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Question

The compressiblity factor (Z) for 1 mole of a real gas at low pressure can be written as: 
 
  1. Z=1+RTPb
  2. Z=1aVRT
  3. Z=1PbRT
  4. Z=1+aVRT


Solution

The correct option is B Z=1aVRT
Compressibility factor (Z)=PVRT
(For one mole of real gas)

van der Waals' equation for 1 mole of a real gas is
(P+aV2)(Vb)=RT

At low pressures, the volume is very large and hence correction term b can be neglected.
i.e, VbV

(P+aV2)V=RT;
PV+aV=RT;
PV=RTaV;
PVRT=1aVRT
Hence, Z=1aVRT

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