A More Direct Feeling for Avogadro's Number N. K. Goh, R. ~ubramaniam,' and L. S. Chia School of Science, National Institute of Education, Nanyang Technological University, Republic of Singapore
As one of the fundamental ~hvsicochemicalwnstants. Avogadm's Number is central to tge understanding of vari: ous chemistrv conce~ts.Several methods have been developed to d e t ~ r m i n e ~ v o ~ a d rNumber o's (1-7). However, grade 9 or 10 students, who are just beginning to learn chemistry, have difficulty grasping this number. Various analogies to help visualize its magnitude have already been proposed (8-10). Nonetheless, they are still only analogies, and some students may dismiss their relevance, thus overlooking their significance. Recently, Bindel has developed a discovery-oriented activity involving the use of X-ray crystallographic data to amve at the number of atoms in a gram atomic mass of an element (11).The procedure described in the article should not present any difficulty for college chemistry students. Nevertheless, the concepts involved in the procedure are well heyond the scope of grade 9 or 10 students. In this oaoer. we use an aooroach based on the intrinsic parameters of an atom to evifuate Avogadro's Number and assess its accuracy. It takes into wnsideration basic concepts of an atom such as those introduced to grade 9 or 10 students: mass number. atomic number, and masses of the fundamental particles..An advantage of this procedure is that it readily lends itself to activity-oriented approaches for learning. Possible pedagogical implications are discussed. ~~
~~
Evaluating Avogadro's Number
When the wncept of an atom is introduced to grade 9 or 10 students, the formalism adopted is that of a nucleus containing an integral number of protons and neutrons, surrounded by an integral number of electrons. (The hydmgen nucleus tH, of course, contains only a pmton-no neutron.) Theoretically, the mass of an atom is given by the sum of the masses of its electrons, protons, and neutrons.The respective masses of these fundamental particles are usually made known to students. Also, the relative isotopicmass is given to a good approximation by the mass number. Students can then simply be asked to calculate the total number of atoms present under the given relative isotopic mass of a particular element. The procedure for calculation is demonstrated below, according to data in ref 12 electron mass
9.1 093897 x 10-" g
proton mass
1.6726231 x I o-'~ g
neutron mass
1.6749286 x 1o-'~ g
where N is Avogadm's Number However, mass of N atoms = m Hence, N=
By substituting the mass number (m)and atomic number (n)of any element into eq 1, an approximate value ofN can be obtained. Table 1gives sample results obtained by such calculations for some elements, which were selected to enwmpass a range of atomic and mass numbers. It can be seen that the values of the Avogadm's Number calculated for the listed sample elements are quite consistent, and they deviate by no more than l%from the accepted value (12). The assumptions that the relative isotopic mass can be approximated by the mass number, and that mass defect contributions are not substantial, are reasonable. If one takes into wnsideration mass-defect contributions but assumes that relative isotopic masses can be approximated by the mass numbers, N is affected by less than 1% (Table 2). Likewise, in the absence of mass defect wnsidrerations, the use of relative isotopic masses in place of mass numbers affects N by less than 1%.For any element, because eq 1reduces to
N thus becomes apparently independent of the atomic number and mass number of the element. Table 1. Evaluation of Avogadro's Number
Element
For an element ;X, the mass of one atom (w)is
We have
'g~b The
'Permanent Address: Singapore Science Centre, Science Centre Road, Singapore 2260, Republic of Singapore. 656
Journal of Chemical Education
m (gImo9 (1.6749286rn - 0.0013946n)x 10.'~(giatam)
N loz3
Accepted Valuea
5.97
99.1
%b
wrrentiy accepted value of Avogadro's Number is 6.0221367 n loz3
1,7 2 ,,.
b ~ o r e aof~ comprehension, e the percentages have been expressed to three significant figures.
Table 2. Evaluation of Avogadro's Numbere
Element
Relative Isotopic Massa
Mass LIefecfb
x 1orz4 g
N Percent ValueC Accept4 x 1oZ3 valued
4.00260
0.0504470
6.0
99.6
23
11Na
22.989767
0.3325849
6.0
99.6
?%I
34.968852
0.5316083
6.0
99.6
%cu
62.939598
0.9663258
6.0
99.6
'8Bpb
207.976627
2,9911557
6.02
$He
100
'Fmm ref 12 ' M ~ S Sdefect
values were calculated using data in ref 12.
'Takes into consideration rnass-defect contributions but assumes relative isotopic masses can be approximated by mass numbers. (The mass defect contribution is subtracted in the denominator of eq 1.) dpercenlage~ have been expressed to only three signAiwnffigumsfor ease
of comprehension.
In this activity, each student can be assigned a particular element and ~rovidedwith values of mass number and atomic number. (In assigning elements, we recommend usine a bmad ranee of elements in the ~eriodictable.) Bv substituting these values into eq 1, anestimate of N c& be obtained. When collating values from the various students, the relative constancy of N among the various elements will become amarent. It should lead students torealize that, despite tgdiversity of elements in the periodic table. there is an underlvine ~arameterthat is rather con" stan< That, of course, is the Avogadro's Number. Reasons for the deviation from the accepted value can then be discussed. Such an exercise not only provides students with a more direct feeling for Avogadm's Number, it also gives teachers a good opportunity to demonstrate the concept of mass defects.
-
-.
Acknowledgment We wish to thank the reviewer for his comments on an earlier version of the manuscript. Lnerature Cited 1. I(ing,L.C.:Neileon,E.K J Chem. Educ. 1%,35,198. 2. White, W. 0. J. Clrern. Edue. 1968, 43,A438. 3. Sloat, C. A. J.Chem. Educ. 1968,43,A438.
Pedagogical Implications
4. Mwihan, C. T: Goldwhite, H.J. J C k m . Edue. 1968.46.779, 5. Hawthrone, R. M.,Jr.J C k m . Edue. 1W70,47,751. 6. Boyko, R.; Belliveau. J. E J. Chem. Edue. 1988, 63, 6l1. 7. Kruglak, H.J C k m . E d u c . 1988,65,732. 8. Alexander, M. J.;Abbott, E T J. C k m . E d u e . 198(,61,591. 9. ~ ~ l t o 8.; ~ iwszonck, ~ , ~ .J. w.; nempetpaisal, P:P O S ~J. A. ~ J. ~ ckm. ~ , E~Z. 1986.63.125. 10. van Lub-k, H.J. Chem. Edue l W , 66,762. 11. Bindel, T H.J. C k m . m e . 1992.69.305. 12. CRCHandMofChemi8tqayondPhysics.7lBted.: Lide,D. R.. CRCRess: Boca Raton. 1990.
E.
D.:Ewing,G.
Because experiments to determine the value ofN are seldom attempted at grade 9 or 10, instructors can use the activitycentered approach suggested in this paper as an exercise for students to estimate N.
Ed.:
Volume 71 Number 8 August 1994
657
