Final answer:
Without the actual van der Waals' pressure, the percent difference between the van der Waals' pressure and the ideal gas law pressure cannot be calculated. To obtain the percent difference, one must apply both the ideal gas law and the van der Waals' equation using the constants 'a' and 'b' for methane.
Step-by-step explanation:
To calculate the percent difference between pressures calculated using the van der Waals' equation and the ideal pressure, we first need the pressure value from the van der Waals' equation. Since the van der Waals' equation accounts for intermolecular forces and the volume occupied by the gas particles, it provides a more realistic pressure for real gases compared to the ideal gas law.
However, without the actual pressure value from the van der Waals' equation, we cannot provide the percent difference directly. The formula for percent difference is given by:
Percent Difference = (|Pvdw - Pideal| / Pideal) × 100%
Where Pvdw is the pressure from the van der Waals' equation and Pideal is the pressure from the ideal gas law. In this case, the ideal pressure is given as 494.7 atm.
To solve this, we would perform the calculations using both the ideal gas law (PV = nRT) and the van der Waals' equation ((P + (n²a/V²))(V - nb) = nRT), with the values of 'a' and 'b' specific to methane.