES.
133
BCIDS.
46 60
74 88 102 116 130 144 158
1.245 1.0701 1.0154 0.9746 .9562 .9446 .935 .9139 .9082
36.9477 56.0695 72.8776 90.2934 106.6722 122.8033 139.0374 157.5664 173.9704
2.066 2.374 2.591 2.783 2.941 3.083 3.213 3.350 3.463
50.3401 66.8414 82.9081 98.8735 107.8586
2.290 2.517 2. $04 2.846 2.953
ETHERS.
C H,O&Gas. CzHgO+ 37 C,H70+ 51 C,HgOQ C,HllO+ C,Hl,O+
65 79 93
.735 .763 .784 .799 .862
The specific gravities are for the temperature of 0%. and have been obtained from Prof. Clarke’s ‘‘ The Constants of Nature.” Instead of writing the f o r m u h of the ethers CnHzn+l, CnHzn+l\ 0 their molecule has been halved so as to obtain volumes comparable with the volumes given by the alcohols, aldehydes and acids, and this has been done only as a matter of convenience in calculation, bearing in mind, however, that the formulse represents only half a molecule which, according to present chemical theories, cannot exist. In the series of the aldehydes we have omitted the methylic aldehyde which is a gas, beginning the curve only a t the nest liquid compound. The aldehydes C D H 1 C, ,H,,O are unknown a t these points, the curve is supplied from the general radius of curvature it assumes. The interpolated curves would furnish a t once very approximately the corresponding ordinates,and by measuring these ordinates on the scale the radii of the spheres, representing the molecular volumes could be obtained. From these radii the molecular volumes could be readily calculated, and
134
GRAPHIC YETHODS I S CEKTAI
