O N THE IIELAITIOSRETIYEEX PRESSURE ASI) EI'LIPORAITIOS BY EDIVIl- H. HAILL
Many years: ago' Thomson showed that the iiiasiiniiiii vapor pressure in contact with tlie concave surface of a liquid, elevated b y capillarj- action, iiiiist be less than tlie iiiaxiiiiiiiii pressure over a flat surface of tlie liquid a t the same temperature. Maswell's reference to this matter leaves it to be supposed that the diminution of \-apor-pressure is due directly to tlie curvatnre of the surface in the tube. But, according to 1-ien.s set forth by Poynting,' the maxii n ~ i i i ipres.sure of a vapor in contact with its liquid at a given temperature is dependent upon the total pressure to nhicli the liquid is subjected : and P o j x t i n g attributes the siiialliiess of the pressure ahox-e a conca1-e surface to tlie small pressnre borne by the liquidjust b r , ~ z ~ r n fthe / i surface. However sound Poyiitixig's theorj-, his statenleiit of it at this point lacks clearness; for the fact is apt to stick in the iiiiiid of the reader that evaporation and condensation occiir, if a t all, 171 the curved snrface, and that this surface is subjected to the full pressure of tlie atmosphere ; so that tlie pertinence of referring the state of the T-apor to the state of the liquid beneath tlie surface is not obvious. Le Blanc,i although he does not mention Poyiiting, maintains n i l opiiiion similar to that expressed by tlie latter, and gives conclusive arguiiients in favor of it. H e refers to an article 1). Schiller4 on the same subject. I
See 3Iaswell's Heat. Phil. 3\Iag., J L I ~1881, ~ , ant1 Octolier, 1896. Eltctro-Clieniistr!-, I j r , English eclitioii. U - i d ;\tin. 53, 396 I, rS94 ~.
T h e special algebraic expression obtained belovi for the relation between teiiiperature, vapordensit!.. and total pressure, ilia!. have been given before, although I do riot reiiieiiiber to ha\-e seen it ; but in ail?. case I hope that the method of its deri\-ation, 11)- following u p a commonlj- neglected term in a familiar operation, will possess a certain interest. Seriist, T/lc.or-c~tisi~/~c C ~ C I I I p. ~ ; ,j, I 0 of the first c'r e r ~ i ~ a ~ i edition, derives tlie i, equation of the reactioii-isotliefiiis," ~
. ( 1'1
............ ................
r,,%
(' '111
I;
('
1
2
collstant,
in the following 1nanner: Starting with a misture in n-hich tlie reaction occiirs according to tlie scheuie,
where every n refers to a solid or to a liciiiid nhicli does not i l l i s with the other substances present mid ex-ery .\ to a gaseous or dissolved constituent, ever!. I' to the number of p i . mol. of its n entering into the reaction :md el-er!. I I to the iiumber of gm. mol. of its A entering into tlie reaction, tlie whole being coiltaitied in a vessel of unchanging voliime. Seriist iiiiagiiies the reactioii to go on from left to right with no change whatever in the condition of the reaction niixture, the left-hand constituents being forced in as fast as they are constimed b!. tlie reaction a i d the right-liand coiistitiieiits forced out as fast as the?. are produced. The whole operation, beiiig carried on reversibly aiid isothermally, gives the same aniount of work n.hicli n-ould be xiveii by any other reversible isotliernial process proceeding from the same initial to the same final conditioiis. Seriist writes this anioutit of work thus,
E'
R T I)it/)/t-, ~
?/:/~i(.~
...
-
)/,'/i/i.'
...
I,
n-11e i i c e
where each
1-
is tlie coiiceiitratioii of the ccn-responding -4 in the
mixtiire. Then, as E', ho\\-e\-er the iiidii-idual ilia!. var!.. i.G a constant, E; iiiiist lie a constant; wliicli \vas the propositioii to he proved. A close esaniiiiatioii of the conditions gi\.eii 1 1 ~ . S e r i i s t slion-s, lio\ve\-erTthat the \-slue of F alm\-e gii-eii is not, in Zenei-al, true. The frill expression for E' is
E* \\-here
KTiilI.;
s
ii,
S'
I/
1-
'
KTl, S 12..
I
I,
1 2 '
*.
* (
1',12,
total pressure per unit surfact:
1)
1.'
...,
ii?'
\ ~ ~ ~ l L lot: l l ql r~1 , ,. ,. r I
\*I
Pi 1-
S'
1'/1, I
~
,
lJ2L1>
\\31iiii
. .., ..., the reactioti mixture.
In this aineiided equation, ( 2 the teriiis E' aiicl K T I S - S ' 1 lieiiig constant at coiistaiit T,the o n l y iiiipeacliinent of tlie coiiclusioii that KT/uE;, and so E;,i h a coiistaiit. lies in the variatioii of the teriii P(Y 1.' \\-it11chaiixe of I>. T h i s cliaiige, thoiigli usuall!. sniall, siiice the nliole teriii Pi 1. 1.' is likel!. to ht. small, is iiiiqiiestioiiahle, and \ve ninst conclude that K 9 as clefiiied b!- S e r n s t wit11 reference to tlie (,'s onl!., is iiot strid!- a )7
~~
.~
.
~
"The iiiitial condition of tlie .I colihtit1ienti outhiile tlie rexction v e s w l . :11i
6
"
I
%
"
atinoi.
2
approxiinatel)-
"
a ,
IO0
',
I '
I
I .000y. 1.oorX. I .09 j o .
I n the presence of liquid water a t oc C, we should ha\-e kr = E
P -
E':'~),
1240
n h e r e f ( T ) is not the same a i i n equation
(9). In this case P
n h e n P i i very iiuall t t
< 6
.,
I
I '
,
I 2
atiiios. *
12.10 ''
approximately 3 .
[
r .oooS, 1.oorh.
/
.'
I00
E
( i
,.
I
.0840
Of course, tlie saiiie results can be found without an:. reference to the general eynation of the reaction-isother~ri." '(
Cainbvirigr~,J i c a ~r , I.\yq
