A compound contains only nitrogen and oxygen and is 30.5%
nitrogen by mass. A gaseous sample of the compound has a density of
3.70 g/L at 954 torr and 107°C. What is the molecular formula of
the compound? (Omit states-of-matter from your answer.)
% mass of oxygen is 100-30.5 = 69.5
atomic ratio of NItrogen and oxygen in the compound
N:O
=:
= 2.178: 4.34 = 1:2
hence, emprical formula of the compound is NO2 and empirical mass is = 46
Now, density of the compound is 3.70 g/L, that means per liter volume (at 654 torr and 1070C ) of the gas weighs 3.7 g.
again using the combination of Charles's and Boyle's law
where , P1 = 954 torr, V1 = 1L, T1 = 1070C = 380K
let the volume at STP is V2 , then P2 = 760 torr, T2 = 273 K
or, V2 =
=
= 0.901 L
at STP, 0.901 L of the compound weighs 3.7 g
and, 22.4 L of the compound weighs = (3.722.4)/0.901
= 91.98 g
so, the molecular mass of the compound is 91.98 g
as we know , empirical mass * n = molecular mass
or, n= 91.88/46 = 1.997 2 (
n is a whole number)
then, the molecular formula is (empirical formula)n = (NO2)2 = N2O4
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