We are designing a new process that uses natural gas, which will be delivered via pipeline at conditions of P = 1000 psia and T = 100°F. In order to size process equipment, we need to know the density of natural gas at this temperature and pressure. Use pure methane as a model for natural gas. Find p in lb_m/ft³ for methane at P = 1000 psia and T = 100°F using:

A. The ideal gas law

B. The van der Waals EOS with the parameters a = 8496 ft⁶ psia/lb-mol² and b = 0.685 ft³/ lb-mol