finding molecuar formula

[chawki]

1. The problem statement, all variables and given/known data
10.7 L of gaseous nitrogen oxide NxOy has a weight of 21.0 g (STP/NTP).

2. Relevant equations
Give the molecular formula for nitrogen oxide. The molar volume of gases (STP/NTP) = 22.4 l/mol

3. The attempt at a solution
22.4=10.7/n
n=0.47mol

[dextercioby]

OK, and what do you do next ?

[chawki]

I don't know..i'm not sure even that what i did above is right.
i mean the molar volume 22.4 = 10.7/n ?

and i know that 14x+16y= molar mass of nitrogen oxide, but it doesn't take us any further..

[dextercioby]

Sure it does, because you know that 0.47 moles of substance weigh 21.0 grams. Which is then the molar mass of the substance ?

[chawki]

The molar mass would be 21/0.47 =44.68g/mol
but then 14x+16y=44.68
how to find x,y

[dextercioby]

Well, x and y must be natural and could have values in the sets: x\in\left\{1,2,3\right\}, \, y\in\left\{1,2\right\} .

Which is the solution then ?

[chawki]

But we don't know. it can be anything...

[dextercioby]

It's not necessarily a problem of elementary math, but you must also use your knowledge of oxydes of nitrogen. Nitrogen is in v-th principle group and together with oxigen it could form (provided all would be stable) 5 possible oxydes.

So you've got mathematical solutions to a diophantic-type equation which should be sought in the set of all 5 possible oxydes of nitrogen.

For example: Can it be NO_2 ? What's the molar mass ? How far is it from 44.68 grams/mol ? Can it be N_2 O ? What's the molar mass ? How far is it from 44.68 grams/mol ? And the same with other solutions/oxydes.

[chawki]

when x=1, y =2
and when x=2, y=1
so i think it can be two formulas: (N1O2) and (N2O1)

[chawki]

Ah ok, that's good point
the formula then is N2O1 because its molar mass (44) is the closest to 44.68
Thank you :)

[chawki]

is it true ?

[dextercioby]

Yes, unfortunately the numbers chosen in the problem's don't lead to exactly 44 as the molar mass of the gas, so this rounding is necessary. Or it could be that the 44.68 comes from a mixture of N_2 O and N O_2 which have masses 44 and 46 respectively, but I don't think this was the intention in the author's mind.