Limiting Reagent Problems Made Simple for Students For years my firat-year chemistry s t w l m ~ shart had tnmbk wilh rlrmmrnry stnrchimnetry problems involving a limiting reagent. I)caling with simple pnqwrtions ot moles of reactants hda been especially frustrating lor fhrm u hen the reactiun'r stoirhi,mrtry was not 1:l. Their uitfirult:w penrsted in spite uf my effow, w e n thwph they undrrstood rhnr suirhiumetric amounts of reagents were the exception rather than the rule and notwithstanding the generally clear treatments presented in texts. Indeed, both the texts' and my own discussions properly emphasized that the limiting reagent is the one present in lea& stoichiometrie amount. Moreover. both the texts and I often exdicitlv. minted out that ignoring this leads to the . ahaurdity of negative nmounts ut some rcagentls). Here I share a procedure my studencs now use nmtinely and successfully. By successful I mean that enaily half of the nonsrience s t u d r n ~ snow treat the limir~ngreagent portion uf the prohlrmr correctly. ~~~
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~
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+
Details of Steps 2 NOa-
1) Reaction
3 Co
2) Start
0.60
0.50
3) Change
-3%
-2x
4) Result
0.60 - 3x
0.50 - 2x
5) Possible x 6) Completion
Remarks Products are 3 Co2+ and 2 NO Initial amounts, in males Change after r males react Resulting amount present; depends upon extent of reaction, 1:
050 - 0.20 3 0.15 (excess)
Upper limit on males ofx 0.20 (excess)
0 (limiting reazent)
Far 100%reaction, x = 0.15. (either other choice for x makes moles of H+ nezative)
Perusal of this method shows that it eliminates having to deal explicitly with mole ratios of reactants. The last step demonstrates that it is fail-safe; no negative quantities may appear here. Writing out thought processes is important to the success of this method; however, we feel that the key lies in steps (4) and (5). Here equating a simple expression, such as 0.60 - 3x, to zero imposes the necessary condition in a familiar, and simple, context. I t will be recognized that this procedure is fairly commonly presented at a later stage in texts, in connection with equilibrium problems. Obviously I have merely introduced part of that procedure earlier-to the clear advantage of the students. Consequently they learn the method in steps, have it reinforced later, and see that it is broadly applicable. I am sure many already incorporate this explicit and clear method far equilibrium problems. I t is hoped that this note will promote its earlier introduction for limiting-reagent problems as well. Useful discussions with R. McClung, F. Birss, and R. Boikess are gratefully acknowledged. A. H. Kalantar University of Alberta Edmonton, Canada
106
Journal of Chemical Education
