1
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Question

# The equation of state of a gas is P(V−nb)=nRT, where b and R are constants. If the pressure and the temperature are such that Vm=10b, what is the value of compressibility factor?

A
109
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B
911
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C
1110
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D
1011
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Solution

## The correct option is A 109Given, P(V−nb)=nRT for 1 mole P(Vm−b)=RT PVm−Pb=RT PVm=Pb+RT PVmRT=PbRT+1 Z=PbRT+1 Z is the compressibility factor. Also, P(Vm−b)=nRT for 1 mole PVm−Pb=RT Given Vm=10b P(10b)−Pb=RT 9Pb=RT Hence, PbRT=19 Therefore compressibility factor, Z=19+1=109

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