Question

The compressibility factor for a van der Waals gas at high pressure is

• A. \(1 + \frac{RT}{Pb}\)
• B. \(1 + \frac{Pb}{RT}\)
• C. \(1 - \frac{Pb}{RT}\)
• D. \(\frac{1}{16}\)

Answer 1

The Correct Option is B

The compressibility factor (Z) is given by:

\( Z = \frac{PV}{RT} \)

The van der Waals equation of state is:

\( \left(P + \frac{a}{V^2}\right)(V - b) = RT \)

At high pressures, the volume V shrinks, making the excluded volume, b, important, while the intermolecular attraction term, a, becomes small. This simplifies to:

\( Z \approx 1 + \frac{Pb}{RT} \)

Consequently, the compressibility factor approximates to \( 1 + \frac{Pb}{RT} \) under high-pressure scenarios.