Vapour density is the density of a gas relative to that of hydrogen at the same temperature and pressure.
#"Vapour density" = "density of mixture"/("density of H"_2) = "mass of mixture"/("mass of H"_2) = "molar mass of mixture"/("molar mass of H"_2) = "Molar mass of mixture"/"2.016 g/mol" = 27.6#
#"Molar mass of mixture" = "27.6 × 2.016 g/mol" = "55.64 g/mol"#
Let #x# = the mole fraction of #"NO"_2#.
Then #1-x# = the mole fraction of #"N"_2"O"_4#.
#x × 46.01 color(red)(cancel(color(black)("g/mol"))) + (1-x) × 92.01 color(red)(cancel(color(black)("g/mol"))) = 55.64color(red)(cancel(color(black)( "g/mol")))#
#46.01x + 92.01(1-x) = 55.64#
#46.01x + 92.01 - 92.01x = 55.64#
#46.00x = 36.37#
#x = 36.37/46.00 = 0.791#
The mole fraction of #"NO"_2# is 0.791.
