What is the molecular formula of a compound that contains 39.0% carbon, 16.0% hydrogen, and 45.0% nitrogen, if 0.1576 g of the compound occupies 125 mL with a pressure of 0.9820 atm at 295.15 K?

• A. CH₃N
• B. CH₅N
• C. C₂H₃N₂
• D. C₂H₅N₂

Answer: (B)

Verified step by step guidance

1. First, convert the percentage composition of each element to grams, assuming you have 100 g of the compound. This means you have 39.0 g of carbon, 16.0 g of hydrogen, and 45.0 g of nitrogen.
2. Next, convert the mass of each element to moles by dividing by their respective molar masses: Carbon (C) is 12.01 g/mol, Hydrogen (H) is 1.008 g/mol, and Nitrogen (N) is 14.01 g/mol.
3. Determine the simplest whole number ratio of moles of each element by dividing each by the smallest number of moles calculated in the previous step.
4. Use the ideal gas law, PV = nRT, to find the number of moles of the compound. Here, P is the pressure (0.9820 atm), V is the volume (0.125 L), R is the ideal gas constant (0.0821 L·atm/mol·K), and T is the temperature (295.15 K). Solve for n, the number of moles.
5. Finally, use the number of moles calculated from the ideal gas law and the mass of the compound (0.1576 g) to find the molar mass. Compare this molar mass with the empirical formula mass to determine the molecular formula.