Final answer:
To find the mole fraction and partial pressure of nitrogen and oxygen, calculate the total moles of air in 1 m³ using the density and average molar mass of air. Then, use the percentages of nitrogen and oxygen to find their mole fractions and calculate their partial pressures using the ideal gas equation.
Step-by-step explanation:
The question involves calculating the mole fraction and partial pressure of nitrogen and oxygen in the air, given the density of air, and assuming air is an ideal gas composed only of these two gases. The molar mass of nitrogen (N2) is 28 g/mol, while the molar mass of oxygen (O2) is 32 g/mol. Using the ideal gas law and the given density, we can find the total moles of air in 1 m3, then calculate the moles of nitrogen and oxygen based on their percentage composition in the air (78% nitrogen and 21% oxygen by mole), and finally find the mole fraction and partial pressure of each component.
To start, the mass of air in 1 m3 is density × volume = 1.146 kg. We then convert this to moles using the average molar mass of air. We know air is approximately 78% nitrogen and 21% oxygen by mole. Therefore, the molar mass of air is approximately 29.0 g/mol (a simplification made based on the weighted average of the molar masses of N2 and O2 and ignoring the other components), which gives us the total moles of air. Finally, by multiplying these total moles by the mole fractions of nitrogen and oxygen, we can get the moles of each gas, and by using the ideal gas equation P = (nRT)/V, we can find their partial pressures.
The molar fraction of a gas is given by the moles of that gas divided by the total moles of all gases. The partial pressure is the product of the mole fraction and the total pressure of the gas mixture. For this problem, since air is assumed to consist of only nitrogen and oxygen, we will use their respective molar fractions and the given total pressure to calculate the partial pressures.