edited by: RON DELORENZO Mime Georgia College Cochran. Georgia 31014
3B 6AX-=9B 2A Direct application of this practice-work can now be made to actual chemical equations. Further use can also be made of the Fruit basket analogy, however. Turning eqn. (1) around (analyzing the reverse reaction), we see that:
The Fruit Basket Analogy
William Bleam, Jr. Radnor High School 130 King of Prussia Road Radnor. PA 19087 '
lFb=2A+3B
(2)
3) How many apples can weobtain from 3 Fruit baskets?The prob-
lem, stated in symbolic form, becomes:
First-year chemistry students a t the high school level seem to have difficulty in understanding the full significance of a balanced chemical equation, as it is used to solve prohlems in stnichiometw. Consider the case where two molecules of hvdrogen gas react with one molecule of oxygen gas to produce two molecules of water. Students will invariablv ask. "What happt.ntd to the other nwleculr" How can two plui~meequal twcl"" When thev are asked u, calculate the number ot molecules or moles of water which can he produced from a given amount of hvdroaen or oxvgen, the ~ r o b l e mbecomes even more perple;ing ior the 3v&e student. It isfvr this t y p e of stt~(li.ntthat the "Fruit I h k e t Analog\." ..- h;h Iwrn developed. Using a fruit basket which has been simplified somewhat (and what model isn't a simplification?), the class might begin by writing out a word equation for our "system":
3Fb=?A To solve,we use the ratio 2 A11 Fb. This ratio is taken directly fmm eqn. (2). Thus we see that 2A 3FbX--6A 1Fb It is here that the teacher might point out to the class that from 3 objects (Fruit baskets or molecules of a given substance) we are able to obtain 6 objects (Apples or molecules of some other substance). There exists no law which states that molecules (or Fruit baskets) must be conserved. More discussion concerning the law of conservation of mass could follow here. As a further example of this phenomenon, consider the next problem. 4) How many pieces of fruit can we obtain from 4 Fruit baskets? The
student would state the problem as follows:
2 APPLES PLUS 3 BANANAS MAKE 1 FRUIT BASKET
4 Fb = ? pieces of fruit
It is a relatively small step (hut an important one) now to write a svmbolic representation (analogous to the chemical eauation) of the ";eaction":
Using the ratio from eqn. (21, we find that 1Fb yields 2 A + 3 B, or 1Fh produces 5 pieces of fruit. Therefore the solution would be:
2A+3B=lFb
4 Fb x 5= 20 pieces of fruit
(1)
Assumiuz students can solve ~ r o h l e m bv s dimensional analysis (we cave already spent 'bout threeeweeks on it by this time in the "vear). .. thev" can use this eauation to solve stoichiometric problems. The following examples represent typical prohlems.
4A=?Fb Our conversion fador for changing Apples to F ~ ibaskets, t which comes from eqn. (I), is 1FbI2 A. Thus the solution to our problem is 1Fb 4AX-=2Fb 2A 2, it w a r e ~iwn6.4pplci.how many Bananasarc required toproduw sufficient Fruit t t a k p b 1,) deplete thesupply < SAppbs?The pr~blrmwould look like rlua: 'Ihe emversion factor, 7' BlL A. wkrn directly frum eqn. (1)is used 1,) i d v e
the problem as ktllt!~~:
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'I'hl; 1. part oi a paper y ~ . ~ n t cas d a poster w r w n at the 6th R I P I I I I I('h~mical ?~ Ed~cath Cunference ~ at the Hoclwswr Institute oi'l'c,.hnc,l~,g?.Rochester, New Ymk, June 22-21;, I9RII. sponsored by the American Chemical Society.
184
Journal of Chemical Education
1 -Fh -.
Returning once again to eqn. (I),we can use this equation to determine the amount of product which can he formed when specified quantities of both reactants are given. This represents a typical "limiting reagent" type of problem. 5) Calculate the maximum number of Fruit baskets which could be yrdured t'rom I6 .\pi,lei and 12 Hananm. Thr c.lurion to the pnhlem is twofuld:Fmt, find the number ut Frtlit bdskets which cnn he made fnm li, Applr. This feature oresents a collection of descriptive appli~tionsand awlogies desogned lo help studems umlersraM some of he 0.Lcuh cmcepl hewntlv encountered n cnem s m, ConlrlbRlons tm1 I orwuca agreater application and knowledg'e of political, religious, economic. historical, and sc entitic &pects 01 I feare enco-ragea
Ron DsLorenzo is an Assuc am Prolessor m me Depanmont of Cnem rtry at MIM e Georgm Co lege ?ieis asso Campus CW(0iwIor Im the MmpUtlng IacllltlPS and t e a m an englneerlngcouse m FORTRAh. He rece u e d h s OS fromSl Jonn'r Jn rersth/ m 1963 and the M S and PhD tn Phvslcab norganoc Cnemlslr) from.ore Tecnno ogcill nsr 1.le in 1967 and 1970. rsrpscl~uel~ Ce.manzo ~~-~ s *or, narencd n rear no cod* maler a
to tne real wwld. He has just com.&da text entitled obiem em Solving in General Chemistry" published by D.C. Heath and Company which emphasizes his applicationsand analogies appmach in teaching. ~
16A=?Fb 1 Fb 1 6 A X = 8 F b 2A Next, in a separate problem, calculate the number of Fruit baskets
one can produce from 12 Bananas.
I2B=?Fb 1 Fb 12BX-=4Fb 3R
Since we run out of Bananas after making only 4 Fruit baskets, 4 represents the maximum number of Fruit baskets we can produce in this problem, even though we have enough Apples to produce 8 Fruit baskets. Once again, a direct application of this analogy can be made by using a mole ratio (or molecule ratio) from an actual chemical equation. Thus the "Fruit Basket Analogy" can serve as a very useful tool in teaching stoichiometric concepts a t the introductory level of high school chemistry.
Volume 58
Number 2
Februaw 1981
185
