Question

$C_x{H}_y{N}_z$ is the empirical formula of an organic compound. When 0.3 g of the given compound is completely burnt in excess of oxygen, it produced 0.792 g of $C{O}_2$ and 0.378 g of $H_{2}O$.
In Dumas' method for the estimation of nitrogen, 0.3 g of the same organic compound gave 33.6 mL of nitrogen gas at 300 K temperature and at 576 mm of Hg pressure, then the value of $X\times Y\times Z$ is. ( Aqueous tension at 300 K is 15 mm of Hg, use R= 0.08 atm-L/mol K)

Answer 1

To calculate the empirical formula we need the moles of C, H and N, which can be calculated as follows,

To calculate the moles of $C$,
0.792 g of $C{O}_2$= 0.018 moles of $C{O}_2$= 0.018 moles of $C$

To calculate the moles of $H$,
0.378 g of $H_{2}O$ = 0.021 moles of $H_{2}O$= 0.042 moles of $H$

To calculates the moles of $N$ (Dumas' method is used here),
$P\times V=n\times R\times T$
$\frac{(576-15)}{760}\times 33.6\times {10}^{-3}=n\times 0.08\times 300$
n= 0.001= moles of $N_2$
moles of $N$ = 0.002

To find the empirical formula, take the simplest ratios of moles,
$C$ : $H$ : $N$
0.018 : 0.042 : 0.002
9 : 21 : 1
$x\times y\times z=9\times 21\times 1=189$