A gaseous compound of nitrogen and hydrogen contains 12.5%(by mass) of...

Empirical formula = NH
2Since Vapour density = 16
∴ mol. wt. = 32
∵ Molecular formula = n × Emp. formula = 2 × NH
2 = N
2H
4
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A gaseous compound of nitrogen and hydrogen contains 12.5%(by mass) of...
Given information:
- The gaseous compound contains 12.5% hydrogen by mass.
- The compound has a density relative to hydrogen of 16.
To find:
- The molecular formula of the compound.
Solution:
Step 1: Determine the empirical formula
The empirical formula gives the simplest ratio of the atoms present in a compound.
Assuming we have 100g of the compound:
- The mass of hydrogen in the compound = 12.5g (12.5% of 100g)
- The mass of nitrogen in the compound = 100g - 12.5g = 87.5g (total mass - mass of hydrogen)
Calculate the moles of hydrogen and nitrogen:
- Moles of hydrogen = mass/molar mass = 12.5g/1g/mol = 12.5 mol
- Moles of nitrogen = mass/molar mass = 87.5g/14g/mol = 6.25 mol
Divide by the smallest number of moles:
- Divide the number of moles of each element by the smallest number of moles to obtain the simplest whole number ratio.
- In this case, the smallest number of moles is 6.25 mol (moles of nitrogen).
- Moles of hydrogen in the empirical formula = 12.5 mol / 6.25 mol = 2
- Moles of nitrogen in the empirical formula = 6.25 mol / 6.25 mol = 1
Therefore, the empirical formula of the compound is NH2.
Step 2: Determine the molecular formula
The molecular formula gives the actual number of atoms of each element present in a compound.
Calculate the molar mass of the empirical formula:
- Molar mass of nitrogen = 14g/mol
- Molar mass of hydrogen = 1g/mol
Molar mass of NH2 = (1g/mol * 2) + 14g/mol = 16g/mol
Calculate the ratio of the molar mass of the compound to the molar mass of the empirical formula:
- Ratio = molar mass of compound / molar mass of empirical formula
= density of compound / density of empirical formula
Given that the density of the compound relative to hydrogen is 16, we can write:
16 = molar mass of compound / 16g/mol
Calculate the molar mass of the compound:
Molar mass of compound = 16g/mol * 16 = 256g/mol
Calculate the ratio of the molar masses:
- Ratio = 256g/mol / 16g/mol = 16
Since the ratio is 16, it means that the molecular formula is 16 times the empirical formula.
Final Answer:
The molecular formula of the compound is N2H4 (16 times the empirical formula NH2). Therefore, the correct answer is option D).