One volume of a gaseous compound of carbon, hydrogen and nitrogen on combustion produced 2 volumes of CO_(2), 3.5 volumes of H_(2)O and 0.5 volume of nitrogen under identical conditions of temperature and pressure. Find the empirical and molecular formulae of the compound.

One volume of a gaseous compound of carbon, hydrogen and nitrogen on c

1.	One volume of a gaseous compound of carbon, hydrogen and nitrogen on combustion produced 2 volumes of CO_(2), 3.5 volumes of H_(2)O and 0.5 volume of nitrogen under identical conditions of temperature and pressure. Find the empirical and molecular formulae of the compound.
Answer» Solution :Avogadro.s principle states that equal volumes of gases contain the same number of molecules or moles `{:("Compound",rarr,CO_(2),+,H_(2)O,+,N_(2)),(1"vol",,2"vol",,3.5"vol",,0.5"vol"),(1 "mole",,2"mole",,3.5"mole",,0.5"mole"):}` Moles of C in `CO_(2)=1 xx` moles of `CO_(2)` `=1 xx 2=2` Moles of H in `H_(2)O=2 xx` moles of `H_(2)O = 2 xx 3.5= 7` Moles of N in `N_(2)=2 xx` moles of `N_(2)= 2XX 0.5=1` Hence the empirical FORMULA is `C_(2)H_(7)N` Now we see that 1 mole of the compound contains 2 moles of `CO_(2)` and 1 mole of `CO_(2)` contains 1 mole of carbon atoms, so 1 mole of the compound should contain 2 moles of carbon atoms which is shown by the empirical formula. Hence, the molecular formula is the same as the empirical formula.