MOLECULES. 682 MOLECULES. are assumed to be iiieapuble of subdivision by any In this formula p dunuten tlje pressure actually means whatever. observed. To conform to the theoretical law, The relative weights of molecules, termed a molecular weights, are among the most impor- '*^'<^ ^'^'^ to p the quantity ^ depending on the tant constants of nature. Their precise experi- ... i i ^^ .^- t ., , , mental deterniination presents no difficultv «^.at- T f , attraction of the molecules, and ever. But it has been shown that even the abso- tI'L-reture also upon the volume occupied by the lute dimensions of molecules, their absolute """l /<= /"^tor r — i » ,n the turnuila repre- weight, their actual nun.ber in a given volume ^"'l the total volume hi ed by the gas. dnnin- of lubstance, their specific gravitvr etc., can be f'": '">' f'""" t-ni^s the volume actually occupied ascertained with some degree of probability, ^y ■'« »'.«l<;"'les, which are assumed to be spher- Brief mention mav be madt^here of some of the "=• ^^^ ' '"^ !'=>" the ideal pressure-i.e. the simpler methods emploved in searching for those P-'f «"« -Iftennined by the motion of the mole- absolute dimensions in 'the unseen world of mole- f}^"^ '•"^, "■"1'>""^<'<1 .v their mutual attrae- cules. Such theoretical researches are carried *'f"~'">' ", V" tl>e actual volume within out mainlv on the i.rin.'iple that when a hvpothe- '"!' "": '"""^^'"'f'* »'•<' f*' to move: the prod- sis is admitted within the scope of an exact sci- ".■ ',' i-v"l'-"tly the same as in the case of the ence, we must have exhaustive knowledge of the ^'"'.'; A"-/"' =/- ""'I- '"», pressures, deductions that can possiblv be made from it. J lie attraction of the molecules and their vol- Onlv bv correlating the deductions with facts """^ 'i;"'"; "l ^J":*- "l'°" tl'e nature of the ean we" judge uh.thcr the bvpothesis is reliable ""f- ^>' "'■'""'.'• '•tenmning he pressures and or not, and ex|H.rien<c teaciies that de.hictions ".l"'"es of various gases, numbers may be sub- seeminglv incapable of experimental verification ^tituted for r, ;., and y m an der Waals's for- mav ulti'matelv not be so at all. Of course, the ""."?• »>"! thus equations may be obtained con- caliulation of" the absolute dimensions of mole- taming only two unknown quantities, a and 6, cules is also fascinating in itself. Like certain *'"= '"V"?'"':)., '"'■ '/r "^ "",! '"," ^™ ^ ^*y speculations in astron.miv, it shows that there is ^"'"•'"te'l-. t^be lollowing tal>le shows the values no limit in the depth of the invisible and inacces- "V -^S? "• "'f /'"<"'»' "f '<" niliimr of a gns sible. bevoncl which exact scientific thought can- "c"'"!/ orcH;)ieaf hy Us molecules) for a few not be expected to penetrate. S^ses and vapors. These values are calculated ABSOLUTE i,iMEX.s,oxs OF MOLECULES. f""", V"" t^'M-erature of freezing water (0° 0.) T,, , , . , , ., J i.1 1 ■ X- ii and for normal atmosplieric pressure: Ine fundamental hypotheses of the kinetic the- orv of gases lead to the proposition that at any „ scbstaxce vj 6 ■ ■ ," , ,11 c ■ ■ Carbnmc Odd gas 0.00050 given teniiicratuic the volume of a gas is in- Nitr.iua oxide gas Oiioow verselv ))roportional to its pressure. This rela- Sulphur dioxide gas o t««i62 tion, which had been known as a matter of fact £'!'■'!'!*; *■?? ""'"55 , , , .. ,,,.,, 1 , ^. , Etliyl elilorule vapor o.tKKHJ" long before it was established deductively, may Alcoliol vapor o ikkisj also be expressed bv saving that the ])rodiict EUht vapor o.imim of the pressure and Volume of a gas is constant: ^^Zl^ J^Zi^y^Por::ZZ:Z:ZZZZ:-: o^l pv =: C. From the point of view of the kinetic, theorv. v " 'th the aid of these figures the specific grav- represents in this formula the emptv space with- "tj' of the molecules, say of carbonic acid, may in which the molecules of the gas move— i.e. the '^e readily calculated as follows: At 0° C. total volume filled bv the gas, minus the volume ""'l "'"'er normal atmospheric pressure, 22..350 actuallv occupied bv its molecules. As long as eubic centimeters of carbonic acid gas weigh the gas is not too "highlv compressed, the total """t 44 grams. The volume actually occupied volume mav be used in the above formula instead ^y the molecules being •22.:{.iO X O.OODoO ciiliic of the unknown intcrmoleeular space. For, eentimeters, one cubic centimeter entirely tilled under low luessurcs. llic difference between the '•.^' earbonie acid molecules, with no space be- volume of :i gas and the volume of its emiity tween them, would evidently weigh intermolecular space is very slight, and hence 44 the en-or coniinitted amounts practically to 22,350 X 00050 nothing. But as the pressure exerted on the gas increases, its volume becomes small, and (ho "■" ahout 4 grams: i.e. the specific gravity of a fraction of that volume actuallv occupied by molecule of carbonic aeid is about 4. Similarly, the molecules becomes considerable. In other the specific gravities of the molecules of other words, the difference between the volume filled substances are found to be as follows: by the gas and the empty intermolecular sjiaee srasTAxcE .sp, gr. of moleeuloe becomes too great to be neglected. At the same •J"'"" '^^'^j ?'2 time, as the distance between the molecules be- "K'tilvl"nt...'.°.. ..*!!!!!!."!!!!!! ."!!!"!!"!"! '. i.i comes smaller, they begin to exercise a certain Kt liyl chloride !.""."!!...".."........"!."...^!"." 2.» amount of attraction upon one another, and plV',"' »"2 therefore the |iressurc exerted by the giis on the BeuWio............!...........!.......!......... !....!!!...!.! vessel eontjiining it is somewhat diminislicd. Carbon disulphide 4.3 Under such circumstances, the simple formula r- , -i . i- c i * . ™«i: .. , , . it I .. ( onsiderations of a somewhat more compli- mentioned above ceases to express the relation , , . _ i i . »i i ■ .i „. „4. no , . iL u J J 1 r ciited nature lead to the conclusion that at between the observed pressure and volume of ,, , . f i . i « „„. ,.,,,,'. , 1 c 1 t ■• and under a pressure of 1 atmosphere, one gases and the f.illowing formula first sng- ,,„,,|,. ,„i|,i,„^ter of „„„ ,!<•■< or n,,,or contains psted by Van der Waals, has to be employed „,,,,roximately o^.non.OOO.OOO.noo.OOn molecules. insteaa. Since 1 cubic millimeter of hydrogen weighs ( p + "]()'— b) = c. O.Onnon milligram, the absolute weight of a ^ '■ ' single molecule of that gas is therefore
