Answer:
5.2 mol
Explanation:
Step 1: Given data
- Total number of moles (n): 7.0 mol
- Total pressure (P): 530 kPa
- Partial pressure of oxygen (pO₂): 140 kPa
Step 2: Calculate the mole fraction of oxygen
We will use the following expression.
pO₂ = P × X(O₂)
X(O₂) = pO₂ / P
X(O₂) = 140 kPa / 530 kPa
X(O₂) = 0.264
Step 3: Calculate the moles of oxygen
We will use the definition of mole fraction of oxygen.
X(O₂) = n(O₂) / n
n(O₂) = X(O₂) × n
n(O₂) = 0.264 × 7.0 mol
n(O₂) = 1.8 mol
Step 4: Calculate the moles of nitrogen
The total number of moles is equal to the sum of moles of the individual gases.
n(O₂) + n(N₂) = n
n(N₂) = n - n(O₂)
n(N₂) = 7.0 mol - 1.8 mol
n(N₂) = 5.2 mol
