The ratio PVmRTfor a gas is known as the compressibility factor. What is the value of this ratio for one mole of a vanderwaal’s gas at it’s Boyle’s temperature?

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1+b2VmVm−b

1+b2Vm2

1+bVm

1−b2Vm2

answer is A.

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Detailed Solution

P+aV2V-b=RT⇒PV+aVV-bV=RT⇒PVRT+aVRT=VV-b⇒PVRT=VV-b-aVRT ∴T=aRb⇒PVRT=VV-b-bV⇒V2-bV+b2V(V-b)=V(V-b)+b2V(V-b)=1+b2V(V-b)

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