At very high pressures the compressibility factor of one mole of a gas is given by: (A) 1 + pb/RT (B) 1 - pb/RT (C) 1 - b/(VRT) (D) pb/RT

The Van der Waals equation for one mole of gas is given by

(P + a/V2) (V – b) = RT

The ratio a/V2 can be neglected in comparison to p at very high pressure

Then the equation becomes,

P(V – b) = RT

PV – Pb = RT

PV = RT + Pb

Dividing by RT in both LHS and RHS, we get,

PV/RT = RT/RT + Pb/RT

Z = PV/RT = 1 + Pb/RT

– is the compressibility factor

So, the correct option is (A)

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