8
THE LAWS OF DEFINITE COMPOSITION AND OF MULTIPLE PROPORTIONS: A GRAPHICAL APPROACH' B. A. FIEKERS, S.J. College of the Holy Cross, Worcester, Massachusetts
T R n ~ m nchemists frequently find it a tedious task to teach the fundamental laws of the kinetic-molecular hypothesis. Some rely heavily on the fund of highschool chemistry that the freshman has carried into college. Many begrudge the time spent on such topics, for which the rest of the syllabus will provide inductive confirmation. Thus the qualities of clear teaching and distinct comprehension are apt to suffer in this part of the course. The remedy, here proposed, may be attractive. The proposal is a graphical method for teaching the laws of definite composition and of multiple proportions. I n this method numerous arithmetical operations are minimized so that fuller meaning of the laws themselves can he realized. The method provides a copious choice of data, from which the most striking may be selected. At an early date in the course the student is introduced to linear mathematical relationships such as he will encounter generally throughout the rest of it. Effistructor and student alike. The law of definite composition states that in every pure compound the ratios of the weights of the elements have a coustailt value (see the table, columns 1, 4, and 8). Limiting our illustration to a compound of two elements, such as nitrogen and oxygen in nitrous oxide, the ratio of the weight of oxygen to that of nitrogen, 0.571,is the constant value for all samples of the pure compound. This can be shown graphically, as in the From a paper presented before the New England Association chemistry Teachers a t Emmanuel College, Boston, Mass., h h y 15, 1054. 1
(1)
Substance
Nitrous oxide Nitric oxide Nitrogen trioxide Nitrogen tetroxide or dioxide Nitrogen pentoxide
(8)
(3)
NIO
100 NO 80
g
60
F
40
.-g
NXO~
NO, N.OS
20
o
o
20
40
60
80
100
wt. ~ x ~ e e n
figure, by plotting a given weight of nitrogen in nitrous oxide against its corresponding weight of oxygen. Sinre most students come to the course ~ r i t ha clear but popular idea of what analysis implies, quantitative data can be used. It is then convenient in practice to plot the percentage of one element against that of the other, as grams per hundred grams, and to draw a straight line through this point and the origin. One invokes numerous other analyses, expressed in weight ratios, to justify the straight line. The constancy of these ratios is then shown from the graph and possibly confirmed on a dem-
(4) Wo/W,,
(5) Wo/17.5
(6) Wo/#8.0
(8)
Known formula
%N
%O
w.
63.7
36.3
0.571
10
16
1
NsO
46.7
53.3
1.142
20
32
2
NO
36.9
63.1
1.713
30
48
3
NnOs
30.4
69.6
2.284
40
64
4
25.9
74.1
2.856
50
80
5
NOSor Nt0' NaO.
8. N
w. N
(7) Integral relationship
JOURNAL OF CHEMICAL EDUCATION
FINDING THE REST POINT OF AN UNDAMPED ANALYTICAL BALANCE' IRVING F. STACY2 Columbia University, New York, N. Y.
IN
two usual derivations, together with the more exad one, are presented below. One proof3 depends upon the assumption that the amplitude of each swing is less than the preceding one by a constant amount k. According to Swift, if the first turning point of the pointer is b divisions away from the actual rest point (the position of the pointer after a very long time), then the next turning point is b- k divisions away, the third b-2k, and so on, as shown in Figure 1. The average of the first two readings on the left is b-k divisions to the left of the rest point and the first reading on the right is the same number of divisions 1 Presented before the Division of Chemical Education at to the right. For a total of five readings, the average of t.ha%fit,h Meetine of the American Chemioal Society, New .-.. the three on the left is b-2k divisions to the left of the York, September, i954. 2 Present address: RCA Victor Division, Radio Corporation rest point while the two readings on the right give an of America, Harrison, New Jersey. average which is b-2k divisions t o the right of the rest point. In each case, the point midway between the I REST POINT I left and right averages is the rest point. Although the result is the desired one, and is valid with negligible error for a good analytical balance, the assumption of a constant decrement implies that after a finite number of swings the pointer will suddenly come to rest. The other proof sometimes referred to4 assumes damped harmonic motion of the beam, i. e . . the MOST textbooks on quantitative analysis, instructions for finding the rest point of an analytical balance are presented without explanation. The student is told to allow the beam of the balance to swing freely and to take three or five consecutive readings of the extremes of the oscillations. The point midway between the left- and right-hand averages is taken as the rest point. Of the two derivations of the method to which reference is sometimes made, neither is completely satisfactory. A mathematitically exact method for finding the rest point from three readings is possible. The
~
AMPLITUDE Fbun 1
SWIFT,E. H., "Introductary Quantitative Analysis," Prentice-Hall, Inc., New York, 1950, p. 18. ~FALES, H. A,, AND F. KENNY,"Inorganic Quantitative Andyeis," Appleton-Century-Crofts, Ino., New Yark, 1939, pp. 678-80.
