DETERMINING AVOGADRO'S NUMBER A Laboratory Experiment RUTH H. ELLIS and ROBERTA B. RAUCH Vassar College, Poughkeepsie, New York
IN o m
interdepartmental chemistry-physics course we have been interestred in devising experiments which will encourage the student to think and which will a t the same time lend themselves t,o active t,eaching on the part of the instructor. Nerhamkin' has recently described an experiment iu \\-hich the very small number representing the charge on the electron has been successfully determined by students in elementary chemistry. In our laborat,ory we have determined Avogadro's Number, which previously had seemed to the student too large to have any meaning or any possibility of being determined by the inexperienced analyst,. The experiment which will be described below involves the electrolysis of water and the collection of the hydrogen and oxygen evolved. From the data obtained it is possible to determine Avogadro's Number quite accurately. The apparatus set up as shown in the figure was complet,ely filled with approximately 10 per rent
Time Barometric pressure Room t e m ~ r r n t u r e Current Volume of H9 Volume of Oa Heieht of H9SOdin central l.ubr a h v e lower level of Hz H ~ i g h tof H$04 in c e n t d t,ul,tr sbovo loher level of OQ Densitv of H3O. solution ~ e n s i t gof ~g Vapor pressure of HBOI a t 24.IDC. Charge on the electron
0.58 amp. 52.0 ml. 25.8 ml. 36.8 em. 24.2 .1Oi 13.6 2.0 -16.0
em. e./ml. g.iml. cm. X 10-'ooulon~bs
Samples of the gases were dmwn off into test. t,uhes and identified by the characteristic tests, ie., supporting combust,ion and burning with a "pop." The student,^ had previously written the equation 2HI0
-
2FL
+ O2
This experiment gives clear evidence that the decomposition of water does give two volumes of hydrogen and one volume of oxygen. The equat,ions represent,ing the electrode reactions
Rheostat
-
Platinum elaotrodes
-tar
and t,he stopcocks closed. It is important for the success of the experiment that the current be kept constant by means of the rheostat,. The current was allowed to run through the apparatus for a carefully measured length of time, aft,er ~vhichit was turned off and the data recorded. The temperature of the room and the barometric pressure !ere read. The volumes of both the hydrogen and oxygen were recorded. A careful measurement of the height of. the sulfuric acid in the center tube above the lower level of the hydrogen was made, and a similar measurement of the height of sulfuric acid above the lower level of the oxygen. The tahle gives a complete t,abulation of the data collected. I
J. CAEM.EDUC., 29.92-4 (1952).
-+ +-
4H+ 4e 2H2 a t lhr rathode 4e at, flw anode 2H20 O* 411 +
+
indicate to t,he student that as four electrons am liberated in the formation of a molecule of oxygen there are four electrons used in the product,ion of two molecules of hydrogen. The students had learned previously that pressure is proportional to density and t.o the height of the column of liquid supported. Jn order to determine t,he height of mercury which would exert t,he same pressure as the mllfuric acid column t.he expression d&
=
rlzuh,
was used, where dl and d z refer to the density of the sulfuric acid solution and of the mercury respectively, and h and h2 refer to the height of t,he sulfuric acid solntion and the height of the mercury column. The value g, representing the acceleration due to gravity, cancels out. Since the densities of the sulfuric acid solution and of the mercury and t,he height of the acid column are all known, the height of the column of mercury exerting the same pressure is easily determined. From these data it is found to he 2.9 cm. of Hg for hydrogen. Using the expression P,. P",,"? = P.tm. Psgo..~l.ti.. it is now possible to cnlculate the pressure exerted
+
+
SEPTEMBER, 1953
by the dry gas. At this point it is well to remind the student that the vapor pressure of the acid solution is lower than that of pure water; also t.hat, Dalton's law of partial pressure is being used. The pressure of the dry hydrogen is found to be 77.5 cm. of Hg. Applying Charles' and Boyle's laws to the data the volume of the dry hydrogen at STP is shown to be 48.7 ml. The relationship I = q / t is used to determine the total charge involved when a current of 0.58 ampere is allowed to pass through the system for 12.0 minutes. ks the charge on one electron is given, the total number of electrons passing through the solution may he calculated. This is found to he 26.1 X lo2'. Two electrons are used in the liberation of one molecule of hydrogen, so it follows that 13.05 X 1020 molecules
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of hydrogen must h a w been formed. Since this number of molecules of hydrogen gas has been shown to occupy 48.7 ml., in 22,400 ml. of the dry gas at STP there are 6.00 X loz3 molecules. By a similar series of calculations using the data for oxygen one ohtains 6.12 X loz3as t,he number of molecules of the gas in one mol. The average of these two values gives 6.06 X loz3which represents a 0.66 per cent. deviation from theaccepted value, 6.02 X loz3. This has seemed an interesting experiment for several reasons. The results are so nearly those of the accepted value that the student feels there is real validity in Avogadro's Number. It gives an opportunity for bringing toget,her and applying several lams and princi-ples studied earlier.
