A COMPARATIVE METHOD FOR DETERMINING VAPOUR DENSITIES1 BY PHILIP BLACKMAN
Method-Two glass bulbs, best made from some graduated tubing (e. g., disused burette tubing), about 4 inches ( I O cm) in length, are joined together by a short piece’ of capillary-tubing, and their free ends are drawn off sufficiently wide to admit a narrow glass “weighing” tube, Fig. I . The graduatipns are merely to permit observing A and noting the heights to which the mercury used in the apparatus rises. ,The apparatus is placed upright and half filled with pure mercury. The substances whose vapor-densi- EL ties are to be compared are weighed out -1 (weights w1 and wz, respectively) in very small ~2 quantities in narrow glass tubes and placed Fig, I one in each bulb. The atmospheric pressure P is observed. One of the bulbs, for example A that containing the substance of weight’w, is sealed off, and when it has cooled to room-temperature t o the difference in height ulz between the mercury levels is measured, and the positions of the mercury levels on the graduations noted so that later on the enclosed volume of air V in the bulb A may be determined, Fig. 2. The other bulb B is now sealed off, and when it has cooled to roomtemperature tI0, the difference mlin height between the mercury levels is measured, .and * the positions of the mercury levels on the graduations noted so that the volumes V1 and VZ of the enclosed air in the bulbs A and klg. 2 B, respectively, may be subsequently determined, Fig. 3. The apparatus is now placed vertically in a deep beaker and completely covered with some suitable
&i >:
Read before a meeting of the (London) Chemical Society, 1915, and continued from the Journal of the Chemical Society, 107,1500 (1915).
226
Philip Blackman
medium which is heated to a temperature t z O sufficiently high to vaporize completely the two substances. The positions of the mercury levels in the two bulbs are noted so that afterwards the enclosed respective volumes u1 and u2 of the gases in A and B may be measured; and the difference mz in : height between the mercury levels is also .--_- _ determined later on, Fig. 4. The bulbs are . now cut off from the connecting tube and Fig 3 the mercury is removed. Mercury is poured into them from a burette reading correctly (,*'C;p] t o 1/20 cc to reach the positions occupied by the mercury in order to determine the volumes V, V1, Vz, V I and vz. The vapor-densitiesdl f and dz can then be compared by the aid of the formula given below, and if one be known the other can be calculated. All measurements are made with the ---. - _ -------. bulbs in a vertical position. k%. 4 Strictly speaking V, V1 and V2 should represent the respective air-volumes less, respectively, the volumes of the substances wl,wl,w2. The method cannot of course be used with substances which react with mercury. If the results are to be trustworthy a substance which is used for the comparison, and hence whose vapor-density is known, must be pure. Theory.-It is assumed that at o o C and 760 mm I gram of hydrogen occupies I I 160 cc. As the vapor-pressure of the mercury is equal in both bulbs it is unnecessary to make allowance for it. (a) In A (before sealing B) at t o , air-pressure = p - m (always - m , because when A is being sealed up the air in i t is heated and because of its expansion it is ultimatelyI on cooling at a lower pressure than the outside air). ( b ) In A (after sealing B) at hO,
Method f o r Determining Vapour Densities
227
= air-pressure also in B a t t I 0 (+ ml when the mercury i n A is on a lower level than in B, and -ml when the mercury in A is on a higher level than in B). (c) In A, a t bo, air-pressure
and vapor-pressure I - 11160 X 760(273 4-~ P ) W......................... 273 divi
(2)
(d) In B, a t i Z o ,air-pressure
:and vapor-pressure - I I 160 X 760(273 +'tz)w2
Now (I)
+
273 d2~2 (2) =
(3)
..........................
(4)
+ (4), whence
&L+-..-=m 31068 wl 31068 w2 273
+
divi
f?
d2vz
#(+ mz or -mz when the mercury in A is on a lower or higher level, respectively, than in B). Now in general t o = t I 0 if the bulbs be both sealed within a short interval of each other, s o the formula reduces to
{v
* m1){-}{~-~}
+ tl
* - = Wz 273
nzz
+ 3 1068w1
273I
+ tz
3 1 0 6 8 ~.2. . . . . . . . . . . . . . . . d2vz
is small in comparison with any of the other quanti+ -ties and may be left out of account unless a very great degree 273
ta
ofaccuracy is required, and the formula then becomes
31068~1 - 31068.~2 +--..... ". . . . . . . . . (11) dit1 d2~2
228
Philip Blackwan
Method for Determilzing Vapour Densities
229
It would be more accurate to substitute V - w;/s1, VI - wl/sl and '/z - w2/s2 (sl and s2 being the respective specific-gravities of wland wzas measured a t tl") for V, VI and Vz, respectively, and the formula will then read ( p -m>(V -- Wl/Sl> * ml V1--1/s1
*-
2 + 1
31068'w1
+-=-
flz2
+
){
j { v1 ; l w l k V2
--2/sz v2
31068w2
\
. . . . . . . . . (111) &vi d2v2 or without the negligibly small quantity * m2/(273 4- h) vz -WZISZ v1 - W J S ,l ( P - .z)(V - WI /SI) * ml 273
v1-
t2
) { 2 G h ) (
WdSl
Vl
v2
31068wl - 31068wz +--. . . . . . . . . . . . . . . . .(IV) divi dzvz
t
The comparative values of these four formulae are shown in table on page 228. Corrections made for the following are of theoretical interest only and of no practical importance: ( I ) the expansion of the glass bulbs between t10 and t20; ( 2 ) the expansion of the mercury between t10 and t z o ; (3) the volumes occupied by the glass of the weighing tubes. It is assumed in each case that the first substance gives the theoretical vapor-density and that the second is the calculated value. Hackney Technical Institate London, N . E. (England)
