One mole of a mixture of `N_(2),NO_(2)` and `N_(2)O_(4)`, has a mean molar mass of `55.4`. On heating to a temperature at which `N_(2)O_(4)` may be dissociated `:N_(2)O_(4)rarr2NO_(2)`, the mean molar mass tends to the lower value of `39.6`. What is the mole ratio of `N_(2) : NO_(2) : N_(2)O_(4)` in the original mixture?

Explanation

Let a,b and c " mol of "`N_(2),NO_(2)` and `N_(2)O_(4)` are present in 1 " mol of "a mixture thus,
`a+b+c=1` ..(i)
Also,
`((axx28)+(bxx46)+(cxx92))/(a+b+c)=55.4`
`therefore28a+46b+92c=55.4` ..(ii)
Also, after heating
`((axx28(+[(b+2c)xx46])/(a+b+2c)=39.6` ..(iii)
`therefore28a+46b+92c=(a+b+2c)xx39.6` ..(iv)
From equation (ii) and (iv) we get
`a+b+2c=(55.4)/(39.6)=1.40` .(v)
From equation (ii) and (iv) we get
`28a+46b+92xx0.4=55.4`
`29a+46b=18.6` .(vi)
From equatio (i) and (iv) `a+b=0.6,b=0.1,a=0.5`
`thereforeN_(2)=0.5,NO_(2)=0.1,N_(2)O_(4)=0.4mol`