A real gas obeys the equation of state `p(V-nb)=nRT` where b is van der Waals constant and R is the gas constant. If the pressure and temperature are such that the molar volume of the gas is 10b, what is the value of compressibility factor?

Options

A. `10//9`
B. `8//9`
C. `12//11`
D. `10//11`

Answer

A

Explanation

We know that `p(V - nb) = nRT implies p(V_(m) - b) = RT " " ` (where `V_(m) = V//n`)
The compressibility factor is given by `Z = (pV_(m))/(RT) = 1 + (pb)/(RT)`
Suppose pressure and temperature are p and T when its molar volume is 10 b , then `p.(V_(m) - b) = RT. implies (p.)/(RT.) = (1)/(10 b - b) = (1)/(9b) or Z = 1 + (p.b)/(RT.) = 1 + (1)/(9) = (10)/(9)`