Final answer:
The volume of the gas sample is calculated using the molar mass and Avogadro's law at STP. The partial pressures are determined by the mole fractions and total pressure. The total pressure at STP is 1 atm, and the molar mass of the mixture is calculated based on the combined masses and moles of the gases.
Step-by-step explanation:
Calculating Volume and Partial Pressures of a Gas Mixture
To solve this problem, we will apply concepts from Chemistry such as molar mass, Avogadro's law, and partial pressures. We'll start by determining the number of moles of each gas using their given masses and molar masses (Oxygen O2: 32.00 g/mol, Nitrogen N2: 28.02 g/mol). After that, we'll use Avogadro's law to find the volume that these gases would occupy at STP.
A. Volume of the Gas Sample:
- Moles of O2 = 1.05 g / 32.00 g/mol = 0.03281 mol
- Moles of N2 = 1.54 g / 28.02 g/mol = 0.05495 mol
- Total volume at STP = (0.03281 mol + 0.05495 mol) * 22.4 L/mol = 1.96 L
B. Partial Pressures of Oxygen and Nitrogen:
- Mole fraction of O2 = 0.03281 mol / (0.03281 mol + 0.05495 mol)
- Mole fraction of N2 = 0.05495 mol / (0.03281 mol + 0.05495 mol)
- Partial pressure of O2 = Mole fraction of O2 * Total pressure at STP
- Partial pressure of N2 = Mole fraction of N2 * Total pressure at STP
C. Total Pressure of the Gas Sample:
- Total pressure at STP = 1 atm (by definition)
D. Molar Mass of the Gas Mixture:
- Molar mass of the mixture = (mass of O2 + mass of N2) / (moles of O2 + moles of N2)
- Calculate the molar mass using the masses and moles of O2 and N2.