Final answer:
To calculate the gas density, the molar mass of C7H12N4O10 is first determined to be 312.184 g/mol. Using the Ideal Gas Law, the volume occupied by one mole of the gas at 4.27 atm and 17.77°C is calculated to be 5.637 L. Dividing the molar mass by this volume gives a density of 55.35 g/L, which does not match the provided options.
Step-by-step explanation:
The student is asking for the density of a gaseous compound with molecular formula C7H12N4O10 at specific conditions of temperature and pressure. To find the density, we must first calculate the molar mass of the compound. Adding the atomic masses of all atoms in the compound gives us a molar mass:
- Carbon (C): 7 atoms × 12.01 g/mol = 84.07 g/mol
- Hydrogen (H): 12 atoms × 1.008 g/mol = 12.096 g/mol
- Nitrogen (N): 4 atoms × 14.007 g/mol = 56.028 g/mol
- Oxygen (O): 10 atoms × 15.999 g/mol = 159.99 g/mol
Summing these values, we get a molar mass of 312.184 g/mol for the compound.
Next, using the Ideal Gas Law (PV = nRT) and converting temperature to Kelvin (17.77°C + 273.15 = 290.92 K), we can find the volume one mole of the gas occupies at the given conditions:
V = \( \frac{{nRT}}{{P}} \) = \( \frac{{1 mol × 0.08206 L atm/mol K × 290.92 K}}{{4.27 atm}} \) = 5.637 L/mol
Finally, the density (ρ) is the mass per unit volume, so:
ρ = \( \frac{{molar mass}}{{volume}} \) = \( \frac{{312.184 g/mol}}{{5.637 L/mol}} \) = 55.35 g/L
This result does not match with any of the options provided (A. 1.2 g/L, B. 2.3 g/L, C. 3.4 g/L, D. 4.5 g/L), suggesting that there may be an error either in the provided options or in the details of the question such as the molecular formula, pressure, or temperature.