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Question

The compressibility factors for 1 mole of real gases at low pressure, high pressure and that of gases of very low molar masses are Z1,Z2 and Z3. These are

A
Z1=(1aRTV), Z2=(1+PbRT), Z3= 1
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B
Z1=(1aRTV), Z2= 1, Z3=(1+PbRT)
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C
Z1=(1+PbRT), Z2=(1aRTV), Z3=(1+PbRT)
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D
Z1=(1aRTV), Z2=(1+PbRT), Z3=(1+PbRT)
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Solution

The correct option is D Z1=(1aRTV), Z2=(1+PbRT), Z3=(1+PbRT)
Van der Waals equation is:
(P+aV2)(Vb)=RT (for 1 mol gas)
Case 1: At low pressure, volume in high, hence taking
(Vb)V
(P+aV2)V=RT
PV+aV=RT
PVRT+aRTV=1
Z1=PVRT=(1aRTV)
Case II: At high pressure, aV2 becomes negligible, so
(P+aV2)P
P(Vb)=RT
PVPb=RT
PVRTPbRT=1
Z2=PVRT=1+PbRT
Case III: Gases are of low molar masses thus, forces of attraction are very small i.e. a is negligible
Thus, (P+aV2)P
As in case II, Z3=1+PbRT

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