Answer:
The mole fraction of nitrogen is 0.52
Explanation:
Provided information:
Temperature = 31.2 °C
Pressure = 870.2 mmHg
Volume = 15.1 L
Mass of the mixture = 24.1 g
Mole fraction of nitrogen =?
Process:
Converting pressure:
870.2 / 760 = 1.12 atm
Converting temperature:
31.2 + 273 = 304.2 K
Total moles calculation:
PV = nRT
n = PV/RT
n = 1.12 atm × 15.1 L / 0.0821 L.atm. mol⁻¹.K⁻¹ × 304.2 K
n = 16.9 L.atm. / 25 L.atm. mol⁻¹
n = 0.676 mol
Let x be the number of moles of nitrogen.
Thus, the moles of CO₂ = 0.676 - x
The mass of nitrogen = x mol × 28 g/mol, and for CO₂ the mass = 44 g/mol (0.676 - x)
We have 24.1 = 28x + (29.7 - 44x)
Rearranging gives: 24.1 - 29.7 = 28x - 44x
-5.6 = -16 x
Therefore, x = 0.35
Mole fraction of nitrogen:
Mole fraction of nitrogen = moles of nitrogen / total moles
Mole fraction of nitrogen = 0.35 mol / 0.676 mol
Mole fraction of nitrogen = 0.52
