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Question Answer (Properties of Gases)

Problem 1:
The Critical constants for water are 647 K, 22.09 MPa and 0.0566 dm³mol⁻¹. Calculate the value of Van der Waals constants a and b.
Answer:

We have Tc = 647 K , Pc = 22.09 MPa = 22.9 × 10³ KPa and Vc = 0.0566 dm³ mol⁻¹
Thus, b = Vc/3 = (0.0566 dm³ mol⁻¹)/3 = 0.0189 dm³ mol⁻¹
Again a = 3PcVc² = (22.9 × 10³ KPa) × (0.0566 dm³ mol⁻¹)² = 212.3 KPa dm⁶ mol⁻¹
Problem 2:
Calculate Van der Waals constants for Ethylene. (Tc = 280.8 K and Pc = 50 atm)
Answer:
We know that, b = (1/8)(RTc/Pc)
∴ b = (1 × 0.082 lit atm mol⁻¹ K⁻¹ × 280.8 K)/(8 × 50 atm) 
= 0.057 lit mol⁻¹
Again, a = (27/64)(R²Tc²/Pc)
Thus, a = {27 × (0.082 lit atm mol⁻¹ K⁻¹)² × (280.8 K)²}/(64 × 50 atm)
= 4.47 lit² atm mol⁻²
Problem:
Argon has (Tc = - 122°C, Pc = 48 atm). What is the radius of the Argon atom?
Answer:

We have Tc = - 122°C = (273 - 122) K = 151 K and Pc = 48 atm
We Know that, b = (1/8)(RTc/Pc)
∴ b = (1 × 0.082 lit atm mol⁻¹ K⁻¹ × 151 K)/(50 atm)
Again from Van der Walls equation, b = 4 × (4/3)πr³ × N₀
 Thus, 4 × (4/3)πr³ × N₀ = (1 × 0.082 lit atm mol⁻¹ K⁻¹ × 151 K)/(50 atm)
∴ r = 1.47 × 10⁻⁸ cm