A gaseous compound of nitrogen and hydrogen contains 12.5 % hydrogen by mass. The molecular formula of the compound if its relative molecular mass is 32, is: [N=14, H=1]

The correct option is C

${\mathrm{N}}_2{\mathrm{H}}_4$

The explanation for the correct answer
The correct option is (c) ${\mathrm{N}}_2{\mathrm{H}}_4$

Determination of the molecular formula

• Step 1: Determination of the percentage of each element
  Percentage Hydrogen present in gaseous compound = 12.5%
  Percentage of Nitrogen present in the gaseous compound = 100 - 12.5%
  Percentage of Hydrogen present in the gaseous hydrocarbon = 87.5%
• Step 2: Determination of the empirical formula

S.No.	Element	Molecular mass	Percentage composition	Number of atoms	Simplest ratio	Nearest whole number rounding off
1	N (Nitrogen)	14	87.5%	$\frac{87.5}{14}=6.25$	$\frac{6.25}{6.25}=1$	1
2	H (Hydrogen)	1	12.5%	$\frac{12.5}{1}=12.5$	$\frac{12.5}{6.25}=2$	2

The empirical formula of gaseous hydrocarbon is = ${\mathrm{NH}}_2$

• Step 3: Determination of empirical formula mass
  The empirical formula mass of ${\mathrm{NH}}_2$ = $14+2\times 1$
  The empirical formula mass of ${\mathrm{NH}}_2$ = 16
• Step 5 Relation between empirical mass and molecular mass
  The molecular mass of gaseous compound = 32
  Molecular mass = $\mathrm{n}\times \mathrm{Empirical}\mathrm{formula}\mathrm{mass}$
  n = $\frac{\mathrm{Molecular}\mathrm{mass}}{\mathrm{Empirical}\mathrm{formula}\mathrm{mass}}$
  n = $\frac{32}{16}$
  n = 2
• Step 6: Determination of Molecular formula
  Molecular formula = $\mathrm{n}\times \mathrm{Empirical}\mathrm{formula}$
  Molecular formula = ${\mathrm{N}}_2{\mathrm{H}}_4$

The explanation for incorrect answers

Options (a), (b), and (d) are all incorrect because the molecular formula of the gaseous compound is ${\mathrm{N}}_2{\mathrm{H}}_4$.

Therefore, the correct option is (c) ${\mathrm{N}}_2{\mathrm{H}}_4$.