edited by DONNABOGNER
in~ightr
Wichita State University Wichita. KS 67208
An Aqueous Problem with an Interesting Solution Nicholas C. Thomas Auburn University at Montgomery Monlgamery. AL 36193
chemists frequently use very large or very small numbers in their calculations. It is therefore not surprising that one of the first skills beginning chemistrv students need to learn is the c o m ~ e t e n t manipulation of these numbers. One of the first such numbers that students of chemistry encounter is Avogadro's number. Developing a mental picture of 6 X 1023tiny particles is not an easy task for many students, but their understanding can be enhanced by using problems that relate chemical principles to familiar substances. For example, shortly after introducing concepts such as the mole and Avogadro's number, problems such as the following can be given:
Molecular
(1) Calculate the number of water molecules in a drop of water. (2) If all these molecules were stretched end to end, how long would the line of molecules extend?
Before students begin calculations, ask them to predict an approximate answer; for example, would they expect the line of molecules to extend 100 miles, 1000 miles, or longer? They will usually underestimate the distance. Such problems are not mathematically complex. but combining some hasic chemical principles wirh n little urithmeric in an interesting prutrlern generatesan enthusiasm tusdve the problem.'l'heabuve problem incorporates the following important stretched end to end chemical principles: ( 1 ) T h e r e l a t i o n s h i p between t h e mass, Flow diagram showing steps involved in problem solving uolume, and density of a liquid. The students c a n h e e i n bv a c t u a l l v m e a s u r i n e t h e volume of a drop of water using a Pasteur pipet and a small Information Given to Students graduated cylinder. They should find that, since there are about 20 drops of water in 1 mL, the volume of one drop of = 13 x loz3g Tmai mass of water on earth mL. water can be calculated to be 5 X
-
5 X lo-' mL H,O 1mL H,O x 1drop H,O = 1drop H,O 20 drops H,O
Molecular weight of water Avwadro's number Length of a water malecuie I km
-
18 glmoi 6 X loz3 moieculeslmoi 2X mlmoiecuie 6 2 X lo-' ml
-
Using the relationship M = D X V, the mass of one drop of water can he derived.
M=
1g H,O
1mL H,O
5 x 10@m~ H,O 1drop HZO
- 5 x lo-'
g H,O
1drop H,O
(2) The relationship between mass and moles. Given that one mole of water has a mass of 18 g, the students can calculate the moles in one drop of water. 5X
10@g H,O 1drop
X
1ma1 H,O
18 g H,O
cules in one drop of water gives the following result: 2.8 X 10@mol H,O 1drop H 2 0
X
6.02 X loz3molecules H,O 1mol H 2 0 =
= 2.8 X
mol H,O/drap H,O
(3) The relationship between moles and the number of molecules, that is Avogadro's numher. Solving for the mole-
1.7 X lo2' molecules H,O 1drop H,O
From this result and the information in the table, the remainder of the ~ r o b l e mmay be solved. The chain of water molecules would extend Volume 64
Number 7
July 1987
611
1.7 X
lo2' molecules H,O
X
2 X 10-lOm
molecule H,O
X
km -m
loz3g H,O 18 g/mol H 2 0
1.2 X
6X
loz3m~leeuleaH,O 1mol H 2 0
....
In other words the chain of molecules from a single drop of water would extend from the earth to the sun and hack again. The flow diagram in the figure will help students work throueh the nrohlem and comurehend the significance of each step. To extend the above urohlem. one might use a question such as, "If all the moiecules of water on the earth were stretched end to end, how long would the line of molecules he?" The chain of water molecules would he
612
Journal of Chemical Education
X
z x 10-10 m 1molecule H,O
.. ~ - ~ ~
T o help students visualize the magnitude of this number, you could tell them that the most distant object in the universe, visible from earth through a telescope, is the 3C 123 galaxy which is a mere 3 X 10slmi away. Finally, students should be challenged to devise similar problems and to ask their colleagues or even their teacher to solve them. The process of designing their own problems will increase their ability to visualize as well as enhance their competence in the manipulation of very large and very small numbers.
