What is the molecular formula for nitrogen oxide?

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Discussion Overview

The discussion revolves around determining the molecular formula for nitrogen oxide based on a given mass and volume of the gas at standard temperature and pressure (STP). Participants explore the relationship between moles, molar mass, and potential molecular formulas, engaging in both mathematical reasoning and conceptual understanding of nitrogen oxides.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant calculates the number of moles of nitrogen oxide using the molar volume of gases at STP, resulting in 0.47 moles.
  • Another participant questions the correctness of the initial calculation regarding the molar volume.
  • It is noted that the molar mass can be derived from the weight and moles calculated, leading to a value of approximately 44.68 g/mol.
  • Participants discuss the equation 14x + 16y = 44.68 to find integer values for x and y, representing the number of nitrogen and oxygen atoms, respectively.
  • One participant suggests that x and y must be natural numbers within specific sets, leading to potential formulas of N1O2 and N2O1.
  • Another participant proposes that the solution involves considering known nitrogen oxides and their molar masses to find the closest match to 44.68 g/mol.
  • There is a suggestion that the final formula could be N2O1, as its molar mass is closest to the calculated value, though this is met with uncertainty.
  • One participant raises the possibility that the discrepancy in molar mass could be due to a mixture of nitrogen oxides rather than a single compound.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the exact molecular formula for nitrogen oxide, with multiple potential formulas being discussed. There is no consensus on a definitive answer, and the discussion remains open to interpretation based on the calculations and assumptions made.

Contextual Notes

The discussion highlights limitations in the problem's parameters, such as the rounding of molar mass and the potential for mixtures of nitrogen oxides, which complicate the determination of a single molecular formula.

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Homework Statement


10.7 L of gaseous nitrogen oxide NxOy has a weight of 21.0 g (STP/NTP).

Homework Equations


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

The Attempt at a Solution


22.4=10.7/n
n=0.47mol
 
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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..
 
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 ?
 
The molar mass would be 21/0.47 =44.68g/mol
but then 14x+16y=44.68
how to find x,y
 
Well, x and y must be natural and could have values in the sets: [itex]x\in\left\{1,2,3\right\}, \, y\in\left\{1,2\right\}[/itex].

Which is the solution then ?
 
But we don't know. it can be anything...
 
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 [itex]NO_2[/itex] ? What's the molar mass ? How far is it from 44.68 grams/mol ? Can it be [itex]N_2 O ?[/itex] What's the molar mass ? How far is it from 44.68 grams/mol ? And the same with other solutions/oxydes.
 
when x=1, y =2
and when x=2, y=1
so i think it can be two formulas: (N1O2) and (N2O1)
 
  • #10
Ah ok, that's good point
the formula then is N2O1 because its molar mass (44) is the closest to 44.68
Thank you :)
 
  • #11
is it true ?
 
  • #12
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.
 

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