Good day! I graduated from an undergrad degree of chemistry almost 3 years ago but I'm frustrated that I fail to reconcile these things:

In gravimetric analysis, to get the correct amount for the desired way of expressing the analysis result, we convert the mass of the acquired substance to the desired form, and in doing this, we should relate the number of moles of the acquired substance to the desired substance. For example, if you desire to get the grams *Al* from a sample which you assayed gravimetrically until you have formed Al2O3$, then you have to use the following formula:

grams Al = grams Al2O3 x (2 MW Al)/(MW Al2O3)

wherein the factor 2 in the numerator was obtained from the term (4 mol Al)/(2 mol Al2O3), which arose from the oxidation reaction

4Al 3O2 --> 2Al2O3.

Now, the question is, should I also use this method of conversion if I just want to express %Al from a %Al2O3 concentration of a certain substance, even if I don't plan to do a gravimetric analysis to find it? Also, this method of conversion is reaction-specific, but there could be many different ways, not only single-step chemical equations but also multiple-step ones in which the overall mole relation of the substances in a given chemical equation is different from that of a different chemical equation.

Also, what about the expression of ppm N from ppm NO3 and ppm NO2? Does their conversion method work in the same way in which you have to know the reaction involving N, NO3 and NO2 to know their mole relations, knowing that monatomic N is not very easy to generate? In this case, I can only see that the conversion method is based on the number of atoms the primary element in each form not on a certain reaction like thee previous case. But if that's the case, then I have another contradicting case to show:

Another one is that of between NaOCl and Cl2 in disinfection solution formulations. If you base it on the last method I mentioned, then the mole ratio should be 2 mol NaOCl:1 mol Cl2 because you only have one Cl atom in NaOCl while Cl2 has 2, but according to all of the reputable resources I have found on the internet, the mole ratio here is 1:1. The reason here is supposed to be because of the chemical equation

Cl2 2NaOH --> NaOCl NaCl H2O.

If the answer is supposed to be obvious after all these, or I am just completely missing the point, I hope you would be kind to point it out clearly because it's really bogging me down.