[Rutherford]

For the reaction: A₂(g) + B₂(g) = 2AB(g), Consider the reaction yield η = n_eq(AB) / n_max(AB) as a function of the initial molar ratio A₂ : B₂ = x : 1 at any fixed temperature (n_max is the maximum amount calculated from the reaction equation). Answer the following questions qualitatively, without exact equilibrium calculations.

1.At what x the yield is extremal (minimal or maximal)?
2.What is the yield at: a) x ∞; b) x 0?
3.Draw the graph of η(x).


I thought that for x=∞ the yield is maximal, as the equilibrium will be shifted far to the right, so if there was 1 mole of B (n_A=∞), I will get 2 moles of AB and the yield will be 100%. If there was 0 mole of A the yield would be 0 (minimal). But why would 1 and 2 be different questions then? Am I missing something?

[curiouscat]

If there was 0 mole of A the yield would be 0 (minimal).

This wasn't obvious to me. Isn't this a 0/0 limit that needs to be evaluated?

[Rutherford]

Yeah, if n_A=0, then the maximum amount of AB that could be produced will be 0, so n_max(AB)=0, and n_eq is 0, too, so the yield would be 100%  , right?

[curiouscat]

Yeah, if n_A=0, then the maximum amount of AB that could be produced will be 0, so n_max(AB)=0, and n_eq is 0, too, so the yield would be 100%  , right?

Why?

If that uses  0/0 =1  you are wrong.

[Rutherford]

According to the reaction equation, from 0 mole of A I would obtain 0 mole of AB. If equilibrium constant is introduced now, again from 0 mole of A I obtain 0 mole of AB, so n_eq(AB) / n_max(AB)=1 or 100%. I know that this is mathematically wrong, but if I am not right, what is the answer then?