# Should I relate the number of moles between substances when converting weight units?

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 $$Al_2O_3$$, then you have to use the following formula:

$$\text{grams } Al = \text{grams } Al_2O_3 \times \frac{2\times MW Al}{MW Al_2O_3}$$

wherein the factor $$2$$ in the numerator was obtained from the term $$\left( \frac{4 \text{ mol } Al}{2 \text{ mol } Al_2O_3} \right)$$, which arose from the oxidation reaction $$4Al + 3O_2 \rightarrow 2Al_2O_3$$.

Now, the question is, should I also use this method of conversion if I just want to express %Al from a %$$Al_2O_3$$ 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 $$NO_3$$ and ppm $$NO_2$$? Does their conversion method work in the same way in which you have to know the reaction involving $$N$$, $$NO_3$$ and $$NO_2$$ 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 $$Cl_2$$ 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 $$Cl_2$$ because you only have one $$Cl$$ atom in $$NaOCl$$ while $$Cl_2$$ has 2, but according to all of the reputable resources I have found in the internet, the mole ratio here is 1:1. The reason here is supposed to be because of the chemical equation $$Cl_2 + 2NaOH \rightarrow NaOCl + NaCl + H_2O$$.

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.

All the trick is the equivalence of both considered forms, according a particular reaction process, regardless of if the process is real or just formal.

If there is a real or formal process/reaction $$\ce{n A + ... -> m B + ...}$$ or $$\ce{n A + m B -> ...}$$ then $$n \cdot M_\mathrm{A}$$ grams of substance $$\ce{A}$$ is equivalent to $$m \cdot M_\mathrm{B}$$ grams of the substance $$\ce{B}$$.

So you may calculate the equivalent in atomic $$\ce{N}$$ without producing atomized nitrogen but just formally.

For particular forms of nitrogen, a particular mass of nitrogen form {in whatever unit} is equivalent to a particular mass of "$$\mathrm{N_{N form}$$". Then total nitrogen equivalent is then the sum of the partial nitrogen equivalents.

About 62 g of nitrates is equivalent to 14 g of "N-NO3", the nitrate nitrogen.
About 46 g of nitrites is equivalent to 14 g of "N-NO2", the nitrite nitrogen.
About 17 g of ammonium it equivalent to 14 g of "N-NH3", the ammonia nitrogen. (The same can be expresses in other units as well, like ppm(w). )

as there can be written formal reactions

$$\ce{NO3- -> N + 3 O + e-}$$ $$\ce{NO2- -> N + 2 O + e-}$$ $$\ce{NH3 -> N + 3 H}$$

Similarly, phosphorus in fertilizers is conventionally expressed as $$\ce{P2O5}$$, even if there is no $$\ce{P2O5}$$ ( ,because there is $$\ce{P4O10}$$ )

For the sodium hypochlorite case, it depends on if you calculate

the total chlorine content : ( 1:1 as $$\ce{Cl}$$, formally only )

$$\ce{NaOCl -> Na + O + Cl}$$

or the active chlorine content: ( 1:1 as $$\ce{Cl2}$$, really) ( or 1:2 as $$\ce{Cl}$$, formally ).

$$\ce{NaOCl + 2 HCl -> NaCl + H2O + Cl2 (-> NaCl + H2O + 2 Cl )}$$

The both ways ( 1:1 vs 1:2 ) are equivalent for obvious reason, as the half molar amount of substance with the double molar mass has the same mass.

Also note that by the same formal manner is determined the oxidation number: $$\ce{ H2SO4 -> 2 H+ + S^6+ + 4 O^2-}$$

• Sorry about this but, I don't get many things from your answer. (A) What do you mean with "equivalence of both considered forms according to a particular reaction process?" (B) Also this sentence, "For particular forms of nitrogen, a particular mass of nitrate {in whatever unit} is equivalent to a particular mass of "NNO3"." (C) And also, what is the difference between total chlorine and active chlorine content? I didn't get what should be obvious here. – Iceheat Mar 31 '20 at 6:40
• See the update. It seems you managed to forget all from the undergraduate studies, as when I was a student, it was all the high school stuff. – Poutnik Mar 31 '20 at 7:15
• Thank you for taking the time to flesh out your explanation. :) We actually didn't learn the chemical equations having a "formal" manner, but I can understand what you're trying to say. Am I correct that you're saying that it's okay to just base it according to the number of atoms between those chemical forms since they are equivalent "formally"? – Iceheat Mar 31 '20 at 7:44
• Yes, that is correct. Also note that by the same formal manner is determined the oxidation number: $\ce{ H2SO4 -> 2 H+ + S^6+ + 4 O^2-}$ – Poutnik Mar 31 '20 at 7:47
• Thanks, I understand. However, for the sodium hypochlorite case, I'm actually meaning to find the wt% available chlorine and its relation with wt% NaOCl, and as we know, the active components in disinfection that we're interested in are hypochlorous acid and sodium hypochlorite, so why do the literature refer to the reaction which produced these active components, instead of the disinfecting action of these active components? – Iceheat Mar 31 '20 at 7:53