[Big-Daddy]

Consider a reaction A+B  C+D. (K is known) We observe that fraction f of reactant B is reacted into products. How many possible mole ratios n₀(B)/n₀(A) can the reactants be reacted in to give this fraction f? Find all possible mole ratios.

My initial thinking was that B, of which fraction f was reacted, could be either the limiting reagent or the non-limiting reagent, so there should be two possible mole ratios. But once I approached the calculation I found only one solution (start from n_eq(B)=n₀(B)*(1-f), n_eq(A) = n₀(A) - f*n₀(B), n_eq(C)=n_eq(D)=f*n₀(B) and there is only one possible solution of n₀(B)/n₀(A) here). How many solutions are there - and why - and how do I get to all?

[mkurek]

You said that K is known? K is meaning the equilibrium constant of this reaction right?

If so, that would be your place to start. Look up equilibrium constants, and then see what it means if K is less than, greater than, or equal to 1. That should get you pushed in the right direction.

[Borek]

Mixing limiting reagents and equilibrium constants makes no sense.

[Big-Daddy]

Mixing limiting reagents and equilibrium constants makes no sense.

You haven't understood my initial thinking, clearly because my initial thinking was wrong. But I won't bother you with this explanation since I think I've got it now. In short, only if information is given pertaining to the limiting reagent or to a non-limiting reagent specifically, and other information does not enable the limiting reagent to be specified for the case studied, you need to work in terms of "limiting reagent" and "non-limiting reagent" and then consider each possible identity for the limiting reagent only after calculations. But this wasn't needed for the OP question.