**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**

Thus, a = {27 × (0.082 lit atm mol⁻¹ K⁻¹)² × (280.8 K)²}/(64 × 50 atm)

**Problem 3:**

**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)Ï€r³ × N₀

Thus, 4 × (4/3)Ï€r³ × N₀ = (1 × 0.082 lit atm mol⁻¹ K⁻¹ × 151 K)/(50 atm)

**∴ r = 1.47 × 10⁻⁸ cm**