When cubic equations of state give three real roots for Z , usually the smallest root is the liquid root and the largest is the vapor root. However, the Peng-Robinson equation can give real roots at high pressure that differ from this pattern. To study this behavior, tabulate all the roots found for the specified gas and pressures. As the highest pressures are approached at this temperature, is the fluid a liquid or gas? Which real root (smallest, middle, or largest) represents this phase at the highest pressure, and what are the Z values at the specified pressures?

(a) Ethylene at 250 K and 1, 3, 10, 100, 150, 170, 175, and 200 MPa

(b) n-Hexane at 400 K and 0.2, 0.5, 1, 10, 100, 130 and 150 MPa

(c) Argon at 420 K and 0.1, 1, 5, and 10 MPa