how to obtain ratio between gases in decomposition reaction

when nitrate of element x is heated it decomposes to form the solid oxide of X, nitrogen dioxide and oxygen. use the following data to work out the ratio between the nitrogen dioxide and oxygen in the gas given off. 0.0865g of the gas was collected occupied a volume of 50.0cm^3 at a temperature of 27ºC and a pressure pf 9.98*10^4Pa.

this is an extension question in our study pack. i am struggling with obtaining the ratio as the number of moles i get is 0.002 after using n=PV/RT. then using M=m/n i get M as 43.25. i dont know what to do with this value as it is too small for any calculations(?). i did find the balanced equation of this kind of decomposition reaction, which states that the ratio of nitrogen dioxide to oxygen is 4:1, but i dont know how to calculate it from the data provided.

Reply 1

Pigster

(1-x) x Mr (NO2) + (x) x Mr (O2) = 43.25

Where x = fraction of total gas that is O2, i.e. if it is all NO2, then x = 0... if all O2, then x = 1... if 20% is O2, then x = 0.2

Reply 2

flyingwhale

Original post by Pigster

(1-x) x Mr (NO2) + (x) x Mr (O2) = 43.25
Where x = fraction of total gas that is O2, i.e. if it is all NO2, then x = 0... if all O2, then x = 1... if 20% is O2, then x = 0.2