Final answer:
The empirical formula of the gaseous nitrogen compound is NH₂, calculated by converting the percentage composition to moles and finding the simplest whole number ratio. The molecular formula is N₂H₄, determined by dividing the given molecular mass by the empirical formula mass and rounding to the nearest whole number.
Step-by-step explanation:
Finding the Empirical Formula
To find the empirical formula of the nitrogen compound, we first convert the given percentages to masses assuming a 100 g sample. This means we have 12.5 g of hydrogen and 87.5 g of nitrogen. Next, we divide these masses by their atomic weights to find the mole ratio:
- Hydrogen: 12.5 g / 1 g/mol = 12.5 moles
- Nitrogen: 87.5 g / 14 g/mol = 6.25 moles
Divide by the smallest number of moles to find the simplest whole number ratio:
- Hydrogen ratio: 12.5 / 6.25 = 2
- Nitrogen ratio: 6.25 / 6.25 = 1
Thus, the empirical formula is NH₂.
Finding the Molecular Formula
The question states that the molecular mass of the compound is 37 g/mol. The empirical formula mass of NH₂ is 14 (for N) + 2 (for H) = 16 g/mol. To find the molecular formula, divide the molecular mass by the empirical formula mass:
Molecular mass / Empirical formula mass = 37 g/mol / 16 g/mol = 2.3125
Since molecular formulas are whole numbers, we round 2.3125 to 2, indicating that the molecular formula contains twice as many atoms as the empirical formula. Therefore, the molecular formula is N₂H₄.