In an industrial process, nitrogen is heated to 500 K at a constant
volume of 1.000 m3
The gas enters the container at 300 K and
100 atm. The mass of the gas in 92.4 kg. Use the van der Waals
equation to determine the approximate pressure of the gas at its
working temperature of 500 K. For N2, a = 1.352 dm6 atm mol-2,
b = 0.0387 dm3 mol-1.
Answers
Answer:
The working temperature, T = 500 K
The volume of the gas, V = 1.000 m³ = 1 Litre
Mass of gas, m = 92.4 kg = 92400 g
The constant “a” for N₂ = 1.352 dm⁶atm mol⁻² = 1.352 L² atm mol⁻²
The constant “b” for N₂ = 0.0387 dm³mol⁻¹ = 0.0387 L mol⁻¹
R = 0.08206 L atm / mole K
Let the approximate pressure of the gas at its working temperature be “p”.
We know,
The molar mass of N₂, M = 28.02 g
No. of moles of N₂, n = (mass of N₂) / (molar mass of N2) = 92400 / 28.02 = 3297.6 ≈ 3298 moles
Using Van der Waals equation for pressure,
p = [{n * R * T} / {V - nb}] – [{a * n²} / V²] ….. (i)
substituting the given values in the equation
p
= [{3298 * 0.08206 * 500} / {1000 – (3298*0.0387)}] – [{ 1.352 * (3298)²} / (1000)²]
= [135316.94 / 872.37] – 14.705
= 155.114 – 14.705
= 140.409 atm
Hence, the approximate pressure of the gas at the working temperature of 500 K is 140.409 atm.