The value of compressibility factor of van der Waals gas at critical point is?a) 8/27b) 27/8c) 3/8d) I8/3

The compressibility factor (Z) of a van der Waals gas at the critical point is given by the formula:

Zc = PcVc/(RTc)

Where:

• Pc is the critical pressure
• Vc is the critical volume
• R is the universal gas constant
• Tc is the critical temperature

For a van der Waals gas, these critical constants are given by:

Pc = a/(27b^2) Vc = 3b Tc = 8a/(27b*R)

Substituting these values into the formula for Zc gives:

Zc = (a/(27b^2))(3b)/(8a/(27bR)) = 3/8

So, the compressibility factor of a van der Waals gas at the critical point is 3/8. Therefore, the correct answer is c) 3/8.