Question

The compression factor (compressibility factor) for one mole of a Van der Waals gas at $0$ and 100 atmosphere pressure is found to be 0.5. Assuming that the volume of gas molecule is negligible, calculate the Van der Waals constant 'a'.

• A. 1.254
• B. 2.87
• C. 3.76
• D. 1.34

Answer 1

The correct option is A 1.254

We know that, Compressibility factor, Z = PV/RT

0.5 = 100 *V/0.082 *273

∴ V = 0.1117L

NOTE : Further when volume of a gas molecule is negligible, van der Waal’s equation becomes

(P + a/V²) (V - 0) = RT

Or PV = RT – a/V or a = RTV – PV²

Substituting the values

A = (0.082 * 0.1119 *273) – (100 * 0.1119 * 0.1119)

= 1.253 atm L² mol^-2