Question

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.)

Answer 1

% 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