Answer:
a
The value is [tex]b = 4.61 *10^{-5} \ m^3 /mol[/tex]
b
[tex]Z = 0.66[/tex]
Explanation:
Generally the pressure of the gas is mathematically represented as
[tex]P = \frac{RT}{V_m -b} - \frac{a}{(V_m)^2}[/tex]
Substituting [tex]8.314 \ m^3\cdot Pa\cdot K^{-1}\cdot mol^{-1}[/tex] for R , 273K for T , [tex]5.00 * 10^{-4} m^3[/tex] for [tex]V_m[/tex] , [tex]0.50 \ m^6 \cdot Pa\cdot mol^{-2}[/tex] for a and [tex]3.0 MPa = 3.0*10^{9} \ Pa[/tex] for P
We have
[tex]3*10^6 = \frac{8.314 * 273}{5.00*10^{-4} - b} - \frac{0.50}{(5.00*10^{-4})^2 }[/tex]
=> [tex]b = 4.61 *10^{-5} \ m^3 /mol[/tex]
Generally the compression factor is mathematically represented as
[tex]Z = \frac{P* V_m }{RT}[/tex]
=> [tex]Z = \frac{3.0 *10^{6}* 5.0 *10^{-4} }{8.314 *273}[/tex]
=> [tex]Z = 0.66[/tex]
