Chemistry Everyday for Everyone edited by
Applications and Analogies
Ronald DeLorenzo Middle Georgia College Cochran, GA 31014
Kids in a Candy Store: An Analogy for Back Titration Arthur M. Last Department of Chemistry, University College of the Fraser Valley, Abbotsford, BC V2S 7M9, Canada
Back titrations remain as standard fare in freshman chemistry courses and experiments describing this technique may be found in many commercially available laboratory manuals (1). Such experiments often entail the analysis of an antacid (1a) or aspirin (1b). In our first-year laboratory program, students determine the percentage purity of sodium carbonate by reacting the sample with excess acid and titrating the unreacted acid with sodium hydroxide. Having successfully used a monetary analogy under different circumstances (2), I developed the following analogy to assist my students in understanding the basis of this procedure. Suppose you give a child a $2 bill or coin 1 and send her into a candy store to buy her favorite candy bar. She emerges from the store and, being an honest child, promptly hands over $1.35 in change. Knowing that only one bar was purchased, you quickly deduce the cost of the bar to have been 65 cents. This is analogous to a situation in which 2.00 mol of a monoprotic acid is added to a quantity of a base such as sodium hydroxide and a subsequent titration reveals that 1.35 mol of the acid had not been consumed. Knowing the acid and base react in a 1:1 ratio, we could readily deduce that 0.65 mol of base must have been present in the original sample. In the above analogy we have assumed that the child was honest. If this had not been the case and the child had returned only $1.25 of the change, you would naturally have deduced the cost of the candy bar to have been 75 cents. This is analogous to a situation in which there is an impurity in the sample which reacts with some of the added acid. The presence of such an impurity would result in less base being required in the titration and an overestimation of the amount of known base in the original sample. Similarly, one could develop an analogy in which the child unknowingly has a 10-cent coin in her possession prior to entering the store. If this coin gets returned to you along with the change received by the child, you would deduce that the candy bar had cost 10 cents less than it really did. Such an analogy could
be applied to a situation in which a student rinses the Erlenmeyer flask with acid instead of deionized water before performing the back titration. Additional base would be required for the titration, leading to the conclusion that the original sample contained less base than it actually did. If we now turn our attention to a situation in which the acid and base do not react in a 1:1 ratio, we might adapt the analogy along the following lines. Suppose you give another child a $2 coin in order to purchase two identical candy bars; one for himself and one for you. If this child, who is just as honest as the first, returns with 60 cents change, you would deduce that the two bars had cost $1.40 and that the cost of each bar was therefore 70 cents. This is analogous to adding 2.00 mol of monoprotic acid to a sample of a base such as calcium hydroxide and finding that 0.60 mol of acid was not consumed. Clearly the amount of acid used was 1.40 mol and, because the acid and base reacted in a 2:1 ratio, the amount of base originally present may be deduced to have been 0.70 mol. Acknowledgment I wish to thank Jean Hoffmann for her helpful comments regarding the use of this analogy. Note 1. In 1996, Canada began to replace its $2 bills with $2 coins. Instructors living in other countries should modify the analogy using local currency and prevailing candy bar prices.
Literature Cited 1. (a) Beran, J. A. Chemistry in the Laboratory; Wiley: New York, 1993. (b) Nelson, J. H.; Kemp, K. C. Laboratory Experiments for Brown and LeMay Chemistry the Central Science, 3rd ed.; Prentice Hall: Englewood Cliffs, NJ, 1985. 2. Last, A. M.; Webb, M. J. J. Chem. Educ. 1993, 70, 234–235.
JChemEd.chem.wisc.edu • Vol. 75 No. 9 September 1998 • Journal of Chemical Education
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