If I want to calculate the number of moles ratio of reactants which, in a revers

Question

If I want to calculate the number of moles ratio of reactants which, in a reversible reaction of equilibrium constant K, will give me a certain yield 'f', what is the mathematical definition of the yield in this case? For instance, in the reaction A + B ? C + D, let's say we can denote extent by ?A such that K=(C0-?A)*(D0-?A)/((A0+?A)*(B0+?A)). Then is yield f=-?A/A0 (i.e. 90% yield would suggest that ?A=-0.9*A0)? The problem becomes that then this is not 90% of everything, because B0 may not be the same as A0, in which case 90% of B0 would not have been converted, only 90% of A0. And if this "90% yield" was done with ?B instead then our definition would involve 90% of B0 being converted but not 90% of A0, which provides two conflicting understandings of the "90% yield" statement.

Explanation / Answer

You have to take into account the limiting reagent. If you have 1 mol of A and 2 mol of B in a flask and the reaction is allowed to go to completion you will get 100% yield if you have (at the end) 0 mol of A, 1 mol of B, 1 mol of C and 1 mol of D. If you instead get something like 0.5 mol of C/D then your yield is 50% etc.

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