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# Derive an expression for the compression factor of a gas

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Derive an expression for the compression factor of a gas that obeys the equation of state

P(V - nb) = nRT

where b and R are constants. If the pressure and temperature are such that Vm = 10b, what is the numerical value of the compression factor?

Extra Info.

As a measure of the deviation from ideality of the behavior of a real gas, we define the compression factor Z of a gas as:

Z(P,T) = PVm/RT

Do not confuse the compressibility factor Z with the isothermal compressibility K. Since Vm is a function of T and P, Z is a function of T and P. For an ideal Z = 1 for all temperatures and pressures. When Z < 1 the gas exerts a lower pressure than an ideal gas would. At high presures, P of a gas can easily be 2 or 3 times larger or smaller than P ideal. IDeal gas behavior (Z = 1) is approached in the limit of P--> 0 and also in the limit T --> infinity. FOr each of these limits, the gas volume goes to inifinity for a fixed quantity of gas, and the density goes to zero.

Physical Chemistry, 5th Edition
Ira N. Levine Pg. 230

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