A Graphical Representation of Limiting Reactant J.C. Phillips Brevard Community College, Science DepartmenffSM-147,Melbourne. FL32935 The concept of limiting reactant (1-7) may be conveniently illustrated by a graphical representation method that is based on a "minimum slope". The success of the method depends on the choice ofthe y-axis as mass and the x-axis as a product of molar coeffkients and molar masses (moleclar weights for - for compounds and atomic weights elements). Agraph is constructed to display products, pi (constant vertical lines: x = constant) and reactants (lines with a slope, S,). The mass, m,, for the reactant, ri, is chosen as the y-axis and C p j or C,(A.W.s is chosen as the x-axis in which Cj is the coeffkient in the balanced equation, M, is the molecular mass and (A.W.), is the atomic weight for a substance, where j = ri or pi. The vertical lines are drawn at CPiL4.WJpior CpjMpjfor the products [hereafter, Mj or (A.W.), is referred to as molar mass, (M,),]. The lines for the reactants are drawn from the ratio of k,mtilk,C,(Mm)ti where k, is an adjustment factor that enlarges or reduces the size of the plottedy and x values for purposes of greater plotting accuracy. So, for a given mass, m,, for reactant, ri, a straight line is drawn from the origin through the point (y, x)=[k,m,, k&,(Mm),I with slope, (1) S,= mtiIC,(Mm),
I u
200
400 600 800 CoefficientX IMolar Mass (g)
1000
1
Mass of reactants versus the product of molar coefficient times molar mass) for the reaction: 4Ag + 2H2S z O2 + 2Ag2S + 2H20. The symbol, x, represents the points [krn,, k,iCti(Mm)J foreach reactant, ri.
and the line with the smallest slope, is the limiting reactant for that particular substance, ri. The intersection of the vertical line(s) for a given product, pi, with the line of minimum slope represents the maximum amount(s) of product obtainable from the reaction. The values of S, and (So)"are, respectively, the same as Kalantar's x-values and the minimum value of x (5). For accurate determinations of masses, m,i, for a given product, pi, the following is calculated: where eq 3 can be rearranged to give:
the limiting reactant and the amounts of H20 and Ag2S were determined for mixing 0.950 g of Ag with 0.140 g of H2S and 0.0800 g of 02. The results are presented in the figure with reactant lines drawn through the points indicated by x (the values of k,, respectively, for 02,Ag, and HqSwere 19.38. 1.63. and 11.07).From the dot.. the limiting reactant is easily dettmnined us Ills lowest slope,; the cstimared amounts of H,O and A e 9 were.. rcs~ertivel\: . 0.080g and 1.00 g [the caiculated results from eqs 2 and3 were, respectively, 0.0740 g and 1.02 g.
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Literature Cited It can be seen that ea 4 includes the reeular stoichiometrv calculations of coeffiiients, moles, and-molar masses that is eenerallv encountered in such ~roblems(1.5). Using the following balanced equation a s a demonstration:
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Journal of Chemical Education
1. Milio, F A . J. Cham. Edue. 1911,48131,155. 2. Bent,H.A. J. Chom. Edvc 13?S,551111,726. 3. Ozsogomonyan, A. J. Chem. Edue. 1979,56
