[sharbeldam]

Sulfur imides are described by the general formula Sn(NH)8-n (n = 4-8) and are 8-membered rings. One of these imides arrived in the laboratory for research.
The sample was completely burned in excess oxygen, the resulting products were left till STP, and a gas mixture with a relative density in air of 1.92 was formed.
Determine the formula of the imide?

My attempt:
Mx = D(air) * M(air) = 1.92 * 29 = 55.68 g/mol
and my products are SO2 + N2 + H2O (please confirm? do they expect me to know the product? its an old olympiad question)
so our gases are SO2 + N2 + H2O
Sn(NH)8-n + O2 -> SO2 + N2 + H2O
nSO2 + (8-n)/2 N2

What do i do next?

[Hunter2]

I think to use the molar mass of air is wrong, because you don't have air alone, you have a mixture of nitrogen, sulfurdioxide and probably some water steam. Additionel air,

[sharbeldam]

Thats what i thought, but its the average mass. but either way, im not gonna debate because i humbly dont know how to solve, any hint?

[Borek]

The way I see it there is a problem with the question.

Assuming gas that is 1.92 heavier than air is just a mixture of products of the burning (that is N₂ and SO₂) problem is rather trivial to approach - ratio of SO₂/N₂ is trivial to express in terms of n (water at STP is a liquid and probably can be ignored). That gives two equations (ratio, apparent molar mass) in two unknows (N₂ and SO₂), just solve.

Trick is, you are being told "in excess oxygen", so the resultant mixture probably contains three components. As molar mass of oxygen is between N₂ and SO₂ it most likely means there is no unique solution to the problem (or more precisely: there is no unique solution for sure, but sometimes in such cases numbers give some limit on possible results, I doubt that's the case here).

Can be the wording is lousy and you will get a reasonable answer just by assuming no oxygen in the mixture.

[sharbeldam]

Thank u borek , i totally agree with u. but it's an olympiad question in russian, i just have a hobby of solving such questions, im not russian but thats how my chemist friend translated it.

if anyone is russian here, thats the original one. it has to have a solution, maybe in mother russia they want us to ignore the excess oxygen? and they just mean all reactant reacted.

[Borek]

I speak a bit Russian, and yes, I can confirm the translation - I feel like it could be a bit more precise.

Still, assuming no oxygen looks like there is perfectly enough data to solve the problem. Ignoring water doesn't produce an exact answer though, just one that looks reasonably. No idea what exact molar masses one is expected to use, perhaps they will make the result more precise.

[Vidya]

Sulfur imides are described by the general formula Sn(NH)8-n (n = 4-8) and are 8-membered rings. One of these imides arrived in the laboratory for research.
The sample was completely burned in excess oxygen, the resulting products were left till STP, and a gas mixture with a relative density in air of 1.92 was formed.
Determine the formula of the imide?

I think we can ignore water because at STP condition water is not a gas.
You have calculated the correct  mass of the gases on combustion of one mole of the substance.
nSO2 + (8-n)/2 N2 = 55.68
However it  gives negative value of n =-3
If we ignore negative sign then formula is S3N5H5.
It is just a tentative solution and I am not very sure of it.